id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,002,716 | OWR-13351-016 | Duplicate Statement of the Mod-$\ell$ Bogomolov–Pop Conjecture | The mod-ell Bogomolov-Pop conjecture states that for function fields K over k and L over l of transcendence degree at least 2 over algebraically closed fields of characteristic different from ell, the canonical map from Frobenius-orbit field isomorphisms to Milnor-K-theory-preserving isomorphisms of K-star modulo ell a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report shows that this declarative extraction and OWR-13351-017 state the same mod-$\ell$ Bogomolov–Pop conjecture; OWR-13351-0) | [
"OWR-13351-017"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13351-016",
"literature-status:partially-solved",
"owr-year:2014"
] | The conjecture is proved for algebraic closures of finite fields and of Q in transcendence degree at least 2, but remains open in full generality. | [
{
"url": "https://arxiv.org/abs/1211.4608",
"label": "Silberstein, anabelian intersection theory"
},
{
"url": "https://doi.org/10.4171/owr/2014/49",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | null | The mod-ell Bogomolov-Pop conjecture states that for function fields K over k and L over l of transcendence degree at least 2 over algebraically closed fields of characteristic different from ell, the canonical map from Frobenius-orbit field isomorphisms to Milnor-K-theory-preserving isomorphisms of K-star modulo ell a... | unrecoverable | The official report shows that this declarative extraction and OWR-13351-017 state the same mod-$\ell$ Bogomolov–Pop conjecture; OWR-13351-017 is the canonical question-form record. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
30,002,717 | OWR-13351-017 | Mod-$\ell$ Bogomolov–Pop Reconstruction Conjecture | Let $K/k$ and $L/l$ be function fields of transcendence degree at least $2$ over algebraically closed fields whose characteristics differ from $\ell$. Is the canonical map from field isomorphisms modulo Frobenius to Milnor-$K$-theory-preserving isomorphisms $K^\times/\ell\to L^\times/\ell$ bijective? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-13351-016"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13351-017",
"literature-status:partially-solved",
"owr-year:2014"
] | Topaz proved a reconstruction theorem with rational-quotient data and stronger transcendence-degree hypotheses, but the stated mod-ell conjecture without those extra data remains unresolved. | [
{
"url": "https://arxiv.org/abs/1408.5194",
"label": "Topaz, rational quotients"
},
{
"url": "https://doi.org/10.1007/S00208-015-1327-4",
"label": "Topaz, published theorem"
},
{
"url": "https://doi.org/10.4171/owr/2014/49",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | Let $K/k$ and $L/l$ be function fields of transcendence degree at least $2$ over algebraically closed fields whose characteristics differ from $\ell$. Is the canonical map from field isomorphisms modulo Frobenius to Milnor-$K$-theory-preserving isomorphisms $K^\times/\ell\to L^\times/\ell$ bijective? | For function fields K over k and L over l as in the mod-ell Bogomolov-Pop setting, with transcendence degree of K over k at least 2, is the canonical map from Frobenius-orbit field isomorphisms to Milnor-K-theory-preserving isomorphisms of K-star modulo ell and L-star modulo ell a bijection? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
30,002,718 | OWR-13352-001 | Random Geometric Graphs in the Hyperbolic Plane | How do finite random geometric graphs and continuum percolation behave when the Euclidean plane is replaced by the hyperbolic plane, in particular for the component-size and connectivity questions of the corresponding Poisson or finite-point models? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Probability, Trees and Algorithms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/50, pp. 2825--2871](https://doi.org/10.4171/owr/2014/50)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13352-001",
"literature-status:partially-solved",
"owr-year:2014"
] | Hyperbolic percolation and random-connection models have rigorous phase diagrams and recent critical-exponent results, but the broad question across the model variants in the record is not fully settled. | [
{
"url": "https://arxiv.org/abs/math/9912233",
"label": "Benjamini--Schramm, hyperbolic percolation"
},
{
"url": "https://doi.org/10.1112/jlms.70345",
"label": "Hyperbolic random connection model"
},
{
"url": "https://doi.org/10.4171/owr/2014/50",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/50 | null | null | null | How do finite random geometric graphs and continuum percolation behave when the Euclidean plane is replaced by the hyperbolic plane, in particular for the component-size and connectivity questions of the corresponding Poisson or finite-point models? | How do finite random geometric graphs and continuum percolation behave when the Euclidean plane is replaced by the hyperbolic plane, in particular for the component-size and connectivity questions of the corresponding Poisson or finite-point models? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Probability, Trees and Algorithms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/50, pp. 2825--2871 |
30,002,719 | OWR-13352-003 | Probabilistic Interpretation of Waring-Polynomial Series | For the Waring-polynomial series $F_n$ arising as approximations to the leading root of the deformed exponential formal power series, is $F_n$ the probability generating function of an explicitly or easily describable random variable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Probability, Trees and Algorithms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/50, pp. 2825--2871](https://doi.org/10.4171/owr/2014/50)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13352-003",
"literature-status:open",
"owr-year:2014"
] | Only small cases and computational evidence are known for the pgf question; no general probabilistic representation for F_n was established. | [
{
"url": "https://arxiv.org/abs/2412.02462",
"label": "Kuznetsov, deformed exponential zeros"
},
{
"url": "https://doi.org/10.4171/owr/2014/50",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/50 | null | null | null | For the Waring-polynomial series $F_n$ arising as approximations to the leading root of the deformed exponential formal power series, is $F_n$ the probability generating function of an explicitly or easily describable random variable? | For the Waring-polynomial series F_n arising as approximations to the leading root of the deformed exponential formal power series, is F_n the probability generating function of an explicitly or easily describable random variable? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Probability, Trees and Algorithms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/50, pp. 2825--2871 |
30,002,720 | OWR-13352-004 | Marginal Limits for Markov-Source Selection Processes | For the bucket-operation process $Y_n$ used for rank selection from strings generated by a Markov source, do the one-dimensional marginals of the appropriately centered and $\sqrt n$-rescaled process converge as $n\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Probability, Trees and Algorithms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/50, pp. 2825--2871](https://doi.org/10.4171/owr/2014/50)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13352-004",
"literature-status:open",
"owr-year:2014"
] | The primary process-convergence paper proves non-tightness for general Markov sources, but explicitly leaves convergence of the marginals open. | [
{
"url": "https://doi.org/10.1016/j.spa.2018.03.009",
"label": "Radix selection on Markov sources"
},
{
"url": "https://arxiv.org/abs/1605.02352",
"label": "Process convergence preprint"
},
{
"url": "https://doi.org/10.4171/owr/2014/50",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/50 | null | null | null | For the bucket-operation process $Y_n$ used for rank selection from strings generated by a Markov source, do the one-dimensional marginals of the appropriately centered and $\sqrt n$-rescaled process converge as $n\to\infty$? | For the bucket-operation process Y_n for rank selection from strings generated by a Markov source, do the one-dimensional marginals of the appropriate centered and square-root-n rescaled process converge as n tends to infinity? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Probability, Trees and Algorithms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/50, pp. 2825--2871 |
30,002,721 | OWR-13352-007 | Limiting Boolean Functions of Random And–Or Trees | Given random trees $T_n$ with uniformly random AND/OR labels, do the Boolean functions computed by $T_n$ converge in distribution as $n\to\infty$? When is the limiting distribution degenerate, and what can be said when it is nondegenerate? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Probability, Trees and Algorithms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/50, pp. 2825--2871](https://doi.org/10.4171/owr/2014/50)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13352-007",
"literature-status:partially-solved",
"owr-year:2014"
] | General convergence and degenerate versus nondegenerate regimes are proved under explicit local-limit and end hypotheses, but no theorem covers every arbitrary random-tree sequence. | [
{
"url": "https://doi.org/10.1002/rsa.20758",
"label": "Broutin--Mailler, local limits"
},
{
"url": "https://arxiv.org/abs/1510.06691",
"label": "And-or trees preprint"
},
{
"url": "https://doi.org/10.4171/owr/2014/50",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/50 | null | null | null | Given random trees $T_n$ with uniformly random AND/OR labels, do the Boolean functions computed by $T_n$ converge in distribution as $n\to\infty$? When is the limiting distribution degenerate, and what can be said when it is nondegenerate? | Given random trees T_n with uniformly random and-or labels, does the sequence of Boolean functions computed by T_n converge in distribution as n tends to infinity, when is the limiting distribution degenerate, and what can be said about it when it is nondegenerate? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Probability, Trees and Algorithms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/50, pp. 2825--2871 |
30,002,722 | OWR-13353-005 | Polynomial-Time Minimization of K-Submodular Functions | Can a $k$-submodular function be minimized in polynomial time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-005",
"literature-status:open",
"owr-year:2014"
] | The min-max theorem and polyhedral structure are known, but polynomial-time minimization for general k-submodular functions with k at least 3 remains unresolved. | [
{
"url": "https://arxiv.org/abs/1309.5469",
"label": "Huber--Kolmogorov, k-submodular minimization"
},
{
"url": "https://doi.org/10.1016/j.disopt.2021.100670",
"label": "Exact k-submodular optimization"
},
{
"url": "https://doi.org/10.4171/owr/2014/51",
"label": "Oberwolfach report"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | Can a $k$-submodular function be minimized in polynomial time? | Can a k-submodular function be minimized in polynomial time? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,723 | OWR-13353-006 | Complexity of Extremality Testing in Infinite Group Problems | Is the pseudo-polynomial running time of the known algorithms for testing extremality of minimal valid functions in the single-row infinite group problem best possible? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-006",
"literature-status:open",
"owr-year:2014"
] | One-row and restricted two-row extremality tests have pseudo-polynomial or restricted polynomial algorithms, while polynomial dependence on binary denominator size and the general higher-dimensional problem remain open. | [
{
"url": "https://arxiv.org/abs/1206.2079",
"label": "Basu--Hildebrand--Koeppel, one-row test"
},
{
"url": "https://arxiv.org/abs/2501.05582",
"label": "General two-dimensional test"
},
{
"url": "https://arxiv.org/abs/1410.8584",
"label": "Infinite group relaxation survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | Is the pseudo-polynomial running time of the known algorithms for testing extremality of minimal valid functions in the single-row infinite group problem best possible? | Is the pseudo-polynomial running time of the known algorithms for testing extremality of minimal valid functions in the single-row infinite group problem best possible? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,724 | OWR-13353-008 | Combinatorial Decompositions of the All-Ones Vector | Can the all-ones vector be represented as a linear or integer combination of combinatorially interesting vectors, such as incidence vectors of tours? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,014 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-13353-008",
"literature-status:partially-solved",
"owr-year:2014"
] | For 3-edge-connected graphs the all-ones vector is proved to lie in the convex hull of tours, and later work improves related uniform-cover constants; the broad question over other vector families remains open. | [
{
"url": "https://arxiv.org/abs/1707.05387",
"label": "Haddadan--Newman--Ravi, uniform covers"
},
{
"url": "https://pagesperso.g-scop.grenoble-inp.fr/~seboa/sebo_files/papers/seboberwolfach14cahiers.pdf",
"label": "Sebo, tours and detours"
},
{
"url": "https://doi.org/10.4171/owr/2014/51... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | Can the all-ones vector be represented as a linear or integer combination of combinatorially interesting vectors, such as incidence vectors of tours? | Can the all-ones vector be represented as a linear or integer combination of combinatorially interesting vectors, such as incidence vectors of tours? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,725 | OWR-13353-009 | Sharper Tour Bounds for the Chinese Postman Problem | For the tour bounds in the Chinese postman problem on a $2$-edge-connected graph, especially when the ear parameter $k$ is large and the lower bound is weak, how can the upper and lower bounds be sharpened? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-009",
"literature-status:open",
"owr-year:2014"
] | The report bounds remain a baseline, and later tour work improves related uniform-cover bounds, but no general resolution of the stated useful-bound question was found. | [
{
"url": "https://doi.org/10.4171/owr/2014/51",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1707.05387",
"label": "Later uniform-cover bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | For the tour bounds in the Chinese postman problem on a $2$-edge-connected graph, especially when the ear parameter $k$ is large and the lower bound is weak, how can the upper and lower bounds be sharpened? | For the tour bounds in the Chinese Postman problem on a 2-edge-connected graph, especially when the ear parameter k is large and the lower bound is weak, how can the upper and lower bounds be improved in a useful way? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,726 | OWR-13353-012 | Complexity of Maximizing Initial Odd Ears | What is the computational complexity of determining $\beta(G)$ for a $2$-vertex-connected graph $G$, where $\beta(G)$ is the maximum number of initial odd ears in an ear decomposition? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,014 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-012",
"literature-status:partially-solved",
"owr-year:2014"
] | The exact complexity of beta remains unknown, but beta at most 1 is decidable in polynomial time and computing beta is fixed-parameter tractable. | [
{
"url": "https://arxiv.org/abs/1509.05586",
"label": "Benchetrit--Sebo, ear decompositions"
},
{
"url": "https://doi.org/10.4171/owr/2014/51",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | What is the computational complexity of determining $\beta(G)$ for a $2$-vertex-connected graph $G$, where $\beta(G)$ is the maximum number of initial odd ears in an ear decomposition? | What is the computational complexity of determining beta of a 2-vertex-connected graph, where beta is the maximum number of starting odd ears in an ear decomposition? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,727 | OWR-13353-015 | Triangle-Cone Characterization of Graphs | Characterize the graphs for which the all-ones edge vector is a nonnegative combination of triangle incidence vectors, equivalently characterize the linear inequalities defining the cone generated by the triangles of a graph. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-13353-016"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-015",
"literature-status:open",
"owr-year:2014"
] | This is a broad research program about packing, covering, and transversals rather than one resolved proposition; the cited triangle-cone problem remains part of an active body of work. | [
{
"url": "https://doi.org/10.4171/owr/2014/51",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1137/15M1014310",
"label": "Dross, fractional triangle decompositions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | Characterize the graphs for which the all-ones edge vector is a nonnegative combination of triangle incidence vectors, equivalently characterize the linear inequalities defining the cone generated by the triangles of a graph. | Characterize the graphs for which the all-ones edge vector is a nonnegative combination of triangle incidence vectors, equivalently characterize the linear inequalities defining the cone generated by the triangles of a graph. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,728 | OWR-13353-016 | Duplicate Triangle-Cone Characterization | Characterize the graphs for which the all-ones edge vector is a nonnegative combination of triangle incidence vectors, equivalently characterize the linear inequalities defining the cone generated by the triangles of a graph. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This extraction repeats verbatim the graph-triangle-cone problem represented canonically by OWR-13353-015. No separate clean statement is pr) | [
"OWR-13353-015"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-016",
"literature-status:partially-solved",
"owr-year:2014"
] | Facet descriptions and fractional-decomposition theorems are known for important graph classes, but no general characterization of all graphs whose edge vector lies in the triangle cone was verified. | [
{
"url": "https://combinatorialpress.com/jcmcc-articles/volume-116/on-the-cone-of-weighted-graphs-generated-by-triangles/",
"label": "cone of weighted graphs generated by triangles"
},
{
"url": "https://doi.org/10.1137/15M1014310",
"label": "Dross, fractional triangle decompositions"
},
{
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | null | Characterize the graphs for which the all-ones edge vector is a nonnegative combination of triangle incidence vectors, equivalently characterize the linear inequalities defining the cone generated by the triangles of a graph. | unrecoverable | This extraction repeats verbatim the graph-triangle-cone problem represented canonically by OWR-13353-015. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,729 | OWR-13353-017 | Additive Integrality Gap for Ring Loading | For every instance of the ring-loading problem, let $L$ be the optimum unsplittable load, let $L^*$ be the optimum splittable load, and let $D$ be the maximum demand. Is $L\leq L^*+11D/10$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,014 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-017",
