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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,002,216 | OWR-12175-005 | Kadison–Kastler Conjecture for Separable $C^*$-Algebras | For a separable Hilbert space $H$, does there exist $\delta>0$ such that every pair of separable $C^*$-algebras $A,B\subset B(H)$ with $d(A,B)<\delta$ are spatially isomorphic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 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-12175-006"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12175-005",
"literature-status:partially-solved",
"owr-year:2012"
] | The Kadison--Kastler conjecture is proved for injective von Neumann algebras and several further classes of factors, but the general assertion for close von Neumann algebras remains unresolved. | [
{
"url": "https://arxiv.org/abs/1209.4116",
"label": "Kadison--Kastler stable factors"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC3528588/",
"label": "spatial-isomorphism status"
},
{
"url": "https://doi.org/10.4171/owr/2012/52",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | For a separable Hilbert space $H$, does there exist $\delta>0$ such that every pair of separable $C^*$-algebras $A,B\subset B(H)$ with $d(A,B)<\delta$ are spatially isomorphic? | For a separable Hilbert space H, does there exist \delta>0 such that every pair of separable C^{*}-algebras A,B\subset B(H) with uniform distance d(A,B)<\delta are spatially isomorphic? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,217 | OWR-12175-006 | Duplicate: Kadison–Kastler Conjecture for $C^*$-Algebras | Does there exist \delta>0 such that every pair of separable C^{*}-algebras A,B\subset B(H) with d(A,B)<\delta are spatially isomorphic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 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 | null | Duplicate/merged OWR extraction (Comparison with the official report and OWR-12175-005 confirms that this is a shortened repeat of the same conjecture. No separate clean sta) | [
"OWR-12175-005"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12175-006",
"literature-status:partially-solved",
"owr-year:2012"
] | Sufficiently close separable C-star algebras are spatially isomorphic when one is nuclear, with further positive results for AF and continuous-trace classes; the unrestricted pair of separable algebras remains unresolved and has no known separable counterexample. | [
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC2818932/",
"label": "close separable nuclear C-star algebras"
},
{
"url": "https://doi.org/10.4171/owr/2012/52",
"label": "original OWR question"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | null | Does there exist \delta>0 such that every pair of separable C^{*}-algebras A,B\subset B(H) with d(A,B)<\delta are spatially isomorphic? | unrecoverable | Comparison with the official report and OWR-12175-005 confirms that this is a shortened repeat of the same conjecture. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,218 | OWR-12175-007 | Perturbation Stability of Jiang–Su Absorption for $C^*$-Algebras | Does there exist $\delta>0$ such that, if a separable $C^*$-algebra $A$ absorbs the Jiang–Su algebra tensorially, $A\cong A\otimes\mathcal Z$, and $d(A,B)<\delta$, then $B\cong B\otimes\mathcal Z$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 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-12175-007",
"literature-status:partially-solved",
"owr-year:2012"
] | Close algebras preserve embeddings of strongly self-absorbing algebras in near-inclusion results and preserve Cuntz-semigroup data under complete closeness, but preservation of Z-stability itself is still not proved in the stated generality. | [
{
"url": "https://arxiv.org/abs/0910.4953",
"label": "perturbations of nuclear C-star algebras"
},
{
"url": "https://arxiv.org/abs/1210.4533",
"label": "Cuntz semigroup stability under closeness"
},
{
"url": "https://doi.org/10.4171/owr/2012/52",
"label": "original OWR question"
}
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | Does there exist $\delta>0$ such that, if a separable $C^*$-algebra $A$ absorbs the Jiang–Su algebra tensorially, $A\cong A\otimes\mathcal Z$, and $d(A,B)<\delta$, then $B\cong B\otimes\mathcal Z$? | Does there exist \delta>0 such that if a separable C^{*}-algebra A absorbs the Jiang--Su algebra tensorially, A\cong A\otimes\mathcal{Z}, and d(A,B)<\delta, then B\cong B\otimes\mathcal{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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,219 | OWR-12175-008 | Generator Rank of Direct Sums | Given separable $C^*$-algebras $A$ and $B$, is $\operatorname{gr}(A\oplus B)=\max\{\operatorname{gr}(A),\operatorname{gr}(B)\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 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-12175-008",
"literature-status:partially-solved",
"owr-year:2012"
] | The direct-sum formula for generator rank is proved for commutative, real-rank-zero, and subhomogeneous summands, but the formula for arbitrary separable C-star algebras is still unclear. | [
{
"url": "https://doi.org/10.1016/j.jfa.2020.108874",
"label": "generator rank of C-star algebras"
},
{
"url": "https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/generator-rank-of-subhomogeneous-calgebras/976DD3CC21BFD2F7688383FC08C8EE9C",