"literature-status:partially-solved",
"owr-year:2014"
] | Skutella disproved the old additive-D conjecture and proved the upper bound 19D/14, while examples give the lower bound 11D/10; the exact optimum between these bounds remains unresolved. | [
{
"url": "https://doi.org/10.1137/14099588X",
"label": "Skutella, a note on ring loading"
},
{
"url": "https://arxiv.org/abs/1904.02119",
"label": "Däubel, improved ring-loading bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | For every instance of the ring-loading problem, let $L$ be the optimum unsplittable load, let $L^*$ be the optimum splittable load, and let $D$ be the maximum demand. Is $L\leq L^*+11D/10$? | For every instance of the Ring Loading Problem, if L is the optimum unsplittable load, L-star is the optimum splittable load, and D is the maximum demand, is L at most L-star plus eleven tenths of D? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,730 | OWR-13353-018 | Dimension Gaps in Lattice Reductions to Learning with Errors | Can the discrepancy between the lattice dimensions in the quantum and classical reductions from GapSVP to learning with errors be removed or explained, namely dimension n for the quantum reduction versus order square-root-n for the classical reduction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-018",
"literature-status:open",
"owr-year:2014"
] | Classical worst-case-to-average-case lattice reductions have been improved and classical variants are known in weaker parameter regimes, but the stated quantum-versus-classical GapSVP dimension discrepancy was not eliminated. | [
{
"url": "https://arxiv.org/abs/2401.03703",
"label": "Regev, lattices and learning with errors"
},
{
"url": "https://www.aimsciences.org/article/doi/10.3934/amc.2021004",
"label": "classical GapSVP-to-LWE analysis"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | Can the discrepancy between the lattice dimensions in the quantum and classical reductions from GapSVP to learning with errors be removed or explained, namely dimension n for the quantum reduction versus order square-root-n for the classical reduction? | Can the discrepancy between the lattice dimensions in the quantum and classical reductions from GapSVP to learning with errors be removed or explained, namely dimension n for the quantum reduction versus order square-root-n for the classical reduction? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,731 | OWR-13353-020 | Exact Integrality Gap for Capacitated Facility Location | What is the exact integrality gap of the strengthened linear-programming relaxation for the capacitated facility location problem based on partial client assignments? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,014 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-020",
"literature-status:partially-solved",
"owr-year:2014"
] | The MFN relaxation has a constant gap and later iterative-rounding work substantially reduced the upper bound, but the exact integrality gap and the requested sharper ratio are still not known. | [
{
"url": "https://doi.org/10.1137/1.9781611977554.ch40",
"label": "Kao, MFN integrality gap"
},
{
"url": "https://arxiv.org/abs/1407.3263",
"label": "An, Singh, and Svensson, MFN relaxation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | What is the exact integrality gap of the strengthened linear-programming relaxation for the capacitated facility location problem based on partial client assignments? | What is the exact integrality gap of the strengthened linear-programming relaxation for the capacitated facility location problem based on partial client assignments? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,732 | OWR-13353-021 | Compact Constant-Gap Relaxations for Capacitated Facility Location | Does there exist a polynomial-size linear-programming relaxation for the capacitated facility location problem whose integrality gap is bounded by a constant? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-13353-022"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-021",
"literature-status:open",
"owr-year:2014"
] | The MFN formulation gives a bounded polynomial-time relaxation but has exponentially many constraints; no compact polynomial-size LP with a constant gap for general capacitated facility location was verified. | [
{
"url": "https://doi.org/10.1137/1.9781611977554.ch40",
"label": "Kao, MFN integrality gap"
},
{
"url": "https://arxiv.org/abs/1312.1819",
"label": "lower bounds for compact formulations"
},
{
"url": "https://doi.org/10.4171/owr/2014/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | Does there exist a polynomial-size linear-programming relaxation for the capacitated facility location problem whose integrality gap is bounded by a constant? | Does there exist a polynomial-size linear-programming relaxation for the capacitated facility location problem whose integrality gap is bounded by a constant? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,733 | OWR-13353-022 | Duplicate Constant-Gap Facility-Location Relaxation | Does there exist a polynomial-size linear-programming relaxation for the capacitated facility location problem whose integrality gap is bounded by a constant? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932](https://doi.org/10.4171/owr/2014/51)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This extraction repeats the capacitated-facility-location relaxation question represented canonically by OWR-13353-021. No separate clean st) | [
"OWR-13353-021"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13353-022",
"literature-status:open",
"owr-year:2014"
] | The record contains only an isolated Open Question label and no mathematical statement; under the requested rule its claim is unresolved rather than inferred from neighboring records. | [
{
"url": "https://doi.org/10.4171/owr/2014/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/51 | null | null | null | null | Does there exist a polynomial-size linear-programming relaxation for the capacitated facility location problem whose integrality gap is bounded by a constant? | unrecoverable | This extraction repeats the capacitated-facility-location relaxation question represented canonically by OWR-13353-021. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Combinatorial Optimization (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/51, pp. 2873--2932 |
30,002,734 | OWR-13354-001 | Weak Duality Proof Complexity and Strongly Polynomial Linear Programming | Does the variable-matrix form of weak linear-programming duality have no polynomial-size proof in the Lovasz-Schrijver system, and do strongly polynomial circuits for linear programming exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/52, pp. 2933--2986](https://doi.org/10.4171/owr/2014/52)
## Literature review (... | 3 | open | null | 2,014 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13354-001",
"literature-status:open",
"owr-year:2014"
] | The conjecture that WD has no polynomial-size LS proof is tied to the unresolved existence of strongly polynomial algorithms for general linear programming; that algorithmic problem remains open. | [
{
"url": "https://topp.openproblem.net/p8",
"label": "TOPP, strongly polynomial linear programming"
},
{
"url": "https://doi.org/10.4171/owr/2014/52",
"label": "original OWR report"
},
{
"url": "https://drops.dagstuhl.de/storage/00lipics/lipics-vol345-mfcs2025/html/LIPIcs.MFCS.2025.33/LI... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/52 | null | null | null | Does the variable-matrix form of weak linear-programming duality have no polynomial-size proof in the Lovasz-Schrijver system, and do strongly polynomial circuits for linear programming exist? | Does the variable-matrix form of weak linear-programming duality have no polynomial-size proof in the Lovasz-Schrijver system, and do strongly polynomial circuits for linear programming exist? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/52, pp. 2933--2986 |
30,002,735 | OWR-13354-003 | Two-Valued Realizability Toposes and Computable Dependent Choice | For the classical realizability topos K obtained from the coherence-space domain equation, is K two-valued, and does dependent choice continue to hold when the domain D is restricted to computable elements? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/52, pp. 2933--2986](https://doi.org/10.4171/owr/2014/52)
## Literature review (... | 3 | partially_solved | null | 2,014 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13354-003",
"literature-status:partially-solved",
"owr-year:2014"
] | For the displayed stable-model construction, later work establishes choice principles including countable choice and dependent choice in broad realizability models, but the 2-valuedness of K and the computable-elements restriction remain unresolved. | [
{
"url": "https://doi.org/10.23638/LMCS-13(4:24)2017",
"label": "Streicher, stable-model classical realizability"
},
{
"url": "https://arxiv.org/abs/1502.00112",
"label": "Krivine, bar recursion and dependent choice"
},
{
"url": "https://doi.org/10.4171/owr/2014/52",
"label": "origin... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/52 | null | null | null | For the classical realizability topos K obtained from the coherence-space domain equation, is K two-valued, and does dependent choice continue to hold when the domain D is restricted to computable elements? | For the classical realizability topos K obtained from the coherence-space domain equation, is K two-valued, and does dependent choice continue to hold when the domain D is restricted to computable elements? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/52, pp. 2933--2986 |
30,002,736 | OWR-13354-004 | Dynamic Induction for Strictly Positive Definitions | Dynamic induction extends from the natural numbers to inductive definitions of the form $I(x)\leftrightarrow B(x)\lor\exists y<x\,I(y)$. Does it extend to arbitrary strictly positive inductive definitions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/52, pp. 2933--2986](https://doi.org/10.4171/owr/2014/52)
## Literature review (... | 3 | partially_solved | null | 2,014 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13354-004",
"literature-status:partially-solved",
"owr-year:2014"
] | Proof systems now support unrestricted strictly positive inductive and coinductive definitions in substantial generality, but the specific dynamic-induction extraction theorem for every strictly positive definition was not established. | [
{
"url": "https://doi.org/10.1007/978-3-030-51466-2_12",
"label": "Berger, Prawf and program extraction"
},
{
"url": "https://arxiv.org/abs/0708.3582",
"label": "Blanqui, Jouannaud, and Rubio on strictly positive types"
},
{
"url": "https://doi.org/10.4171/owr/2014/52",
"label": "ori... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/52 | null | null | null | Dynamic induction extends from the natural numbers to inductive definitions of the form $I(x)\leftrightarrow B(x)\lor\exists y<x\,I(y)$. Does it extend to arbitrary strictly positive inductive definitions? | Can dynamic induction, known for inductive definitions of the form I of x equals B of x or there exists y less than x with I of y, be extended to arbitrary strictly positive inductive definitions? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/52, pp. 2933--2986 |
30,002,737 | OWR-13355-001 | Absolutely Continuous Diffraction and Dynamical Spectra | If the diffraction spectrum of a quasicrystalline system has no absolutely continuous component, must the dynamical spectrum also have no absolutely continuous component? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013](https://doi.org/10.4171/owr/2014/53)... | 3 | open | null | 2,014 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-13355-002"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13355-001",
"literature-status:open",
"owr-year:2014"
] | The extracted record introduces the conjecture relating absolutely continuous diffraction and dynamical spectrum; available work proves important special cases but not the general implication. | [
{
"url": "https://doi.org/10.4171/owr/2014/53",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2011.14375",
"label": "Nagai, absence of absolutely continuous diffraction"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/53 | null | null | null | If the diffraction spectrum of a quasicrystalline system has no absolutely continuous component, must the dynamical spectrum also have no absolutely continuous component? | If the diffraction spectrum of a quasicrystalline system has no absolutely continuous component, must the dynamical spectrum also have no absolutely continuous component? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013 |
30,002,738 | OWR-13355-002 | Duplicate Diffraction-to-Dynamical-Spectrum Conjecture | If the diffraction spectrum has no absolutely continuous component, then the dynamical spectrum has no absolutely continuous component. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013](https://doi.org/10.4171/owr/2014/53)... | 3 | open | null | 2,014 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This declarative extraction is the same conjecture as the question represented canonically by OWR-13355-001. No separate clean statement is ) | [
"OWR-13355-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13355-002",
"literature-status:open",
"owr-year:2014"
] | The same diffraction-to-dynamical-spectrum conjecture is still unresolved in general; later results concern special tiling families and do not prove the stated universal implication. | [
{
"url": "https://doi.org/10.4171/owr/2014/53",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1088/1361-6544/ac2a51",
"label": "Nagai, S-adic tiling spectra"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/53 | null | null | null | null | If the diffraction spectrum has no absolutely continuous component, then the dynamical spectrum has no absolutely continuous component. | unrecoverable | This declarative extraction is the same conjecture as the question represented canonically by OWR-13355-001. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013 |
30,002,739 | OWR-13355-003 | Periodic Gibbs Phases in Two Dimensions | At positive temperature, is every extremal Gibbs measure for a finite-range interaction in two dimensions periodic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013](https://doi.org/10.4171/owr/2014/53)... | 3 | open | null | 2,014 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13355-003",
"literature-status:open",
"owr-year:2014"
] | No general theorem was found proving that every two-dimensional finite-range positive-temperature extremal Gibbs state is periodic; known results and models leave the proposed no-quasicrystal statement unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/53",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s10955-009-9896-9",
"label": "Koch and Radin, positive-temperature quasicrystal model"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/53 | null | null | null | At positive temperature, is every extremal Gibbs measure for a finite-range interaction in two dimensions periodic? | No-quasicrystals conjecture in dimension two: at positive temperature, every extremal Gibbs measure for a finite-range interaction in two dimensions is periodic. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013 |
30,002,740 | OWR-13355-004 | Quasicrystalline Gibbs Phases in Higher Dimensions | In every dimension at least $3$, does there exist a translation-invariant Gibbs measure for a short-range interaction whose extremal decomposition contains nonperiodic Gibbs measures? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013](https://doi.org/10.4171/owr/2014/53)... | 3 | partially_solved | null | 2,014 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13355-004",
"literature-status:partially-solved",
"owr-year:2014"
] | Nonperiodic Gibbs states have been constructed in higher-dimensional finite-range models, including a four-dimensional construction, but the stated threshold claim for three or more dimensions was not fully established, especially in dimension three. | [
{
"url": "https://arxiv.org/abs/2512.24436",
"label": "Taati and Miękisz, finite-range quasicrystalline Gibbs states"
},
{
"url": "https://doi.org/10.4171/owr/2014/53",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/53 | null | null | null | In every dimension at least $3$, does there exist a translation-invariant Gibbs measure for a short-range interaction whose extremal decomposition contains nonperiodic Gibbs measures? | Conjecture: In three or more dimensions, there exists a translation-invariant Gibbs measure for a short-range interaction that decomposes into non-periodic extremal Gibbs measures (that is, quasicrystalline phases occur). | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013 |
30,002,741 | OWR-13355-005 | Failure Rates in Sequential Aperiodic Tiling | For a finite aperiodic tile set, determine how often a finite patch that cannot extend to a tiling of the whole plane causes an attempt to assemble a tiling one tile at a time to fail. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013](https://doi.org/10.4171/owr/2014/53)... | 3 | open | null | 2,014 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13355-005",
"literature-status:open",
"owr-year:2014"
] | Aperiodic tile sets are known to contain finite patches that cannot extend to a global tiling, but a general quantitative theory of the frequency or probability of failure in sequential assembly remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/53",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s10955-009-9896-9",
"label": "Koch and Radin, aperiodic tiling model"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/53 | null | null | null | For a finite aperiodic tile set, determine how often a finite patch that cannot extend to a tiling of the whole plane causes an attempt to assemble a tiling one tile at a time to fail. | For a finite aperiodic tile set, determine how often a finite patch that cannot extend to a tiling of the whole plane causes an attempt to assemble a tiling one tile at a time to fail. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013 |
30,002,742 | OWR-13355-006 | Laplacian Spectra of Penrose Tiling Graphs | Determine the spectral properties of the Laplacian on a Penrose-tiling graph or on a graph arising from a higher-dimensional quasicrystal model. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013](https://doi.org/10.4171/owr/2014/53)... | 3 | partially_solved | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13355-006",
"literature-status:partially-solved",
"owr-year:2014"
] | Recent work proves locally supported eigenfunctions and discontinuities in the integrated density of states for Penrose-related Laplacians, but the overall spectral type, gaps, and transport remain incompletely understood. | [
{
"url": "https://doi.org/10.1080/10586458.2023.2206589",
"label": "Damanik et al., Laplacians on Penrose tilings"
},
{
"url": "https://doi.org/10.1007/s10208-022-09598-0",
"label": "geometric features of spectra"
},
{
"url": "https://doi.org/10.4171/owr/2014/53",
"label": "original ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/53 | null | null | null | Determine the spectral properties of the Laplacian on a Penrose-tiling graph or on a graph arising from a higher-dimensional quasicrystal model. | Determine the spectral properties of the Laplacian on the graph defined by a Penrose tiling, or by another higher-dimensional model of a quasicrystal. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/53, pp. 2987--3013 |
30,002,743 | OWR-13357-002 | Commutants and Factor Types of Brownian Energy Representations | For the left and right Brownian energy representations, determine whether the von Neumann algebras they generate are mutual commutants; if so, determine the type of the resulting factor. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Reflection Positivity in Representation Theory, Stochastics and Physics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/55, pp. 3059--3102](https://doi.org/10.4171/owr/2014... | 3 | partially_solved | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13357-002",
"literature-status:partially-solved",
"owr-year:2014"
] | The Brownian and energy representations have been shown equivalent and several structural properties are known, but the left-right commutant equality and the resulting factor type asked about in the record remain unresolved. | [
{
"url": "https://doi.org/10.1007/s10958-016-3134-1",
"label": "Albeverio et al., Brownian and energy representations"
},
{
"url": "https://doi.org/10.4171/owr/2014/55",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/55 | null | null | null | For the left and right Brownian energy representations, determine whether the von Neumann algebras they generate are mutual commutants; if so, determine the type of the resulting factor. | For the left and right Brownian energy representations, determine whether the von Neumann algebras they generate are mutual commutants; if so, determine the type of the resulting factor. | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Reflection Positivity in Representation Theory, Stochastics and Physics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/55, pp. 3059--3102 |
30,002,744 | OWR-13357-003 | Reflection-Positivity Research Questions | Resolve the following questions about reflection positivity: describe super versions of massive free fields and reflection-positive Hilbert spaces; determine the role of antiunitary involutions; construct Euclidean realizations of Borchers triples and algebraic quantum field theories; find diffeomorphism-invariant exam... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Reflection Positivity in Representation Theory, Stochastics and Physics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/55, pp. 3059--3102](https://doi.org/10.4171/owr/2014... | 3 | open | null | 2,014 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13357-003",
"literature-status:open",
"owr-year:2014"
] | The record is a list of twenty heterogeneous reflection-positivity questions, some conceptual and some deep; no single later result resolves the list as a whole. | [
{
"url": "https://doi.org/10.4171/owr/2014/55",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/55 | null | null | null | Resolve the following questions about reflection positivity: describe super versions of massive free fields and reflection-positive Hilbert spaces; determine the role of antiunitary involutions; construct Euclidean realizations of Borchers triples and algebraic quantum field theories; find diffeomorphism-invariant exam... | Determine the answers to the listed open problems concerning reflection positivity, including super versions of free fields and reflection-positive Hilbert spaces, Euclidean realizations of Borchers triples and algebraic QFT, diffeomorphism-invariant and non-commutative-geometric examples, connections with complex meas... | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Mini-Workshop: Reflection Positivity in Representation Theory, Stochastics and Physics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/55, pp. 3059--3102 |
30,002,745 | OWR-13358-003 | Individual Conceptions and Classroom Mathematical Norms | What conceptions do individual students bring to their mathematical work, what normative ways of reasoning emerge in a particular classroom, and how do those contributions coordinate with the students' production-design roles? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/... | 3 | open | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Mathematics Education and Classroom Pedagogy workshop report (didactics, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13358-003",
"literature-status:open",
"owr-year:2014"
] | This is a broad empirical question about individual conceptions, classroom norms, and participation; existing classroom studies operationalize these constructs but do not provide a general resolution. | [
{
"url": "https://doi.org/10.4171/owr/2014/56",
"label": "original OWR report"
},
{
"url": "https://sci.sdsu.edu/crmse/msed/papers/rasmussen2.pdf",
"label": "Rasmussen and Stephan, classroom progress study"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/56 | null | null | null | What conceptions do individual students bring to their mathematical work, what normative ways of reasoning emerge in a particular classroom, and how do those contributions coordinate with the students' production-design roles? | What conceptions do individual students bring to their mathematical work, what normative ways of reasoning emerge in a particular classroom, and how do those contributions coordinate with the students' production-design roles? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/56, pp. 3103--3175 |
30,002,746 | OWR-13358-004 | Classroom Participation and Mathematical Growth Trajectories | Are different classroom participation patterns correlated with different trajectories of students' mathematical growth? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/... | 3 | open | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Mathematics Education and Classroom Pedagogy workshop report (didactics, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13358-004",
"literature-status:open",
"owr-year:2014"
] | Studies can coordinate individual and collective classroom analyses, but no general law establishing the proposed correlation between participation patterns and mathematical growth trajectories has been proved. | [
{
"url": "https://doi.org/10.4171/owr/2014/56",
"label": "original OWR report"
},
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0732312313001053",
"label": "Tabach et al., knowledge shifts in mathematics classrooms"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/56 | null | null | null | Are different classroom participation patterns correlated with different trajectories of students' mathematical growth? | Are different classroom participation patterns correlated with different trajectories of students' mathematical growth? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/56, pp. 3103--3175 |
30,002,747 | OWR-13358-005 | Learning Trajectories in History-Based Mathematics Curricula | For a history-based mathematics unit, determine how to sequence its ideas, what ways of thinking it affords, the target students' background and cognitive abilities, the feasible instructional time, and its compatibility with current programs; then determine students' learning trajectories, acquisition, retention, and ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/... | 3 | open | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Mathematics Education and Classroom Pedagogy workshop report (didactics, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13358-005",
"literature-status:open",
"owr-year:2014"
] | The listed curriculum, population, retention, and achievement questions remain a research agenda; a design-based study reports local course findings but does not settle the proposed learning trajectories or transfer effects in general. | [
{
"url": "https://doi.org/10.4171/owr/2014/56",
"label": "original OWR report"
},
{
"url": "https://d-nb.info/1155236289/34",
"label": "Kempen, design-based study of proof learning"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/56 | null | null | null | For a history-based mathematics unit, determine how to sequence its ideas, what ways of thinking it affords, the target students' background and cognitive abilities, the feasible instructional time, and its compatibility with current programs; then determine students' learning trajectories, acquisition, retention, and ... | For a history-based mathematics unit, determine how to sequence its ideas, what ways of thinking it affords, the target students' background and cognitive abilities, the feasible instructional time, and its compatibility with current programs; then determine students' learning trajectories, acquisition, retention, and ... | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/56, pp. 3103--3175 |
30,002,748 | OWR-13358-006 | Perceived Difficulty in Mathematical Activity | What are the points of difficulty in the mathematical situation, and how is perceived difficulty treated? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/... | 3 | open | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Mathematics Education and Classroom Pedagogy workshop report (didactics, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13358-006",
"literature-status:open",
"owr-year:2014"
] | Proof-script studies identify selected points of difficulty and how participants address them, but they do not establish a general theory answering how perceived mathematical difficulty is treated across settings. | [
{
"url": "https://doi.org/10.4171/owr/2014/56",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s10763-014-9595-0",
"label": "Zazkis and Zazkis, proof-comprehension study"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/56 | null | null | null | What are the points of difficulty in the mathematical situation, and how is perceived difficulty treated? | What are the points of difficulty in the mathematical situation, and how is perceived difficulty treated? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/56, pp. 3103--3175 |
30,002,749 | OWR-13358-007 | Proof Scripts and Proof Comprehension | Do proof scripts—dialogues written around a mathematical proof—provide an effective method for investigating and improving students’ proof comprehension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/... | 3 | partially_solved | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Mathematics Education and Classroom Pedagogy workshop report (didactics, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13358-007",
"literature-status:partially-solved",
"owr-year:2014"
] | Several primary studies support proof scripts as a useful diagnostic and pedagogical tool, but the stronger conjecture that they generally enhance proof comprehension remains unverified. | [
{
"url": "https://ems.press/content/serial-article-files/46547",
"label": "Zazkis, proof scripts report"
},
{
"url": "https://doi.org/10.1007/s10763-014-9595-0",
"label": "Zazkis and Zazkis, proof-comprehension study"
},
{
"url": "https://doi.org/10.1007/s11858-023-01518-y",
"label":... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/56 | null | null | null | Do proof scripts—dialogues written around a mathematical proof—provide an effective method for investigating and improving students’ proof comprehension? | Conjecture: Proof scripts provide an excellent vehicle for investigating and enhancing proof comprehension. | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/56, pp. 3103--3175 |
30,002,750 | OWR-13358-008 | Subject Matter Effects on Mathematical Structures | What structural differences are determined by the mathematical subject matter itself? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/... | 3 | open | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Mathematics Education and Classroom Pedagogy workshop report (didactics, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13358-008",
"literature-status:open",
"owr-year:2014"
] | Research frameworks describe subject-specific classroom and disciplinary practices, but no general account has resolved which structural differences are determined by mathematical subject matter itself. | [
{
"url": "https://doi.org/10.4171/owr/2014/56",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1080/10508406.2002.9672137",
"label": "Cobb, classroom mathematical practices"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/56 | null | null | null | What structural differences are determined by the mathematical subject matter itself? | What structural differences are determined by the mathematical subject matter itself? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/56, pp. 3103--3175 |
30,002,751 | OWR-13359-001 | Large-Deviation Explanation of Driven TASEP Boundary Behavior | Can the different behavior of the boundary conditions, as a function of $\alpha$ in the driven TASEP, be understood through a large-deviation argument? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/57, pp. 3177--3254](https://doi.org/10.4171/owr/2014/57)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13359-001",
"literature-status:open",
"owr-year:2014"
] | Large-deviation analyses give model-specific rate functions and phase diagrams for boundary-driven systems, but no general derivation of the reported alpha-dependent boundary behavior has been established. | [
{
"url": "https://doi.org/10.4171/owr/2014/57",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s00440-026-01486-w",
"label": "current open ASEP large-deviation analysis"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/57 | null | null | null | Can the different behavior of the boundary conditions, as a function of $\alpha$ in the driven TASEP, be understood through a large-deviation argument? | Can the different behavior of the boundary conditions, as a function of \alpha in the driven TASEP, be understood through a large-deviation argument? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Variational Methods for Evolution (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/57, pp. 3177--3254 |
30,002,752 | OWR-13359-002 | Origins of Synchronization in Interacting Systems | What is the origin of synchronization and rhythmic behavior in systems of interacting units? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/57, pp. 3177--3254](https://doi.org/10.4171/owr/2014/57)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13359-002",
"literature-status:open",
"owr-year:2014"
] | Pacemaker models and mean-field oscillator systems explain particular synchronization mechanisms, but the general origin of synchronization and rhythms across the stated class remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/57",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1088/0951-7715/25/5/1247",
"label": "Giacomin et al., Kuramoto asymptotic dynamics"
},
{
"url": "https://doi.org/10.1007/s00440-013-0536-6",
"label": "Bertini et al., synchr... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/57 | null | null | null | What is the origin of synchronization and rhythmic behavior in systems of interacting units? | What is the origin of synchronization and rhythmic behavior in systems of interacting units? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Variational Methods for Evolution (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/57, pp. 3177--3254 |
30,002,753 | OWR-13359-003 | Optimal Geodesic Curvature for Random Transpositions | For the random transposition model on the symmetric group $S_n$, determine the correct order in $n$ of the optimal geodesic-convexity constant $\kappa$, known to satisfy $4/(n^2-n) \leq \kappa \leq 2/(n-1)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/57, pp. 3177--3254](https://doi.org/10.4171/owr/2014/57)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13359-003",
"literature-status:open",
"owr-year:2014"
] | For the random-transposition model the cited bounds leave the optimal entropic curvature constant between different powers of the system size, and later treatments still describe the exact order as unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/57",
"label": "original OWR report"
},
{
"url": "https://www.numdam.org/item/10.5802/afst.1464.pdf",
"label": "Erbar, Maas, and Tetali, discrete Ricci bounds"
},
{
"url": "https://tetali.math.gatech.edu/PUBLIS/BT_ENT.pdf",
"label": "Bobkov a... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/57 | null | null | null | For the random transposition model on the symmetric group $S_n$, determine the correct order in $n$ of the optimal geodesic-convexity constant $\kappa$, known to satisfy $4/(n^2-n) \leq \kappa \leq 2/(n-1)$. | For the random transposition model on the symmetric group S_n, determine the correct order in n of the optimal geodesic-convexity constant \kappa, known to satisfy 4/(n^2-n) \leq \kappa \leq 2/(n-1). | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Variational Methods for Evolution (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/57, pp. 3177--3254 |
30,002,754 | OWR-13486-001 | Existence and Uniqueness of Sobolev Traces on Continuous Domains | If $\Omega$ has continuous boundary, does every element of $H^1(\Omega)$ have at most one trace, and does existence of a trace imply uniqueness? In particular, if every element of $\widetilde{H}^1(\Omega)$ has a trace, does every element of $H^1(\Omega)$ have at most one trace? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86](https://doi.org/10.4171/owr/2015/1)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13486-001",
"literature-status:partially-solved",
"owr-year:2015"
] | Sauter proves uniqueness of the approximative trace for continuous-boundary domains, answering the first listed open problem, but explicitly leaves the implication from existence of traces on the smaller space to uniqueness on H^1 unresolved. | [
{
"url": "https://arxiv.org/abs/1607.07109",
"label": "Sauter, uniqueness of the approximative trace"
},
{
"url": "https://doi.org/10.4171/owr/2015/1",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/1 | null | null | null | If $\Omega$ has continuous boundary, does every element of $H^1(\Omega)$ have at most one trace, and does existence of a trace imply uniqueness? In particular, if every element of $\widetilde{H}^1(\Omega)$ has a trace, does every element of $H^1(\Omega)$ have at most one trace? | If \Omega has continuous boundary, does every element of H^1(\Omega) have at most one trace, and does existence of a trace imply uniqueness? In particular, if every element of \widetilde{H}^1(\Omega) has a trace, does every element of H^1(\Omega) have at most one trace? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86 |
30,002,755 | OWR-13486-002 | Determination of Domains by Diffusion | Does diffusion determine a domain? Equivalently, under suitable hypotheses, if two domains have the same diffusion dynamics or heat semigroup, must they be congruent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86](https://doi.org/10.4171/owr/2015/1)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,015 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13486-002",