"label": "subhomogeneous d... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | Given separable $C^*$-algebras $A$ and $B$, is $\operatorname{gr}(A\oplus B)=\max\{\operatorname{gr}(A),\operatorname{gr}(B)\}$? | Given separable C*-algebras A and B, is \operatorname{gr}(A\oplus B)=\max\{\operatorname{gr}(A),\operatorname{gr}(B)\}? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,220 | OWR-12175-009 | Generator Rank of $\mathcal Z$-Stable $C^*$-Algebras | If $A$ is unital and separable and absorbs the Jiang–Su algebra $\mathcal Z$, or is unital, separable, nuclear, of real rank zero, and of stable rank one, must $\operatorname{gr}(A)\leq1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 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-12175-009",
"literature-status:partially-solved",
"owr-year:2012"
] | Dense single generators are known for important Z-stable subclasses, including classifiable algebras with real rank zero and Z-stable approximately subhomogeneous algebras, but generator rank at most one for every algebra in the stated generality remains open. | [
{
"url": "https://arxiv.org/abs/2006.08404",
"label": "generators in Z-stable real-rank-zero algebras"
},
{
"url": "https://arxiv.org/abs/2006.03624",
"label": "generator rank of subhomogeneous algebras"
},
{
"url": "https://doi.org/10.4171/owr/2012/52",
"label": "original OWR proble... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | If $A$ is unital and separable and absorbs the Jiang–Su algebra $\mathcal Z$, or is unital, separable, nuclear, of real rank zero, and of stable rank one, must $\operatorname{gr}(A)\leq1$? | If A is unital and separable and absorbs the Jiang-Su algebra Z, or is unital, separable, nuclear, of real rank zero and stable rank one, must \operatorname{gr}(A)\leq 1? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,221 | OWR-12175-010 | Classification Complexity of Unitary Equivalence | For a separable $C^*$-algebra $A$ with nonsmooth unitary-equivalence relation $E_A^{\mathrm{u.e.}}$, is $E_A^{\mathrm{u.e.}}$ nonclassifiable by countable structures? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,012 | 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-12175-010",
"literature-status:open",
"owr-year:2012"
] | The isolated symbol E_A is undefined in the extracted record; related unitary-equivalence results settle non-classifiability for non-continuous-trace algebras and smoothness in a unital continuous-trace case, but the intended general assertion cannot be verified. | [
{
"url": "https://doi.org/10.4171/owr/2012/52",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1304.3502",
"label": "unitary equivalence of automorphisms"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | For a separable $C^*$-algebra $A$ with nonsmooth unitary-equivalence relation $E_A^{\mathrm{u.e.}}$, is $E_A^{\mathrm{u.e.}}$ nonclassifiable by countable structures? | For a separable C*-algebra A with non-smooth unitary-equivalence relation E_A^{\mathrm{u.e.}}, is E_A^{\mathrm{u.e.}} non-classifiable by countable structures? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,222 | OWR-12175-012 | Metric Mean Dimension for Amenable Group Actions | For a continuous action of a countable amenable group on a compact metrizable space, is mean topological dimension equal to the minimum metric mean dimension over all compatible metrics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 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-12175-012",
"literature-status:partially-solved",
"owr-year:2012"
] | The dynamical Pontryagin--Schnirelmann equality is proved for algebraic actions of amenable groups and for several Z-actions with marker or minimal-factor hypotheses, but the general continuous amenable action question remains open. | [
{
"url": "https://arxiv.org/abs/1307.5471",
"label": "mean dimension for algebraic actions"
},
{
"url": "https://doi.org/10.1007/BF02698858",
"label": "mean dimension and minimal factors"
},
{
"url": "https://doi.org/10.4171/owr/2012/52",
"label": "original OWR question"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | For a continuous action of a countable amenable group on a compact metrizable space, is mean topological dimension equal to the minimum metric mean dimension over all compatible metrics? | For a continuous action of a countable amenable group on a compact metrizable space, is mean topological dimension equal to the minimum metric mean dimension over all compatible metrics? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,223 | OWR-12175-015 | Extensions of Graph $C^*$-Algebras | If $I$ and $A/I$ are graph $C^*$-algebras, when is $A$ a graph $C^*$-algebra, and can the obstructions be described using $K$-theoretic data? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 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-12175-015",
"literature-status:partially-solved",
"owr-year:2012"
] | The broad extension question is not fully settled, but a complete K-theoretical criterion is known for essential extensions of two simple graph C^*-algebras; earlier results cover further restricted classes. | [
{
"url": "https://doi.org/10.2140/akt.2020.5.295",
"label": "Eilers--Gabe--Katsura--Ruiz--Tomforde, extension problem"
},
{
"url": "https://arxiv.org/abs/1106.1551",
"label": "Eilers--Restorff--Ruiz, ordered K-theory of extensions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | If $I$ and $A/I$ are graph $C^*$-algebras, when is $A$ a graph $C^*$-algebra, and can the obstructions be described using $K$-theoretic data? | If I and A/I are graph C*-algebras, when is A a graph C*-algebra, and can the obstructions be described using K-theoretic data? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,224 | OWR-12175-018 | $K$-Theory of Easy Quantum Group $C^*$-Algebras | What is the $K$-theory of the $C^*$-algebras associated with easy quantum groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,012 | 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-12175-018",