"literature-status:partially-solved",
"owr-year:2015"
] | Diffusion determines a Lipschitz domain when the heat semigroups are intertwined by an order isomorphism, but ordinary isospectrality does not determine the domain; the broad title therefore has only a restricted positive resolution. | [
{
"url": "https://doi.org/10.1515/crll.2002.076",
"label": "Arendt, Does diffusion determine the body"
},
{
"url": "https://doi.org/10.1090/S0273-0979-1992-00289-6",
"label": "Gordon, Webb, and Wolpert, isospectral drums"
},
{
"url": "https://doi.org/10.4171/owr/2015/1",
"label": "or... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/1 | null | null | null | Does diffusion determine a domain? Equivalently, under suitable hypotheses, if two domains have the same diffusion dynamics or heat semigroup, must they be congruent? | Does diffusion determine a domain? Equivalently, under suitable hypotheses, if two domains have the same diffusion dynamics or heat semigroup, must they be congruent? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86 |
30,002,756 | OWR-13486-005 | Congruence from Complete Robin and Dirichlet Spectra | Let $\Omega_1$ and $\Omega_2$ be Lipschitz domains whose Robin Laplacians have the same eigenvalue sequence for every $\beta \geq 0$ and for Dirichlet boundary conditions. Must $\Omega_1$ and $\Omega_2$ be congruent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86](https://doi.org/10.4171/owr/2015/1)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13486-005",
"literature-status:open",
"owr-year:2015"
] | The report explicitly poses the all-Robin-parameters plus Dirichlet spectral-family question as open; later work rules out a Robin intertwining for the standard counterexample but does not prove spectral-family congruence. | [
{
"url": "https://doi.org/10.4171/owr/2015/1",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1305.1775",
"label": "Arendt, ter Elst, and Kennedy, analytical aspects of isospectral drums"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/1 | null | null | null | Let $\Omega_1$ and $\Omega_2$ be Lipschitz domains whose Robin Laplacians have the same eigenvalue sequence for every $\beta \geq 0$ and for Dirichlet boundary conditions. Must $\Omega_1$ and $\Omega_2$ be congruent? | Let \Omega_1 and \Omega_2 be Lipschitz domains whose Robin Laplacians have the same eigenvalue sequence for every \beta \geq 0 and for Dirichlet boundary conditions. Must \Omega_1 and \Omega_2 be congruent? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86 |
30,002,757 | OWR-13486-006 | Canonical Endpoint Normalizations for Singular Sturm–Liouville Problems | Formulate satisfactory normalizations of a fundamental system of solutions near endpoints of limit-point or limit-circle type that are not regular singular points, for example for the Lennard–Jones potential $q(x)=4\epsilon((\sigma/x)^{12}-(\sigma/x)^6)$, with $\epsilon>0$ and $\sigma>0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86](https://doi.org/10.4171/owr/2015/1)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13486-006",
"literature-status:open",
"owr-year:2015"
] | The cited connection theory treats regular-singular and other special endpoints, but current literature does not supply the requested satisfactory normalization for general LP/N endpoints such as the Lennard-Jones potential. | [
{
"url": "https://doi.org/10.4171/owr/2015/1",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2211.08744",
"label": "Kostenko et al., singular Sturm-Liouville boundary triples"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/1 | null | null | null | Formulate satisfactory normalizations of a fundamental system of solutions near endpoints of limit-point or limit-circle type that are not regular singular points, for example for the Lennard–Jones potential $q(x)=4\epsilon((\sigma/x)^{12}-(\sigma/x)^6)$, with $\epsilon>0$ and $\sigma>0$. | Formulate satisfactory normalizations of a fundamental system of solutions near endpoints of limit-point or limit-circle type that are not regular singular points, for example for the Lennard--Jones potential q(x)=4\epsilon((\sigma/x)^{12}-(\sigma/x)^6), with \epsilon>0 and \sigma>0. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86 |
30,002,758 | OWR-13486-007 | First-Singularity Profiles in Nonlocal Transport Models | Consider the transport equation $\theta_t+u\theta_x=0$. Compare the Córdoba–Córdoba–Fontelos velocity
$$u(x,t)=\operatorname{PV}\int_{\mathbb R}\frac{\theta(y,t)}{y-x}\,dy$$
with the less singular velocity
$$u(x,t)=\int_{\mathbb R}\lvert y-x\rvert^{-\gamma}\theta(y,t)\,dy,\qquad 0<\gamma<1.$$
For symmetric nonnegat... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86](https://doi.org/10.4171/owr/2015/1)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,015 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13486-007",
"literature-status:open",
"owr-year:2015"
] | The report leaves the cusp, square-root profile, location, and prescribed first-singularity questions open; no primary result located by the cutoff establishes these claims for the stated nonlocal blowup models. | [
{
"url": "https://doi.org/10.4171/owr/2015/1",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/1 | null | null | null | Consider the transport equation $\theta_t+u\theta_x=0$. Compare the Córdoba–Córdoba–Fontelos velocity
$$u(x,t)=\operatorname{PV}\int_{\mathbb R}\frac{\theta(y,t)}{y-x}\,dy$$
with the less singular velocity
$$u(x,t)=\int_{\mathbb R}\lvert y-x\rvert^{-\gamma}\theta(y,t)\,dy,\qquad 0<\gamma<1.$$
For symmetric nonnegat... | For the stated nonlocal transport models, determine whether the first singularity for symmetric nonnegative data with maximum at the origin is always a cusp or can have square-root behavior; determine whether singularities for model (4) form only where \theta'\ne 0 and those for model (3) only where \theta'=0; and cons... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86 |
30,002,759 | OWR-13486-008 | Concise Inverse Spectral Theory for Indefinite Strings | Find an equally concise analogue of the solution of the inverse spectral problem for indefinite strings. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86](https://doi.org/10.4171/owr/2015/1)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13486-008",
"literature-status:partially-solved",
"owr-year:2015"
] | Inverse spectral theory has produced concise complete results for important generalized string classes, including an indefinite analogue of Krein theory, but the exact real-measure class still lacks a comparable full characterization. | [
{
"url": "https://arxiv.org/abs/1409.0139",
"label": "Eckhardt and Kostenko, inverse spectral problem for indefinite strings"
},
{
"url": "https://arxiv.org/abs/1305.2486",
"label": "Eckhardt, inverse problem for star graphs of Krein strings"
},
{
"url": "https://doi.org/10.4171/owr/2015... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/1 | null | null | null | Find an equally concise analogue of the solution of the inverse spectral problem for indefinite strings. | Find an equally concise analogue of the solution of the inverse spectral problem for indefinite strings. | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Spectral Theory and Weyl Functions (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/1, pp. 5--86 |
30,002,760 | OWR-13487-001 | Optimal Adaptive Approximation of Transport-Dominated Equations | Does adaptive finite-element approximation of an elliptic or parabolic transport-dominated diffusion equation attain the convergence rate of the best partition generated by a refinement method such as newest-vertex bisection? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Discretization Methods for the Numerical Approximation of PDEs (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/2, pp. 87--185](https://doi.org/10.4171/owr/2015/2)
## Literature revie... | 3 | open | null | 2,015 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13487-001",
"literature-status:open",
"owr-year:2015"
] | Adaptive finite-element theory has advanced, but the report's exact optimality question for transport-dominated diffusion and isotropic newest-vertex-bisection classes remains identified as an open challenge. | [
{
"url": "https://doi.org/10.4171/owr/2015/2",
"label": "original OWR report"
},
{
"url": "https://oa.tib.eu/renate/items/3429c126-b128-463f-9075-31c40105b9ef/full",
"label": "current report summary of remaining challenges"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/2 | null | null | null | Does adaptive finite-element approximation of an elliptic or parabolic transport-dominated diffusion equation attain the convergence rate of the best partition generated by a refinement method such as newest-vertex bisection? | Does adaptive finite-element approximation of an elliptic or parabolic transport-dominated diffusion equation attain the convergence rate of the best partition generated by a refinement method such as newest-vertex bisection? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | New Discretization Methods for the Numerical Approximation of PDEs (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/2, pp. 87--185 |
30,002,761 | OWR-13488-004 | Coarse Baum–Connes Failure without Embedded Expanders | Let a finitely generated group $G$ act ergodically by measure-preserving Lipschitz homeomorphisms on a compact metric probability space $M$, and suppose the action has a spectral gap. Must the warped cone $\mathcal O_G(M)$ fail the coarse Baum–Connes conjecture? Does there exist such an action for which $\mathcal O_G(M... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233](https://doi.org/10.4171/owr/2015/3)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,015 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13488-004",
"literature-status:partially-solved",
"owr-year:2015"
] | Later work proves coarse Baum-Connes failure for important spectral-gap warped cones and characterizes expander graph models under regularity assumptions, but the unrestricted existence question in the extracted wording is not fully settled. | [
{
"url": "https://www.impan.pl/~dsawicki/files/counterexamples.pdf",
"label": "Sawicki, warped cones violating coarse Baum-Connes"
},
{
"url": "https://arxiv.org/abs/2504.21811",
"label": "Kitsios, Schick, and Vigolo, warped cones"
},
{
"url": "https://doi.org/10.5802/aif.3373",
"lab... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/3 | null | null | null | Let a finitely generated group $G$ act ergodically by measure-preserving Lipschitz homeomorphisms on a compact metric probability space $M$, and suppose the action has a spectral gap. Must the warped cone $\mathcal O_G(M)$ fail the coarse Baum–Connes conjecture? Does there exist such an action for which $\mathcal O_G(M... | Conjecture: the coarse Baum--Connes conjecture fails for the warped cones in the stated construction. Question: does there exist an action with a spectral gap whose warped cone does not contain a coarsely embedded sequence of expanders? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233 |
30,002,762 | OWR-13488-005 | Finitely Presented Counterexamples for Conjugation-Invariant Norms | Does there exist a finitely presented group $G$, generated by a finite union of conjugacy classes and equipped with the associated conjugation-invariant word norm, such that either some cyclic subgroup is neither bounded nor undistorted, or some cyclic subgroup is neither bounded nor detected by a homogeneous quasimorp... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233](https://doi.org/10.4171/owr/2015/3)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,015 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13488-005",
"literature-status:open",
"owr-year:2015"
] | The cited work proves the two dichotomies for many geometric classes and gives counterexamples outside the finitely presented setting, but no finitely presented group violating either dichotomy was identified. | [
{
"url": "https://doi.org/10.1017/S0017089515000129",
"label": "Brandenbursky, Gal, Kedra, and Marcinkowski, bi-invariant word metrics"
},
{
"url": "https://doi.org/10.4171/owr/2015/3",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/3 | null | null | null | Does there exist a finitely presented group $G$, generated by a finite union of conjugacy classes and equipped with the associated conjugation-invariant word norm, such that either some cyclic subgroup is neither bounded nor undistorted, or some cyclic subgroup is neither bounded nor detected by a homogeneous quasimorp... | Find a finitely presented group that violates either of the stated dichotomies for conjugation-invariant word norms. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233 |
30,002,763 | OWR-13488-006 | Action Dimension versus $L^{2}$ Cohomological Dimension | Does every group $G$ satisfy the action-dimension inequality $\operatorname{actdim}(G)\geq2\dim_{(2)}(G)$, where $\dim_{(2)}(G)$ is its $L^2$-cohomological dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233](https://doi.org/10.4171/owr/2015/3)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,015 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13488-006",
"literature-status:open",
"owr-year:2015"
] | The action dimension conjecture remains unproved in general; the primary RAAG paper establishes many cases and explicitly describes the general conjecture as unresolved. | [
{
"url": "https://doi.org/10.1112/blms/bdv083",
"label": "Avramidi--Davis--Okun--Schreve, BLMS"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/3 | null | null | null | Does every group $G$ satisfy the action-dimension inequality $\operatorname{actdim}(G)\geq2\dim_{(2)}(G)$, where $\dim_{(2)}(G)$ is its $L^2$-cohomological dimension? | Action Dimension Conjecture: for every group G, \operatorname{actdim}(G) \geq 2 \ell^2\operatorname{dim}(G). | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233 |
30,002,764 | OWR-13488-007 | Determinant Approximation for $L^{2}-Torsion$ | Let $G$ be residually finite and let $G=G_0\supset G_1\supset\cdots$ be a chain of normal finite-index subgroups with trivial intersection. For a matrix $A$ over $\mathbb QG$, is its Fuglede–Kadison determinant over $G$ the limit of the normalized Fuglede–Kadison determinants of the induced matrices over the finite quo... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233](https://doi.org/10.4171/owr/2015/3)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,015 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13488-007",
"literature-status:open",
"owr-year:2015"
] | The determinant approximation conjecture for l2-torsion is still treated as a major open problem; known results cover special residual systems but not the general claim. | [
{
"url": "https://doi.org/10.4171/owr/2015/3",
"label": "Grabowski, Oberwolfach Report"
},
{
"url": "https://arxiv.org/abs/1501.07446",
"label": "Lueck, approximation survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/3 | null | null | null | Let $G$ be residually finite and let $G=G_0\supset G_1\supset\cdots$ be a chain of normal finite-index subgroups with trivial intersection. For a matrix $A$ over $\mathbb QG$, is its Fuglede–Kadison determinant over $G$ the limit of the normalized Fuglede–Kadison determinants of the induced matrices over the finite quo... | The determinant approximation conjecture asks for an analogue of L\ddot{u}ck approximation for \ell^2-torsion.} | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233 |
30,002,765 | OWR-13488-009 | Homology Growth in Residual Towers | For a residual tower of finite covers $M_i\to M$, how does the size of $H_k(M_i)$ grow as $i\to\infty$, when size is measured by mod-$p$ Betti numbers or by $|\operatorname{tors}H_k(M_i;\mathbb Z)|$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233](https://doi.org/10.4171/owr/2015/3)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,015 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13488-009",
"literature-status:open",
"owr-year:2015"
] | The question about asymptotic homology size in residual towers has important upper bounds and special-case results, but no general growth law resolving the extracted question. | [
{
"url": "https://doi.org/10.2140/gt.2016.20.1035",
"label": "Sauer, Geometry and Topology"
},
{
"url": "https://arxiv.org/abs/1501.07446",
"label": "Lueck, approximation survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/3 | null | null | null | For a residual tower of finite covers $M_i\to M$, how does the size of $H_k(M_i)$ grow as $i\to\infty$, when size is measured by mod-$p$ Betti numbers or by $|\operatorname{tors}H_k(M_i;\mathbb Z)|$? | For a residual tower of finite covers M_i \to M, how does the size of H_k(M_i) grow as i \to \infty, when size is measured by mod-p Betti numbers or by |\operatorname{tors} H_k(M_i;\mathbb{Z})|? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233 |
30,002,766 | OWR-13488-010 | Countable Groups of Prescribed Transitivity Degree | Does there exist an infinite countable group of transitivity degree $k$ for every $k\in\mathbb N$? More generally, is there a reasonable classification of highly transitive groups or of groups of high transitivity degree? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233](https://doi.org/10.4171/owr/2015/3)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,015 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13488-010",
"literature-status:open",
"owr-year:2015"
] | The existence of countable groups of every finite transitivity degree remains unresolved; the primary source records that even degree four was open. | [
{
"url": "https://doi.org/10.4171/owr/2015/3",
"label": "Osin, Oberwolfach Report"
},
{
"url": "https://ems.press/content/serial-article-files/46555",
"label": "Osin, primary report text"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/3 | null | null | null | Does there exist an infinite countable group of transitivity degree $k$ for every $k\in\mathbb N$? More generally, is there a reasonable classification of highly transitive groups or of groups of high transitivity degree? | Does there exist an infinite countable group of transitivity degree k for every k \in \mathbb{N}? More generally, is there a reasonable classification of highly transitive groups or of groups of high transitivity degree? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233 |
30,002,767 | OWR-13488-011 | Bestvina–Davis Candidates for the Eilenberg–Ganea Conjecture | Let $L$ be a finite acyclic two-dimensional flag complex whose fundamental group has a nontrivial unitary representation, let $W_L$ be the associated right-angled Coxeter group, and let $H\leq W_L$ be torsion-free of finite index. Although $\operatorname{cd}(H)=2$, must $\operatorname{gd}(H)=3$, making $H$ a counterexa... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233](https://doi.org/10.4171/owr/2015/3)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,015 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13488-011",
"literature-status:open",
"owr-year:2015"
] | The Eilenberg--Ganea question for torsion-free groups of cohomological dimension two remains open; the Bestvina--Davis construction gives candidates but not a definitive resolution. | [
{
"url": "https://people.math.osu.edu/davis.12/courses/8800-20/Bestvina-Brady.pdf",
"label": "Bestvina--Brady, Inventiones Mathematicae"
},
{
"url": "https://people.math.osu.edu/davis.12/np1.pdf",
"label": "Davis, Eilenberg--Ganea survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/3 | null | null | null | Let $L$ be a finite acyclic two-dimensional flag complex whose fundamental group has a nontrivial unitary representation, let $W_L$ be the associated right-angled Coxeter group, and let $H\leq W_L$ be torsion-free of finite index. Although $\operatorname{cd}(H)=2$, must $\operatorname{gd}(H)=3$, making $H$ a counterexa... | Are the torsion-free finite-index subgroups H arising from the Bestvina--Davis construction, with cd(H)=2, counterexamples to the Eilenberg--Ganea conjecture, i.e. do they have gd(H)=3? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233 |
30,002,768 | OWR-13488-012 | Composite of Unrelated Hyperbolic-Group Questions | Does Kaplansky's zero-divisor conjecture hold for the torsion-free hyperbolic groups constructed in the report, and do the specified groups belong to the class for which the Farrell--Jones conjecture is known? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233](https://doi.org/10.4171/owr/2015/3)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,015 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report shows that the extraction combines Steenbock's Kaplansky zero-divisor question with Rüping's separate Farrell–Jones ques) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13488-012",
"literature-status:open",
"owr-year:2015"
] | Kaplansky's zero-divisor conjecture is not settled for the extracted torsion-free hyperbolic groups without unique product; later work constructs such groups while retaining the conjecture as open. | [
{
"url": "https://doi.org/10.2140/pjm.2023.322.1",
"label": "Arzhantseva--Steenbock, Pacific Journal of Mathematics"
},
{
"url": "https://doi.org/10.4171/owr/2015/3",
"label": "Steenbock, Oberwolfach Report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/3 | null | null | null | null | Does Kaplansky's zero-divisor conjecture hold for the torsion-free hyperbolic groups constructed in the report, and do the specified groups belong to the class for which the Farrell--Jones conjecture is known? | unrecoverable | The official report shows that the extraction combines Steenbock's Kaplansky zero-divisor question with Rüping's separate Farrell–Jones question about unspecified groups, so it is not one recoverable mathematical problem. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Geometric Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/3, pp. 187--233 |
30,002,769 | OWR-13489-002 | Realizing Complex Manifolds Transversely to Algebraic Foliations | For any compact complex manifold $(X,J)$, does there exist a smooth complex projective variety Z, an algebraic foliation D on Z, and an isotopy class $\alpha$ of transverse embeddings $X\to Z$ such that $J=J_f$ for some $f\in\alpha$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/4, pp. 235--283](https://doi.org/10.4171/owr/2015/4)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,015 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13489-002",
"literature-status:open",
"owr-year:2015"
] | Demailly--Gaussier realize every compact almost complex manifold using an algebraic distribution, but the stronger Bogomolov question requiring an algebraic foliation on a projective variety remains posed as a basic question. | [
{
"url": "https://doi.org/10.4171/JEMS/742",
"label": "Demailly--Gaussier, JEMS"
},
{
"url": "https://arxiv.org/abs/1905.06016",
"label": "Demailly--Gaussier, universal embedding spaces"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/4 | null | null | null | For any compact complex manifold $(X,J)$, does there exist a smooth complex projective variety Z, an algebraic foliation D on Z, and an isotopy class $\alpha$ of transverse embeddings $X\to Z$ such that $J=J_f$ for some $f\in\alpha$? | For any compact complex manifold (X,J), does there exist a smooth complex projective variety Z, an algebraic foliation D on Z, and an isotopy class \alpha of transverse embeddings X \to Z such that J=J_f for some f\in\alpha? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Geometric Methods of Complex Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/4, pp. 235--283 |
30,002,770 | OWR-13489-004 | Riemannian Control of Bergman Geometry | Let $M$ be an open Riemann surface whose complex structure is induced by a complete Riemannian metric $ds^2$. How does the Riemannian geometry of $ds^2$ control the Bergman kernel and Bergman metric of $M$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/4, pp. 235--283](https://doi.org/10.4171/owr/2015/4)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13489-004",
"literature-status:partially-solved",
"owr-year:2015"
] | Under positive isoperimetric constants and curvature or volume hypotheses, the cited work proves Bergman completeness, distance comparison, kernel decay, and convergence; no general geometric classification is known. | [
{
"url": "https://doi.org/10.4171/owr/2015/4",
"label": "Chen, Oberwolfach Report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/4 | null | null | null | Let $M$ be an open Riemann surface whose complex structure is induced by a complete Riemannian metric $ds^2$. How does the Riemannian geometry of $ds^2$ control the Bergman kernel and Bergman metric of $M$? | How does the Riemannian geometry of a complete metric ds^2 on an open Riemann surface influence the behavior of its Bergman kernel or metric? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Geometric Methods of Complex Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/4, pp. 235--283 |
30,002,771 | OWR-13489-005 | Minimal Ambient Dimension for Complete Bounded Complex Submanifolds | For $k>1$, complete bounded embedded complex $k$-dimensional submanifolds of $\mathbb{C}^{2k}$ exist. Is $2k$ the smallest ambient complex dimension in which such submanifolds can exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/4, pp. 235--283](https://doi.org/10.4171/owr/2015/4)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,015 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (no; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no; answered in the source)**. J. Globevnik (OWR 4/2015, pp. 266–267) recalls that complete bounded embedded complex k-submanifolds of C^{2k} exist and that minimality of 2k was open (Alarcón–López); his Corollary answers it: the ball of C^N contains complete clos... | [
"owr",
"oberwolfach-reports",
"OWR-13489-005",
"literature-status:open",
"owr-year:2015"
] | Complete bounded embedded k-dimensional examples exist in complex dimension 2k, but the minimality of the ambient dimension 2k remains an open question in the current survey literature. | [
{
"url": "https://doi.org/10.4007/annals.2015.182.3.4",
"label": "Globevnik, Annals of Mathematics"
},
{
"url": "https://arxiv.org/abs/2212.08521",
"label": "Alarcon, Yang problem survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/4 | null | null | null | For $k>1$, complete bounded embedded complex $k$-dimensional submanifolds of $\mathbb{C}^{2k}$ exist. Is $2k$ the smallest ambient complex dimension in which such submanifolds can exist? | If there are complete bounded embedded complex k-dimensional submanifolds of \mathbb{C}^{2k}, is N=2k the minimal possible ambient dimension for such submanifolds? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Geometric Methods of Complex Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/4, pp. 235--283 |
30,002,772 | OWR-13489-006 | Pseudoconvex Domains and Their Cores | For a domain $\Omega$ in a complex manifold, let $c(\Omega)$ be the set where the Levi form of every bounded-above plurisubharmonic function on $\Omega$ degenerates. How are geometric properties of $\Omega$ related to those of $c(\Omega)$; in particular, how is pseudoconvexity of $\Omega$ related to pluripolarity of it... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/4, pp. 235--283](https://doi.org/10.4171/owr/2015/4)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,015 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13489-006",
"literature-status:partially-solved",
"owr-year:2015"
] | The core is proved 1-pseudoconcave and specific relations between domain geometry and the core are established, but the general relationship between properties of the domain and its core remains open. | [
{
"url": "https://doi.org/10.4171/owr/2015/4",
"label": "Merker--Porten, Oberwolfach Report"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3451/OWR_2015_04.pdf?isAllowed=y&sequence=1",
"label": "MFO primary report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/4 | null | null | null | For a domain $\Omega$ in a complex manifold, let $c(\Omega)$ be the set where the Levi form of every bounded-above plurisubharmonic function on $\Omega$ degenerates. How are geometric properties of $\Omega$ related to those of $c(\Omega)$; in particular, how is pseudoconvexity of $\Omega$ related to pluripolarity of it... | Understand how properties of \Omega are related to properties of c(\Omega). | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Geometric Methods of Complex Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/4, pp. 235--283 |
30,002,773 | OWR-13490-006 | Ramos Conjecture for Equipartitions by Hyperplanes | For $j,k\geq 1$, let $\Delta(j,k)$ be the least dimension in which any j masses can be simultaneously cut into $2^k$ equal orthants by k affine hyperplanes. The Ramos conjecture asserts that the known lower bound for $\Delta(j,k)$ is tight for all j and k. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13490-006",
"literature-status:open",
"owr-year:2015"
] | The Ramos conjecture remains unresolved in general; rigorous work proves many parameter families and bounds, but not equality with the lower bound for all j and k. | [
{
"url": "https://doi.org/10.4171/DM/544",
"label": "Haase--Blagojevic--Frick--Ziegler, Documenta Mathematica"
},
{
"url": "https://arxiv.org/abs/1509.02959",
"label": "primary arXiv version"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | For $j,k\geq 1$, let $\Delta(j,k)$ be the least dimension in which any j masses can be simultaneously cut into $2^k$ equal orthants by k affine hyperplanes. The Ramos conjecture asserts that the known lower bound for $\Delta(j,k)$ is tight for all j and k. | For j,k\geq 1, let \Delta(j,k) be the least dimension in which any j masses can be simultaneously cut into 2^k equal orthants by k affine hyperplanes. The Ramos conjecture asserts that the known lower bound for \Delta(j,k) is tight for all j and k. | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,774 | OWR-13490-008 | Real-Rootedness of Generalized Chebyshev Polynomials | For which triangulations $L$ are all roots of the generalized Tchebyshev polynomial $T_n^L(x)$ real for every $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,015 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13490-008",
"literature-status:open",
"owr-year:2015"
] | Real-rootedness is proved for important subclasses, including all valid subdivisions of a two-dimensional simplex, while a simple three-dimensional subdivision gives a counterexample; a full characterization of L remains open. | [
{
"url": "https://doi.org/10.1016/j.jcta.2015.08.004",
"label": "Hetyei--Nevo, JCTA"
},
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "Geometric and Algebraic Combinatorics report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | For which triangulations $L$ are all roots of the generalized Tchebyshev polynomial $T_n^L(x)$ real for every $n$? | For which triangulations L are all roots of the generalized Tchebyshev polynomial T_n^L(x) real for every n? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,775 | OWR-13490-009 | Equality Cases in the Balanced Lower Bound Conjecture | For every balanced simplicial d-polytope P, the normalized h-numbers satisfy $\frac{h_0(P)}{\binom{d}{0}}\leq\cdots\leq\frac{h_{\lfloor d/2\rfloor}(P)}{\binom{d}{\lfloor d/2\rfloor}}$; equality at the relevant adjacent terms should characterize the balanced stacked property. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,015 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13490-009",
"literature-status:partially-solved",
"owr-year:2015"
] | Juhnke--Kubitzke and Murai prove the inequality part of the balanced generalized lower bound conjecture, while the equality characterization remains unresolved in the extracted context. | [
{
"url": "https://arxiv.org/abs/1503.06430",
"label": "Juhnke--Kubitzke--Murai, primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "Murai, Oberwolfach Report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | For every balanced simplicial d-polytope P, the normalized h-numbers satisfy $\frac{h_0(P)}{\binom{d}{0}}\leq\cdots\leq\frac{h_{\lfloor d/2\rfloor}(P)}{\binom{d}{\lfloor d/2\rfloor}}$; equality at the relevant adjacent terms should characterize the balanced stacked property. | For every balanced simplicial d-polytope P, the normalized h-numbers satisfy h_0(P)/\binom{d}{0} \leq \cdots \leq h_{\lfloor d/2\rfloor}(P)/\binom{d}{\lfloor d/2\rfloor}; equality at the relevant adjacent terms should characterize the balanced stacked property. | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,776 | OWR-13490-010 | Duplicate Lefschetz-Injectivity Extraction | Does the Stanley--Reisner ring of every doubly Cohen--Macaulay simplicial complex admit parameters \Theta and a linear form \omega satisfying the injectivity conclusion of Theorem 4? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,015 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | Duplicate/merged OWR extraction (The passage duplicates the same Lefschetz-injectivity question recorded in OWR-13490-011 and adds no independent problem. No separate clean ) | [
"OWR-13490-011"
] | null | [Discussion #4 literature review, 2026-10-14] and its duplicate `OWR-13490-010` → **solved (yes; preprint)**; the dataset currently labels both partially solved. Question of A. Björner and E. Swartz recalled by S. Murai (with M. Juhnke-Kubitzke), OWR 5/2015, p. 344: does the Stanley–Reisner ring R of every doubly Cohen... | [
"owr",
"oberwolfach-reports",
"OWR-13490-010",
"literature-status:partially-solved",
"owr-year:2015"
] | The cited theorem proves the first inequality part of the balanced generalized lower bound conjecture; the remaining equality and full conjectural structure are not established by that result. | [
{
"url": "https://arxiv.org/abs/1503.06430",
"label": "Juhnke--Kubitzke--Murai, primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "Murai, Oberwolfach Report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | null | Does the Stanley--Reisner ring of every doubly Cohen--Macaulay simplicial complex admit parameters \Theta and a linear form \omega satisfying the injectivity conclusion of Theorem 4? | unrecoverable | The passage duplicates the same Lefschetz-injectivity question recorded in OWR-13490-011 and adds no independent problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,777 | OWR-13490-011 | Lefschetz Injectivity for Doubly Cohen–Macaulay Complexes | Does the Stanley–Reisner ring $R$ of every doubly Cohen–Macaulay simplicial complex admit a linear system of parameters $\Theta$ and a linear form $\omega$ such that $\omega^{s-2i}:(R/\Theta R)_i\to(R/\Theta R)_{s-i}$ is injective for every $i\leq s/2$, where $s$ is the rank of the complex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,015 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-13490-010"
] | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] and its duplicate `OWR-13490-010` → **solved (yes; preprint)**; the dataset currently labels both partially solved. Question of A. Björner and E. Swartz recalled by S. Murai (with M. Juhnke-Kubitzke), OWR 5/2015, p. 344: does the Stanley–Reisner ring R of every doubly Cohen... | [
"owr",
"oberwolfach-reports",
"OWR-13490-011",
"literature-status:partially-solved",
"owr-year:2015"
] | The Lefschetz-type conclusion is proved for rank-selected subcomplexes of balanced simplicial polytopes, giving a partial affirmative answer; the all-doubly-Cohen--Macaulay statement remains open. | [
{
"url": "https://arxiv.org/abs/1503.06430",
"label": "Juhnke--Kubitzke--Murai, primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "Murai, Oberwolfach Report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | Does the Stanley–Reisner ring $R$ of every doubly Cohen–Macaulay simplicial complex admit a linear system of parameters $\Theta$ and a linear form $\omega$ such that $\omega^{s-2i}:(R/\Theta R)_i\to(R/\Theta R)_{s-i}$ is injective for every $i\leq s/2$, where $s$ is the rank of the complex? | Does the Stanley--Reisner ring of every doubly Cohen--Macaulay simplicial complex satisfy the injectivity conclusion of Theorem 4, namely that \omega^{\#S-2i}:(R/\Theta R)_i\to(R/\Theta R)_{\#S-i} is injective for i\leq\#S/2? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,778 | OWR-13490-013 | Vertex-Symmetry Criteria for Mod-Two Tightness | If X is a 2-dimensional simplicial complex such that $c_Y(y_1,y_2)=c_Y(y_2,y_1)$ for every induced subcomplex Y and every pair of distinct vertices $y_1,y_2$ of Y, must X be $\mathbb{Z}_2$-tight? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,015 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13490-013",
"literature-status:open",
"owr-year:2015"
] | The extracted record contains only the sentence `We conjecture the following' and omits the conjectured statement, so no determinate mathematical claim can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | If X is a 2-dimensional simplicial complex such that $c_Y(y_1,y_2)=c_Y(y_2,y_1)$ for every induced subcomplex Y and every pair of distinct vertices $y_1,y_2$ of Y, must X be $\mathbb{Z}_2$-tight? | If X is a 2-dimensional simplicial complex such that c_Y(y_1,y_2)=c_Y(y_2,y_1) for every induced subcomplex Y and every pair of distinct vertices y_1,y_2 of Y, must X be \mathbb{Z}_2-tight? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,779 | OWR-13490-014 | Polyhedrality of Cones of Nonnegative Valuations | For the cone $\overline{V}_+$ of lattice-invariant $h^*$-nonnegative valuations, is $\overline{V}_+$ a polyhedral cone, and in the stronger form is it linearly isomorphic to $\mathbb{R}_{\geq 0}^{d+1}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,015 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13490-014",
"literature-status:open",
"owr-year:2015"
] | The record reports verification in dimensions at most three but does not identify the underlying conjecture or its strong version; the extracted claim is therefore unresolved as stated. | [
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | For the cone $\overline{V}_+$ of lattice-invariant $h^*$-nonnegative valuations, is $\overline{V}_+$ a polyhedral cone, and in the stronger form is it linearly isomorphic to $\mathbb{R}_{\geq 0}^{d+1}$? | For the cone \overline{V}_+ of lattice-invariant h^*-nonnegative valuations, is \overline{V}_+ a polyhedral cone, and in the stronger form is it linearly isomorphic to \mathbb{R}_{\geq 0}^{d+1}?} | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,780 | OWR-13490-017 | Bagchi’s Lower Bound for Triangulated Manifolds | For a $d$-dimensional triangulated homology manifold and every relevant index $i$, is $g_i\geq\binom{d+1}{i}\left((-1)^i+\sum_{j=1}^{i}(-1)^{i-j}\mu_{j-1}\right)$, where the $\mu_j$ are the averaged discrete Morse numbers of the triangulation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,015 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13490-017",
"literature-status:partially-solved",
"owr-year:2015"
] | The mu-vector lower-bound conjecture is proved for connected closed combinatorial 3-manifolds and for broader locally tame classes, but the general homology-manifold statement in the record remains unproved. | [
{
"url": "https://doi.org/10.1016/j.ejc.2015.04.007",
"label": "Bagchi, the mu vector and generalized lower bounds"
},
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | For a $d$-dimensional triangulated homology manifold and every relevant index $i$, is $g_i\geq\binom{d+1}{i}\left((-1)^i+\sum_{j=1}^{i}(-1)^{i-j}\mu_{j-1}\right)$, where the $\mu_j$ are the averaged discrete Morse numbers of the triangulation? | Bagchi's conjecture asserts that g_i \geq \binom{d+1}{i}\left[(-1)^i+\sum_{j=1}^{i}(-1)^{i-j}\mu_{j-1}\right] for the relevant triangulated manifolds and indices i. | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,781 | OWR-13490-018 | Averaged Morse Numbers and Lefschetz Theory | How is Bagchi’s lower-bound conjecture for the $g$-vector related to the $g$-conjecture? How are the averaged discrete Morse invariants $\mu_i$ related to discrete Morse theory, and is $\mu_1$ a lower bound for the minimum number of generators of the fundamental group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,015 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13490-018",
"literature-status:open",
"owr-year:2015"
] | The record asks several broad relationship and lower-bound questions about the mu-vector; known Morse inequalities and low-dimensional results do not resolve the listed questions in general. | [
{
"url": "https://doi.org/10.1016/j.ejc.2015.04.007",
"label": "Bagchi, the mu vector and generalized lower bounds"
},
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | How is Bagchi’s lower-bound conjecture for the $g$-vector related to the $g$-conjecture? How are the averaged discrete Morse invariants $\mu_i$ related to discrete Morse theory, and is $\mu_1$ a lower bound for the minimum number of generators of the fundamental group? | What is the relationship between Bagchi's conjecture and the g-conjecture? What is the relationship between the \mu_i and discrete Morse theory? Is \mu_1 a lower bound for the number of generators of the fundamental group? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,782 | OWR-13490-020 | Independence Complexes and Alternating-Sign Matrices | Let $G$ be a graph whose independence complex has one cohomology generator, let $e$ be an edge, and form $G_k$ by replacing $e$ with a path of $3k+1$ edges. Find a closed formula and a natural generating function for the largest weight in a cohomology representative of $G_k$. Also, find independence complexes that real... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,015 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13490-020",
"literature-status:partially-solved",
"owr-year:2015"
] | The cycle and path families in the record have explicit alternating-sign-matrix sequences and suspension recurrences, but no general closed formula for every graph-edge replacement or realization of all Kuperberg symmetry classes was verified. | [
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.2307/3597283",
"label": "Kuperberg, symmetry classes of alternating-sign matrices"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | Let $G$ be a graph whose independence complex has one cohomology generator, let $e$ be an edge, and form $G_k$ by replacing $e$ with a path of $3k+1$ edges. Find a closed formula and a natural generating function for the largest weight in a cohomology representative of $G_k$. Also, find independence complexes that real... | Problem 1: for a graph G whose independence complex has exactly one cohomology generator and an edge e, replacing e by a path with 3k+1 edges, find a closed formula and a nice generating function for the largest weight of the cohomology representatives. Problem 2: find the independence complexes realizing Kuperberg's s... | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,783 | OWR-13490-021 | Tverberg Intersections Under Good Cover Conditions | For continuous maps in the topological Tverberg setting: does the Tverberg conclusion hold when images of faces form a good cover or are contractible; is there a common point in all images of faces of dimension m-r; and does the disjoint-face intersection assertion hold for affine maps from an m-polytope? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,015 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13490-021",
"literature-status:partially-solved",
"owr-year:2015"
] | The affine Tverberg theorem, prime-power topological cases, and the stated central-point consequence are established, while Frick's counterexamples disprove unrestricted continuous TTC beyond prime powers and the good-cover variants remain unresolved. | [
{
"url": "https://arxiv.org/abs/1502.00947",
"label": "Frick, counterexamples to topological Tverberg"
},
{
"url": "https://doi.org/10.1016/j.topol.2011.12.002",
"label": "Karasev, topological central point theorem"
},
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "original... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | For continuous maps in the topological Tverberg setting: does the Tverberg conclusion hold when images of faces form a good cover or are contractible; is there a common point in all images of faces of dimension m-r; and does the disjoint-face intersection assertion hold for affine maps from an m-polytope? | For continuous maps in the topological Tverberg setting: does the Tverberg conclusion hold when images of faces form a good cover or are contractible; is there a common point in all images of faces of dimension m-r; and does the disjoint-face intersection assertion hold for affine maps from an m-polytope? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,784 | OWR-13490-022 | Labeled Floor Diagrams in Three Dimensions | Determine the combinatorics and enumeration of labeled floor diagrams for tropical curves in three-dimensional projective space. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368](https://doi.org/10.4171/owr/2015/5)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,015 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13490-022",
"literature-status:partially-solved",
"owr-year:2015"
] | Floor-diagram methods now give correspondence and enumeration results for important tropical space-curve problems in three dimensions, but the broad 3D labeled-floor-diagram enumeration requested here has no general resolution verified. | [
{
"url": "https://arxiv.org/abs/2003.06174",
"label": "Rau, counting tropical rational space curves"
},
{
"url": "https://doi.org/10.4171/owr/2015/5",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/5 | null | null | null | Determine the combinatorics and enumeration of labeled floor diagrams for tropical curves in three-dimensional projective space. | What can be said about the three-dimensional case, especially about the number of labeled floor diagrams? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Geometric and Algebraic Combinatorics (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/5, pp. 285--368 |
30,002,785 | OWR-13491-001 | Inclusions and Approximability in Operator Ideals | For operator ideals generated by $s$-numbers, is $L_q^{\mathrm{hilb}}$ contained in $L_p^{\mathrm{app}}$ whenever $1/q$ is at least $1/p+1$, and for which $p$ are all operators in $L_p^{\mathrm{ent}}$ approximable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Modern Applications of \$s\$-numbers and Operator Ideals (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/6, pp. 369--397](https://doi.org/10.4171/owr/2015/6)
## Literature... | 3 | open | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13491-001",
"literature-status:open",
"owr-year:2015"
] | The record is a collection of operator-ideal questions, including unresolved inclusion and approximability problems; standard inequalities between s-numbers do not settle the stated favorites. | [
{
"url": "https://doi.org/10.4171/owr/2015/6",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s43036-024-00386-x",
"label": "recent inequalities between s-numbers"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/6 | null | null | null | For operator ideals generated by $s$-numbers, is $L_q^{\mathrm{hilb}}$ contained in $L_p^{\mathrm{app}}$ whenever $1/q$ is at least $1/p+1$, and for which $p$ are all operators in $L_p^{\mathrm{ent}}$ approximable? | For operator ideals generated by s-numbers, is L_q^{\mathrm{hilb}} contained in L_p^{\mathrm{app}} whenever 1/q is at least 1/p+1, and for which p are all operators in L_p^{\mathrm{ent}} approximable? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Modern Applications of \$s\$-numbers and Operator Ideals (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/6, pp. 369--397 |
30,002,786 | OWR-13493-001 | Uniqueness of the Bryant–Salamon $G_{2}$ Metric on the Spin Bundle | Is the asymptotically conical holonomy-$G_2$ metric on the spin bundle $S(S^3)$ unique? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singularities in \$\\\\mathrm G\_2\$-geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/8, pp. 449--488](https://doi.org/10.4171/owr/2015/8)
## Literature review (ch... | 3 | open | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13493-001",
"literature-status:open",
"owr-year:2015"
] | The known Bryant--Salamon AC G2 metrics on the spin bundle of S^3 are locally unique, but global uniqueness of the metric remains tied to an unresolved classification of cohomogeneity-one G2 manifolds. | [
{
"url": "https://doi.org/10.4171/owr/2015/8",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1805.02612",
"label": "Foscolo, Haskins, and Nordstrom, cohomogeneity-one G2 manifolds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/8 | null | null | null | Is the asymptotically conical holonomy-$G_2$ metric on the spin bundle $S(S^3)$ unique? | Is the AC holonomy G_2 metric on S(S^3) unique? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Singularities in \$\\\\mathrm G\_2\$-geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/8, pp. 449--488 |
30,002,787 | OWR-13494-005 | Additivity of Waring Rank in Independent Variables | If $F_1,\ldots,F_r$ are forms in independent sets of variables, is their Waring rank additive, namely $\operatorname{rank}(F_1+\cdots+F_r)=\operatorname{rank}(F_1)+\cdots+\operatorname{rank}(F_r)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | partially_solved | null | 2,015 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13494-005",
"literature-status:partially-solved",
"owr-year:2015"
] | Strassen additivity for Waring rank is proved for several substantial classes, including monomials, binary forms, and linearly computable forms, but the general independent-variable conjecture remains open. | [
{
"url": "https://doi.org/10.1016/j.jpaa.2014.10.006",
"label": "Carlini, Catalisano, and Chiantini, symmetric Strassen progress"
},
{
"url": "https://doi.org/10.1215/ijm/1488186021",
"label": "Teitler, sufficient conditions for Strassen additivity"
},
{
"url": "https://doi.org/10.4171/o... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | If $F_1,\ldots,F_r$ are forms in independent sets of variables, is their Waring rank additive, namely $\operatorname{rank}(F_1+\cdots+F_r)=\operatorname{rank}(F_1)+\cdots+\operatorname{rank}(F_r)$? | If F_1,\ldots,F_r are forms in independent sets of variables, is their Waring rank additive, namely rank(F_1+\cdots+F_r)=rank(F_1)+\cdots+rank(F_r)? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,788 | OWR-13494-006 | Linear Computability Under Addition of Forms | Is the sum of two linearly computable forms always linearly computable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | partially_solved | null | 2,015 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13494-006",
"literature-status:partially-solved",
"owr-year:2015"
] | The record itself gives a counterexample to the claim that all forms are linearly computable, while additivity and closure of linearly computable forms are established only in special cases and the stated closure question remains open. | [
{
"url": "https://arxiv.org/abs/1604.07691",
"label": "Teitler, sufficient conditions for Strassen additivity"
},
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | Is the sum of two linearly computable forms always linearly computable? | Is the sum of two linearly computable forms always linearly computable? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,789 | OWR-13494-007 | Resurgence Bounds for Linear Arrangements in Multiprojective Spaces | For ideals of line arrangements, which further arrangements admit useful resurgence bounds? Can analogous containment and resurgence results be extended to higher-dimensional linear arrangements in products of projective spaces, and what upper bounds hold for concrete subschemes of multiprojective spaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | open | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13494-007",
"literature-status:open",
"owr-year:2015"
] | The three questions about other line arrangements, higher-dimensional analogues, and resurgence bounds are broad research problems; no general classification or bound resolving them was verified. | [
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | For ideals of line arrangements, which further arrangements admit useful resurgence bounds? Can analogous containment and resurgence results be extended to higher-dimensional linear arrangements in products of projective spaces, and what upper bounds hold for concrete subschemes of multiprojective spaces? | For ideals of linear arrangements, what can be said for other arrangements of lines; can analogous results extend to higher-dimensional linear spaces using products of projective spaces; and what upper bounds exist for the resurgence of particular subschemes in multiprojective spaces? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,790 | OWR-13494-009 | Symbolic Containment for Roulleau–Urzúa Configurations | For the Roulleau–Urzúa configurations $C_n$ of cubics, with $I$ the ideal of their singular points, does $I^{(3)}\subseteq I^2$ hold for all $n$; and are there interesting analogous configurations of conics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | open | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23365899",
"checked_at": "2026-10-14",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-14] I have released an unrefereed preprint, **Containment of the Symbolic Cube in the Square for the Roulleau–Urzúa Configurations of Cubics** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23365899) | [
"owr",
"oberwolfach-reports",
"OWR-13494-009",
"literature-status:open",
"owr-year:2015"
] | The C3 member is verified in the record, but no authoritative result was found that settles the symbolic-cube containment for the full Roulleau--Urzua family Cn or the analogous conic question. | [
{
"url": "https://doi.org/10.1007/s13348-016-0172-4",
"label": "Bauer, Harbourne, Roe, and Szemberg, Halphen cubics"
},
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | For the Roulleau–Urzúa configurations $C_n$ of cubics, with $I$ the ideal of their singular points, does $I^{(3)}\subseteq I^2$ hold for all $n$; and are there interesting analogous configurations of conics? | For the Roulleau--Urzu\acute{a} configurations C_n of cubics, with I the ideal of their singular points, does I^{(3)}\subseteq I^2 hold for all n; and are there interesting analogous configurations of conics? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,791 | OWR-13494-010 | Irreducible Curves with Strongly Negative Harbourne Constants | For a reduced plane curve $C \subset \mathbb{P}^2_{\mathbb{C}}$, let $\widetilde{\mathbb{P}^2} \to \mathbb{P}^2$ be the blow-up of the singular points of $C$, let $\widetilde{C}$ be its strict transform, and let $H(C) = (\widetilde{C})^2 / s$ be the Harbourne constant (where $s$ is the number of singular points blown u... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | partially_solved | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13494-010",
"literature-status:partially-solved",
"owr-year:2015"
] | Irreducible plane curves with H(C)\leq-2 are known in positive characteristic and strong lower bounds hold in several restricted cases, but existence over the complex numbers and the analogous surface-wide questions remain unresolved. | [
{
"url": "https://arxiv.org/abs/2101.07187",
"label": "Dimca, Harbourne, and Sticlaru, bounded negativity and singular curves"
},
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | For a reduced plane curve $C \subset \mathbb{P}^2_{\mathbb{C}}$, let $\widetilde{\mathbb{P}^2} \to \mathbb{P}^2$ be the blow-up of the singular points of $C$, let $\widetilde{C}$ be its strict transform, and let $H(C) = (\widetilde{C})^2 / s$ be the Harbourne constant (where $s$ is the number of singular points blown u... | Do there exist irreducible curves C with H(C)\leq -2, and what analogous questions or constructions arise for other surfaces? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,792 | OWR-13494-011 | Non-ACM Line Configurations with Minimal Symbolic Initial-Degree Gap | Does there exist a non-ACM configuration of lines $L$ in $\mathbb P^3$ whose ideal $I$ satisfies $\alpha(I^{(2)})-\alpha(I)=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | open | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23284413",
"checked_at": "2026-10-10",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-10] I have released an unrefereed preprint, **Line Configurations in P^3 Whose Symbolic Square Has Initial Degree α(I)+1 Are Coplanar or Pseudostars: A Negative Answer to a Question of Janssen** (Alper Ferudun, Mercury Software GmbH). It proves that the answer to the question is... | [
"owr",
"oberwolfach-reports",
"OWR-13494-011",
"literature-status:open",
"owr-year:2015"
] | The ACM hypothesis yields a classification for pseudostars and coplanar configurations, but no result was found deciding whether a non-ACM line configuration in P^3 can have the stated alpha difference one. | [
{
"url": "https://doi.org/10.1016/j.jpaa.2014.05.033",
"label": "Janssen, fattening of lines in P3"
},
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | Does there exist a non-ACM configuration of lines $L$ in $\mathbb P^3$ whose ideal $I$ satisfies $\alpha(I^{(2)})-\alpha(I)=1$? | Does there exist a non-ACM configuration of lines L in P^3 whose ideal I satisfies \alpha(I^{(2)})-\alpha(I)=1? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,793 | OWR-13494-012 | ACM Line Configurations and Symbolic Initial Degrees | Which configurations of lines in $\mathbb P^3$ are arithmetically Cohen–Macaulay? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | open | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13494-012",
"literature-status:open",
"owr-year:2015"
] | The ACM subcase is classified by the cited theorem, but the existence of a non-ACM line configuration with the stated initial-degree gap remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2014.05.033",
"label": "Janssen, On the fattening of lines in P3"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | Which configurations of lines in $\mathbb P^3$ are arithmetically Cohen–Macaulay? | Which configurations of lines in P^3 are ACM, and which reduced, possibly irreducible, curves C in P^3 satisfy \alpha(I(C)^{(2)})-\alpha(I(C))=1? | corrected_verified | The official report lists the ACM classification question separately from the symbolic-initial-degree question for curves. The latter is represented by OWR-13494-013 and was removed from this clean statement. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,794 | OWR-13494-013 | Curves with Minimal Symbolic Initial-Degree Gap | Which reduced, possibly irreducible, curves $C$ in $\mathbb P^3$ have ideal $I(C)$ satisfying $\alpha(I(C)^{(2)})-\alpha(I(C))=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | open | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13494-013",
"literature-status:open",
"owr-year:2015"
] | Results cover ACM arrangements and special configurations, but no complete classification of all reduced curves in P3 with this symbolic-degree gap is established. | [
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2014.05.033",
"label": "Janssen, On the fattening of lines in P3"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | Which reduced, possibly irreducible, curves $C$ in $\mathbb P^3$ have ideal $I(C)$ satisfying $\alpha(I(C)^{(2)})-\alpha(I(C))=1$? | Which reduced, possibly irreducible, curves C in P^3 have ideal I(C) satisfying \alpha(I(C)^{(2)})-\alpha(I(C))=1? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,795 | OWR-13494-014 | Weak Lefschetz Properties of Complete Intersections | Does every complete-intersection quotient of $k[x_1,\ldots,x_r]$ have the weak Lefschetz property when $r\geq4$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | open | null | 2,015 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13494-014",
"literature-status:open",
"owr-year:2015"
] | The characteristic-zero question for arbitrary Artinian complete intersections in at least four variables remains open; later work treats restricted height-four and equigenerated cases. | [
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2212.09890",
"label": "On the weak Lefschetz property for height four complete intersections"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | Does every complete-intersection quotient of $k[x_1,\ldots,x_r]$ have the weak Lefschetz property when $r\geq4$? | Do all complete-intersection quotients of k[x_1,\ldots,x_r] have the weak Lefschetz property for r\geq4, and what happens for more than r+1 forms? | corrected_verified | The official report states this as one question. The extraction appended a distinct question about more than r+1 generators, whose unrestricted form already has negative examples, so that clause was removed. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,796 | OWR-13494-016 | Lefschetz Elements for Powers of General Linear Forms | For the Cohen–Macaulay codimension-two algebras arising from tangent-space ideals to the variety $X_{n,\lambda}$ of reducible degree-$d$ forms of factorization type $\lambda$, do the Lefschetz elements needed to determine improper intersections always exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | open | null | 2,015 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13494-016",
"literature-status:open",
"owr-year:2015"
] | The relevant secant-variety formula and the assertion that the associated algebras always have enough Lefschetz elements remain conjectural beyond established special cases. | [
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2019.03.014",
"label": "Primary secant-variety result"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | For the Cohen–Macaulay codimension-two algebras arising from tangent-space ideals to the variety $X_{n,\lambda}$ of reducible degree-$d$ forms of factorization type $\lambda$, do the Lefschetz elements needed to determine improper intersections always exist? | In the setting of ideals generated by powers of general linear forms, do the relevant algebras always have enough Lefschetz elements? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,797 | OWR-13494-017 | Genus Thresholds for Curves of Fixed Gonality | Does there exist an affine linear function $f$ such that for every $g\geq f(\gamma)$ there is an algebraic curve over the rational numbers with genus $g$ and gonality $\gamma$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | open | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13494-017",
"literature-status:open",
"owr-year:2015"
] | Roé--Xarles obtain partial construction and descent results, but a single affine-linear threshold guaranteeing every rational genus and gonality pair remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1405.5991",
"label": "Roé and Xarles, curves over Q"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | Does there exist an affine linear function $f$ such that for every $g\geq f(\gamma)$ there is an algebraic curve over the rational numbers with genus $g$ and gonality $\gamma$? | Does there exist an affine linear function f such that for every g\geq f(\gamma) there is an algebraic curve over the rational numbers with genus g and gonality \gamma? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,798 | OWR-13494-019 | Extremal Fat-Point Initial Degrees and Star Configurations | Let $Z$ be a finite set of points in $\mathbb P^n$. If $d=\alpha(nZ)=\alpha(Z)+n-1$, must $Z$ either lie in a hyperplane or be the star configuration from $d$ general hyperplanes, with every degree-$d$ hypersurface vanishing to order $n$ on $Z$ splitting into those hyperplanes? In $(\mathbb P^1)^n$, if $d=\alpha(nZ)=\a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | partially_solved | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1016/j.jpaa.2010.04.010",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved**. T. Szemberg (joint with T. Bauer, S. Di Rocco, E. Guardo and Z. Teitler; OWR 9/2015, p. 526) conjectures (1) that a finite set Z ⊂ Pⁿ with α(nZ) = α(Z) + n − 1 lies in a hyperplane or is a star configuration, and (2) that Z ⊂ (P¹)ⁿ with α(nZ) = α(Z) is... | [
"owr",
"oberwolfach-reports",
"OWR-13494-019",
"literature-status:open",
"owr-year:2015"
] | The star-configuration assertion is proved in dimension three, but the higher-dimensional statement and the multiprojective grid conjecture remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1308.4983",
"label": "Bauer and Szemberg, fattening points"
},
{
"url": "https://doi.org/10.1017/CBO9781107416000.002",
"label": "Cambridge survey chapter"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | Let $Z$ be a finite set of points in $\mathbb P^n$. If $d=\alpha(nZ)=\alpha(Z)+n-1$, must $Z$ either lie in a hyperplane or be the star configuration from $d$ general hyperplanes, with every degree-$d$ hypersurface vanishing to order $n$ on $Z$ splitting into those hyperplanes? In $(\mathbb P^1)^n$, if $d=\alpha(nZ)=\a... | Let Z be a finite set of points in P^n. If d=\alpha(nZ)=\alpha(Z)+n-1, must Z either lie in a hyperplane or be the star configuration from d general hyperplanes, with every degree-d hypersurface vanishing to order n on Z splitting into those hyperplanes? In (P^1)^n, if d=\alpha(nZ)=\alpha(Z), must Z be a d by \cdots by... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,799 | OWR-13494-020 | Ordinary and Symbolic Powers of Point-Set Ideals | Which Cohen–Macaulay point sets $X$ in $\mathbb P^1\times\mathbb P^1$, equivalently line unions in $\mathbb P^3$, satisfy $I(X)^3=I(X)^{(3)}$; and for every positive integer $t$, does there exist an ideal $I_t$ with $I_t^m=I_t^{(m)}$ for $m\leq\operatorname{bight}(I_t)+t-1$ but $I_t^m\ne I_t^{(m)}$ when $m=\operatornam... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532](https://doi.org/10.4171/owr/2015/9)
... | 3 | open | null | 2,015 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13494-020",
"literature-status:open",
"owr-year:2015"
] | For ACM point sets in P1 times P1, equality of symbolic and ordinary powers is characterized through the cubic case, but the requested general geometric characterization and ideal-family threshold remain unsettled. | [
{
"url": "https://doi.org/10.4171/owr/2015/9",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2013.12.007",
"label": "Points fattening on P1 times P1"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/9 | null | null | null | Which Cohen–Macaulay point sets $X$ in $\mathbb P^1\times\mathbb P^1$, equivalently line unions in $\mathbb P^3$, satisfy $I(X)^3=I(X)^{(3)}$; and for every positive integer $t$, does there exist an ideal $I_t$ with $I_t^m=I_t^{(m)}$ for $m\leq\operatorname{bight}(I_t)+t-1$ but $I_t^m\ne I_t^{(m)}$ when $m=\operatornam... | Which Cohen--Macaulay point sets X in P^1\times P^1, equivalently line unions in P^3, satisfy I(X)^3=I(X)^{(3)}; and for every positive integer t, does there exist an ideal I_t with I_t^m=I_t^{(m)} for m\leq\operatorname{bight}(I_t)+t-1 but I_t^m\ne I_t^{(m)} when m=\operatorname{bight}(I_t)+t? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/9, pp. 489--532 |
30,002,800 | OWR-13495-001 | Hopf Algebra Extensions and Their Conformal Field Theories | Classify all extensions $u\longrightarrow H\longrightarrow U(\mathfrak g'')$ of finite-dimensional pointed Hopf algebras $u$ by universal enveloping algebras, and determine the corresponding conformal field theories. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Coideal Subalgebras of Quantum Groups (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/10, pp. 533--569](https://doi.org/10.4171/owr/2015/10)
## Literature review (checked ... | 3 | open | null | 2,015 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13495-001",
"literature-status:open",
"owr-year:2015"
] | Classification exists for important restricted families of pointed Hopf algebras, but no general classification of all requested extensions and corresponding CFTs is available. | [
{
"url": "https://doi.org/10.4171/owr/2015/10",
"label": "Oberwolfach report"
},
{
"url": "https://annals.math.princeton.edu/2010/171-1/p07",
"label": "Andruskiewitsch and Schneider"
},
{
"url": "https://doi.org/10.1016/j.aim.2015.05.009",
"label": "Wang, connected Hopf algebras"
}... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/10 | null | null | null | Classify all extensions $u\longrightarrow H\longrightarrow U(\mathfrak g'')$ of finite-dimensional pointed Hopf algebras $u$ by universal enveloping algebras, and determine the corresponding conformal field theories. | Classify all extensions of finite-dimensional pointed Hopf algebras by universal enveloping algebras, u\longrightarrow H\longrightarrow U(g''), and determine the corresponding conformal field theories. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Coideal Subalgebras of Quantum Groups (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/10, pp. 533--569 |
30,002,801 | OWR-13495-002 | Construction of K-Matrices for Coideal Subalgebras | Develop a general method for constructing rational and trigonometric $K$-matrices satisfying the matrix reflection equations associated with twisted Yangians and quantum-symmetric-pair coideal subalgebras. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Coideal Subalgebras of Quantum Groups (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/10, pp. 533--569](https://doi.org/10.4171/owr/2015/10)
## Literature review (checked ... | 3 | partially_solved | null | 2,015 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://arxiv.org/abs/1602.08471",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved** (trigonometric case). V. Regelskis (joint with B. Vlaar; OWR 10/2015, p. 555) notes that no universal method is known for finding general solutions of the reflection equations of twisted Yangians (rational K-matrices), and outlines one for trigonometric... | [
"owr",
"oberwolfach-reports",
"OWR-13495-002",
"literature-status:open",
"owr-year:2015"
] | Explicit K-matrices are known for quantum symmetric pairs and several affine classical types, but a general construction or classification of all solutions remains open. | [
{
"url": "https://doi.org/10.4171/owr/2015/10",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1602.08471",
"label": "Regelskis and Vlaar, reflection matrices"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2026.108210",
"label": "Recent K-matrix classification"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/10 | null | null | null | Develop a general method for constructing rational and trigonometric $K$-matrices satisfying the matrix reflection equations associated with twisted Yangians and quantum-symmetric-pair coideal subalgebras. | How can one construct K-matrices K(u) satisfying the relevant reflection equations in the coideal-subalgebra setting? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Coideal Subalgebras of Quantum Groups (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/10, pp. 533--569 |
30,002,802 | OWR-13495-003 | Quantum-Group and Affine-Hecke Solutions of Boundary qKZ Equations | Determine the relation between the special boundary quantum Knizhnik–Zamolodchikov solutions obtained as quantum correlation functions or $q$-integrals and the affine-Hecke-algebra basis characterized by its asymptotics in a Weyl chamber. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Coideal Subalgebras of Quantum Groups (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/10, pp. 533--569](https://doi.org/10.4171/owr/2015/10)
## Literature review (checked ... | 3 | open | null | 2,015 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13495-003",
"literature-status:open",
"owr-year:2015"
] | The relation between quantum-group correlation or integral solutions and affine-Hecke asymptotic solution bases for qKZ equations still lacks a general theorem. | [
{
"url": "https://doi.org/10.4171/owr/2015/10",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/10 | null | null | null | Determine the relation between the special boundary quantum Knizhnik–Zamolodchikov solutions obtained as quantum correlation functions or $q$-integrals and the affine-Hecke-algebra basis characterized by its asymptotics in a Weyl chamber. | What is the relation among the different types of K-matrix solutions in the coideal-subalgebra and quantum-group setting? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Coideal Subalgebras of Quantum Groups (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/10, pp. 533--569 |
30,002,803 | OWR-13496-001 | Analytic Structures for Nonformal Deformation Quantization | What are the essential ingredients of a non-formal deformation quantization, including the associated Hilbert-algebra or von Neumann-algebra structure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Deformation quantization: between formal to strict (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/11, pp. 571--595](https://doi.org/10.4171/owr/2015/11)
## Literature rev... | 3 | partially_solved | null | 2,015 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13496-001",
"literature-status:partially-solved",
"owr-year:2015"
] | Rieffel's strict framework supplies the core ingredients of a non-formal deformation quantization, while a universal existence criterion and canonical smooth subalgebra are not known. | [
{
"url": "https://doi.org/10.4171/owr/2015/11",
"label": "Oberwolfach report"
},
{
"url": "https://math.berkeley.edu/~rieffel/papers/quantization.pdf",
"label": "Rieffel, Quantization and C*-algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/11 | null | null | null | What are the essential ingredients of a non-formal deformation quantization, including the associated Hilbert-algebra or von Neumann-algebra structure? | What are the essential ingredients of a non-formal deformation quantization, including the associated Hilbert-algebra or von Neumann-algebra structure? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Deformation quantization: between formal to strict (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/11, pp. 571--595 |
30,002,804 | OWR-13497-001 | Duplicate Four-Agent Formation-Control Heading | Does a four-vehicle formation-control system have global convergence to a formation shape? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659](https://doi.org/10.4171/owr/2015/12)
## Literature ... | 3 | open | null | 2,015 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report poses a specific saddle-point question for incorrect equilibria, represented by OWR-13497-006. This broad heading-level ) | [
"OWR-13497-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13497-001",
"literature-status:open",
"owr-year:2015"
] | The record is a contents-list fragment naming several open problems and contains no single mathematical claim that can be resolved. | [
{
"url": "https://doi.org/10.4171/owr/2015/12",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/12 | null | null | null | null | Does a four-vehicle formation-control system have global convergence to a formation shape? | unrecoverable | The official report poses a specific saddle-point question for incorrect equilibria, represented by OWR-13497-006. This broad heading-level extraction does not state an additional mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659 |
30,002,805 | OWR-13497-002 | Expository Packet-Scheduling and Traffic-Control Results | For packets sent at discrete times over an unreliable medium, with node i succeeding independently with probability p_i and requiring throughput q_i per unit time, characterize exactly which tuples (p_i,q_i)_{i=1}^{N} and deadline period T are feasible. For the associated autonomous-traffic system of communicating unic... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659](https://doi.org/10.4171/owr/2015/12)
## Literature ... | 3 | partially_solved | null | 2,015 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report presents two illustrative cyber-physical-systems results, not unresolved problems: it says a sharp characterization of f) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13497-002",
"literature-status:partially-solved",
"owr-year:2015"
] | The communication subproblem receives a sharp feasibility characterization, and provably safe control laws exist for restricted roadway and intersection models, but the combined general feasibility and control question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2015/12",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1605.00604",
"label": "Mitsch, Ghorbal, Vogelbacher and Platzer"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/12 | null | null | null | null | For packets sent at discrete times over an unreliable medium, with node i succeeding independently with probability p_i and requiring throughput q_i per unit time, characterize exactly which tuples (p_i,q_i)_{i=1}^{N} and deadline period T are feasible. For the associated autonomous-traffic system of communicating unic... | unrecoverable | The official report presents two illustrative cyber-physical-systems results, not unresolved problems: it says a sharp characterization of feasible packet-throughput tuples is provided and that provably safe traffic-control laws are developed. The extraction joins their motivating questions into one purported open prob... | null | null | null | null | null | Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659 |
30,002,806 | OWR-13497-003 | Commutation of Variational Discretization and Optimal Control | For general classes of variational integrators used to discretize controlled Euler–Lagrange systems and their optimal-control problems, determine whether discretization and optimization commute, i.e. whether the discrete adjoint and optimality conditions have the same approximation order as the variational state discre... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659](https://doi.org/10.4171/owr/2015/12)
## Literature ... | 3 | open | null | 2,015 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13497-003",
"literature-status:open",
"owr-year:2015"
] | Commutation of discretization and dualization is proved for symplectic Runge--Kutta and symplectic Galerkin subclasses, but remains open for general variational integrators. | [
{
"url": "https://doi.org/10.4171/owr/2015/12",
"label": "Oberwolfach report"
},
{
"url": "https://www.ljll.fr/~trelat/fichiers/CamposOberBlobaumTrelat_DCDS2015.pdf",
"label": "Campos, Ober-Blaubaum and Trelat"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/12 | null | null | null | For general classes of variational integrators used to discretize controlled Euler–Lagrange systems and their optimal-control problems, determine whether discretization and optimization commute, i.e. whether the discrete adjoint and optimality conditions have the same approximation order as the variational state discre... | For general classes of variational integrators used to discretize controlled Euler--Lagrange systems and their optimal-control problems, determine whether discretization and optimization commute, i.e. whether the discrete adjoint and optimality conditions have the same approximation order as the variational state discr... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659 |
30,002,807 | OWR-13497-004 | Inferred Stronger Four-Agent Formation Claim | For four point agents p=[p_1,p_2,p_3,p_4]^\top\in\mathbb{R}^{8} in the plane, governed by \dot p_i=\sum_{j\ne i}e_{ij}(p_j-p_i) with e_{ij}=\lVert p_i-p_j\rVert^2-\bar d_{ij}^{ 2}, prove global convergence to the desired formation when the target is a nonrectangular quadrilateral or a triangle with an interior agent, a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659](https://doi.org/10.4171/owr/2015/12)
## Literature ... | 3 | open | null | 2,015 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report asks whether incorrect equilibria are saddle points; it does not pose this stronger global-convergence assertion as a se) | [
"OWR-13497-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13497-004",
"literature-status:open",
"owr-year:2015"
] | Almost-global convergence is established for rectangular four-agent formations under stated conditions, but the extension to general quadrilaterals or a triangle with an interior agent remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2015/12",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1109/CDC.2009.5399780",
"label": "Summers, Yu, Anderson and Dasgupta"
},
{
"url": "https://openresearch-repository.anu.edu.au/bitstream/1885/198778/6/201704\\%20Kn\\%20formation\... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/12 | null | null | null | null | For four point agents p=[p_1,p_2,p_3,p_4]^\top\in\mathbb{R}^{8} in the plane, governed by \dot p_i=\sum_{j\ne i}e_{ij}(p_j-p_i) with e_{ij}=\lVert p_i-p_j\rVert^2-\bar d_{ij}^{ 2}, prove global convergence to the desired formation when the target is a nonrectangular quadrilateral or a triangle with an interior agent, a... | unrecoverable | The official report asks whether incorrect equilibria are saddle points; it does not pose this stronger global-convergence assertion as a separate problem. The source-backed question is represented by OWR-13497-006. No separate clean statement is promoted; the original record remains publicly visible and retained for p... | null | null | null | null | null | Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659 |
30,002,808 | OWR-13497-005 | Duplicate General Four-Agent Formation Question | For the four-agent distance-based formation-control law \dot p_i=\sum_{j\ne i}e_{ij}(p_j-p_i), do the attractive convergence properties known for rectangular desired formations continue to hold globally for a general quadrilateral or for three agents forming a triangle with the fourth inside it? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659](https://doi.org/10.4171/owr/2015/12)
## Literature ... | 3 | open | null | 2,015 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This is a broad restatement of the same-report question represented precisely by OWR-13497-006, rather than a separate mathematical problem.) | [
"OWR-13497-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13497-005",
"literature-status:open",
"owr-year:2015"
] | The extracted record repeats the four-agent global-convergence question; rectangular cases have partial results, while the stated nonrectangular extension remains open. | [
{
"url": "https://doi.org/10.4171/owr/2015/12",
"label": "Oberwolfach report"
},
{
"url": "https://openresearch-repository.anu.edu.au/bitstream/1885/198778/6/201704\\%20Kn\\%20formation\\%20TAC.pdf",
"label": "Later K4 formation analysis"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/12 | null | null | null | null | For the four-agent distance-based formation-control law \dot p_i=\sum_{j\ne i}e_{ij}(p_j-p_i), do the attractive convergence properties known for rectangular desired formations continue to hold globally for a general quadrilateral or for three agents forming a triangle with the fourth inside it? | unrecoverable | This is a broad restatement of the same-report question represented precisely by OWR-13497-006, rather than a separate mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659 |
30,002,809 | OWR-13497-006 | Saddle Structure of Incorrect Formation Equilibria | Let four point agents $p_i\in\mathbb R^2$ obey
$$\dot p_i=\sum_{j\neq i}e_{ij}(p_j-p_i),\qquad e_{ij}=\lVert p_i-p_j\rVert^2-\bar d_{ij}^{2}.$$
When the desired shape is a general quadrilateral, or a triangle with the fourth agent in its interior, is every equilibrium with some $e_{ij}\neq0$ a saddle point? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659](https://doi.org/10.4171/owr/2015/12)
## Literature ... | 3 | open | null | 2,015 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-13497-001",
"OWR-13497-004",
"OWR-13497-005"
] | {
"source_url": "https://zenodo.org/records/23072208",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **All Incorrect Equilibria of the Planar Four-Agent Formation Law Are Unstable** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23072208) | [
"owr",
"oberwolfach-reports",
"OWR-13497-006",
"literature-status:open",
"owr-year:2015"
] | Known analyses show incorrect rectangular equilibria are saddles, but no general proof covers every incorrect equilibrium for the quadrilateral and triangle-with-interior-agent shapes in the record. | [
{
"url": "https://doi.org/10.4171/owr/2015/12",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1307.2089",
"label": "Summers, Yu, Dasgupta and Anderson"
},
{
"url": "https://openresearch-repository.anu.edu.au/bitstream/1885/198778/6/201704\\%20Kn\\%20formation\\%20TAC.p... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/12 | null | null | null | Let four point agents $p_i\in\mathbb R^2$ obey
$$\dot p_i=\sum_{j\neq i}e_{ij}(p_j-p_i),\qquad e_{ij}=\lVert p_i-p_j\rVert^2-\bar d_{ij}^{2}.$$
When the desired shape is a general quadrilateral, or a triangle with the fourth agent in its interior, is every equilibrium with some $e_{ij}\neq0$ a saddle point? | For the distance-based four-agent formation-control law \dot p_i=\sum_{j\ne i}e_{ij}(p_j-p_i), where e_{ij}=d_{ij}^{2}-\bar d_{ij}^{2}, and a desired shape that is a general quadrilateral or a triangle with an interior agent, are all incorrect equilibria saddle points? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659 |
30,002,810 | OWR-13497-007 | Formal Languages for Hybrid-System Control | Specify suitable formal languages, analogous to finite-state languages defined by accepting states, for controlling hybrid systems whose inputs combine a continuous control function $u$ on a finite interval with a symbol string $v$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659](https://doi.org/10.4171/owr/2015/12)
## Literature ... | 3 | open | null | 2,015 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13497-007",
"literature-status:open",
"owr-year:2015"
] | Many hybrid-system languages and compositional semantics now exist, but no generally accepted language framework fully resolves the specification problem posed in the record. | [
{
"url": "https://doi.org/10.4171/owr/2015/12",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.ic.2024.105189",
"label": "A computable and compositional semantics for hybrid systems"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/12 | null | null | null | Specify suitable formal languages, analogous to finite-state languages defined by accepting states, for controlling hybrid systems whose inputs combine a continuous control function $u$ on a finite interval with a symbol string $v$. | Specify suitable formal languages, analogous to finite-state languages defined by accepting states, for controlling hybrid systems whose inputs combine a continuous control function u on a finite interval with a symbol string v. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659 |
30,002,811 | OWR-13497-008 | Turnpike Properties as Criteria for Strict Dissipativity | For the discrete-time optimal-control problem $x(k+1)=f(x(k),u(k))$ with stage cost $\ell(x,u)$, under which assumptions does the turnpike property imply strict dissipativity? Here strict dissipativity means that for some equilibrium $(x_e,u_e)$, storage function $\lambda$, and $\rho\in\mathcal K_\infty$, one has $\ell... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659](https://doi.org/10.4171/owr/2015/12)
## Literature ... | 3 | partially_solved | null | 2,015 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13497-008",
"literature-status:partially-solved",
"owr-year:2015"
] | Under controllability and structural assumptions, strict dissipativity and several turnpike variants are equivalent, but a converse theorem under minimal general assumptions remains unavailable. | [
{
"url": "https://doi.org/10.4171/owr/2015/12",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.sysconle.2016.01.003",
"label": "Grune and Muller, strict dissipativity"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/12 | null | null | null | For the discrete-time optimal-control problem $x(k+1)=f(x(k),u(k))$ with stage cost $\ell(x,u)$, under which assumptions does the turnpike property imply strict dissipativity? Here strict dissipativity means that for some equilibrium $(x_e,u_e)$, storage function $\lambda$, and $\rho\in\mathcal K_\infty$, one has $\ell... | For the discrete-time optimal-control problem x(k+1)=f(x(k),u(k)) with stage cost \ell(x,u), under which assumptions does the turnpike property imply strict dissipativity? Here strict dissipativity means that for some equilibrium (x_e,u_e), storage function \lambda, and \rho\in\mathcal K_\infty, one has \ell(x,u)-\ell(... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659 |
30,002,812 | OWR-13497-010 | Finite Fourier Feedback for Driftless-System Stabilization | For a driftless control-affine system $\dot x=\sum_{j=1}^{m}u_jf_j(x)$ on $D\subset\mathbb R^n$ satisfying $\operatorname{Lie}_{x=0}\{f_j:1\leq j\leq m\}=\mathbb R^n$, can one construct a finite trigonometric time-varying feedback $u_j=\sum_{k=-N}^{N}v_{kj}(x)e^{i\omega kt}$ whose closed-loop trivial solution is asympt... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659](https://doi.org/10.4171/owr/2015/12)
## Literature ... | 3 | partially_solved | null | 2,015 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13497-010",
"literature-status:partially-solved",
"owr-year:2015"
] | Explicit time-varying trigonometric-polynomial stabilizers are proved for driftless systems and selected drift systems under finite Lie-bracket rank conditions, but not for arbitrary controllable nonlinear systems. | [
{
"url": "https://doi.org/10.4171/owr/2015/12",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1137/140999955",
"label": "Zuyev, exponential stabilization"
},
{
"url": "https://arxiv.org/abs/1904.10219",
"label": "Zuyev and Grushkovskaya, systems with drift"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/12 | null | null | null | For a driftless control-affine system $\dot x=\sum_{j=1}^{m}u_jf_j(x)$ on $D\subset\mathbb R^n$ satisfying $\operatorname{Lie}_{x=0}\{f_j:1\leq j\leq m\}=\mathbb R^n$, can one construct a finite trigonometric time-varying feedback $u_j=\sum_{k=-N}^{N}v_{kj}(x)e^{i\omega kt}$ whose closed-loop trivial solution is asympt... | For a driftless control-affine system \dot x=\sum_{j=1}^{m}u_jf_j(x) on D\subset\mathbb R^n satisfying \operatorname{Lie}_{x=0}\{f_j:1\leq j\leq m\}=\mathbb R^n, can one construct a finite trigonometric time-varying feedback u_j=\sum_{k=-N}^{N}v_{kj}(x)e^{i\omega kt} whose closed-loop trivial solution is asymptotically... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659 |
30,002,813 | OWR-13497-011 | Trigonometric-Polynomial Feedback for Nonlinear Stabilization | Let $\dot x=f(x,u)$ be smooth near $(x,u)=(0,0)$ with $f(0,0)=0$. Assume the Lie algebra rank condition holds at the origin, the origin is locally continuously reachable in arbitrarily small time, and the state dimension is not $2$ or $3$. Can one construct a stabilizing feedback $u=k(x,t)$ that is a trigonometric poly... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659](https://doi.org/10.4171/owr/2015/12)
## Literature ... | 3 | open | null | 2,015 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13497-011",
"literature-status:open",
"owr-year:2015"
] | The extracted record does not state a complete claim; available constructive feedback laws cover restricted controllability classes, not the general trigonometric-polynomial stabilization question. | [
{
"url": "https://doi.org/10.4171/owr/2015/12",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1904.10219",
"label": "Zuyev and Grushkovskaya, systems with drift"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/12 | null | null | null | Let $\dot x=f(x,u)$ be smooth near $(x,u)=(0,0)$ with $f(0,0)=0$. Assume the Lie algebra rank condition holds at the origin, the origin is locally continuously reachable in arbitrarily small time, and the state dimension is not $2$ or $3$. Can one construct a stabilizing feedback $u=k(x,t)$ that is a trigonometric poly... | Under Coron's hypotheses for a controllable nonlinear system \dot x=f(x,u), can a stabilizing controller u=k(x,t) always be constructed as a trigonometric polynomial in t with coefficients depending on x? In the driftless case, this asks for the finite Fourier feedback and asymptotic stability specified in the report. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Control Theory: A Mathematical Perspective on Cyber-Physical Systems (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/12, pp. 597--659 |
30,002,814 | OWR-13498-002 | Discrete Riemann Mapping by Conformal Triangulations | Discrete Riemann mapping conjecture: let $\Omega$ be a Jordan domain with distinct boundary points $p,q,r$. For each $\varepsilon>0$, triangulate a maximal simply connected $\Omega_\varepsilon\subset\Omega$ by equilateral triangles of edge length $\varepsilon$, choose boundary vertices $p_\varepsilon,q_\varepsilon,r_\v... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729](https://doi.org/10.4171/owr/2015/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13498-002",
"literature-status:open",
"owr-year:2015"
] | The stated convergence conjecture for the discrete-conformal metric doubles of Jordan domains remains without a proof or counterexample in the checked primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2015/13",
"label": "OWR Report 13/2015"
},
{
"url": "https://arxiv.org/abs/1005.2698",
"label": "Bobenko--Pinkall--Springborn"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/13 | null | null | null | Discrete Riemann mapping conjecture: let $\Omega$ be a Jordan domain with distinct boundary points $p,q,r$. For each $\varepsilon>0$, triangulate a maximal simply connected $\Omega_\varepsilon\subset\Omega$ by equilateral triangles of edge length $\varepsilon$, choose boundary vertices $p_\varepsilon,q_\varepsilon,r_\v... | Discrete Riemann mapping conjecture: let \Omega be a Jordan domain with distinct boundary points p,q,r. For each \varepsilon>0, triangulate a maximal simply connected \Omega_\varepsilon\subset\Omega by equilateral triangles of edge length \varepsilon, choose boundary vertices p_\varepsilon,q_\varepsilon,r_\varepsilon w... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729 |
30,002,815 | OWR-13498-003 | Rigid Miura Tessellations Approximating Curved Surfaces | Given an arbitrary surface with intrinsic curvature, does there exist a Miura-like tessellation of the plane whose folded realization approximates that surface, and can the tessellation be made rigidly foldable with one degree of freedom? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729](https://doi.org/10.4171/owr/2015/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,015 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13498-003",
"literature-status:partially-solved",
"owr-year:2015"
] | Origami constructions approximate broad classes of curved surfaces, but a universal Miura-like approximation with a rigid one-degree-of-freedom folding mechanism is not established; positive Gaussian curvature has known rigidity obstructions. | [
{
"url": "https://doi.org/10.4171/owr/2015/13",
"label": "OWR Report 13/2015"
},
{
"url": "https://doi.org/10.1038/s41378-021-00319-1",
"label": "Curved display based on origami tessellations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/13 | null | null | null | Given an arbitrary surface with intrinsic curvature, does there exist a Miura-like tessellation of the plane whose folded realization approximates that surface, and can the tessellation be made rigidly foldable with one degree of freedom? | Given an arbitrary surface with intrinsic curvature, does there exist a Miura-like tessellation of the plane whose folded realization approximates that surface, and can the tessellation be made rigidly foldable with one degree of freedom? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729 |
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