"literature-status:open",
"owr-year:2012"
] | Important subclasses have computable K-theory, including free quantum groups and fixed-point algebras, but the general K-theory of the C^*-algebras of easy quantum groups remains unresolved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3323/OWR_2012_52.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach report, original open problem"
},
{
"url": "https://doi.org/10.1007/s00208-013-0902-9",
"label": "Vergnioux--Voigt, K-theory of free quantum groups"
},
{
"url": ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | What is the $K$-theory of the $C^*$-algebras associated with easy quantum groups? | What is the K-theory of the C*-algebras associated with easy quantum groups, in general? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,225 | OWR-12175-020 | Trace-Cone Classification after Razak–Jacelon Stabilization | For separable nuclear $C^*$-algebras $A$ and $B$, does $T(A)\cong T(B)$ if and only if $A\otimes\mathcal W\otimes\mathcal K\cong B\otimes\mathcal W\otimes\mathcal K$, assuming the trace-cone isomorphism is a linear homeomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,012 | 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-12175-020",
"literature-status:open",
"owr-year:2012"
] | Robert's trace-cone classification conjecture remains open in full generality; positive cases include AF and O_2-absorbing algebras, with reductions for direct limits of homogeneous algebras. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3323/OWR_2012_52.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach report, Robert conjecture"
},
{
"url": "https://arxiv.org/abs/1211.7159",
"label": "Santiago, reduction of nuclear dimension"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | For separable nuclear $C^*$-algebras $A$ and $B$, does $T(A)\cong T(B)$ if and only if $A\otimes\mathcal W\otimes\mathcal K\cong B\otimes\mathcal W\otimes\mathcal K$, assuming the trace-cone isomorphism is a linear homeomorphism? | For separable nuclear C*-algebras A and B, does T(A)\cong T(B) if and only if A\otimes W\otimes K\cong B\otimes W\otimes K, assuming the trace-cone isomorphism is a linear homeomorphism? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,226 | OWR-12175-021 | Z-Stability of Elliott Classification Counterexamples | Are all nonelementary counterexamples to the Elliott classification conjecture $C^*$-algebras that do not absorb the Jiang–Su algebra $\mathcal Z$? Equivalently, for every such unital algebra $A$, does $\mathcal Z$ fail to embed unitally into $A_\omega\cap A'$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,012 | 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-12175-021",
"literature-status:open",
"owr-year:2012"
] | The record is a contextual assertion about known Elliott counterexamples rather than a precise theorem; the universal claim that every counterexample is non-Z-stable is not established in this form. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3323/OWR_2012_52.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach report, original assertion"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | Are all nonelementary counterexamples to the Elliott classification conjecture $C^*$-algebras that do not absorb the Jiang–Su algebra $\mathcal Z$? Equivalently, for every such unital algebra $A$, does $\mathcal Z$ fail to embed unitally into $A_\omega\cap A'$? | Conjecture: all non-elementary counterexamples to the Elliott classification conjecture are C*-algebras that do not absorb the Jiang-Su algebra Z; equivalently, Z does not embed unitally into A_\omega\cap A' for each such unital A. | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,227 | OWR-12175-022 | Central Sequence Invariants for $C^*$-Algebra Classification | Does the invariant $F(A)$ contain all technical information needed to decide whether $A$ is classifiable, together with information about its class? Do the $K$-groups of $F_{\mathrm{cont}}(A)$ determine the $KK$-equivalence class of $A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,012 | 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-12175-022",
"literature-status:open",
"owr-year:2012"
] | The proposed completeness of F(A) and F-cont(A) is stated as a conjecture; known structural facts do not prove that these invariants decide classification or KK-equivalence. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3323/OWR_2012_52.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach report, Conjecture 2"
},
{
"url": "https://arxiv.org/abs/1209.5311",
"label": "Kirchberg--Rordam, central sequence algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | Does the invariant $F(A)$ contain all technical information needed to decide whether $A$ is classifiable, together with information about its class? Do the $K$-groups of $F_{\mathrm{cont}}(A)$ determine the $KK$-equivalence class of $A$? | Conjecture: the invariant F(A) contains all technical information needed to decide whether A is classifiable and some information about its class; the K-groups of F_{\mathrm{cont}}(A) should determine the KK-equivalence class of A. | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,228 | OWR-12175-023 | Jiang–Su Embeddings in Character-Free Central Sequence Algebras | If $F(A)$ has no characters, must it contain a unital copy of $\mathcal Z$? Does $\mathcal Z$ embed unitally into $\bigotimes_{n=1}^{\infty}D$ for every unital $C^*$-algebra $D$ without characters? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,012 | 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-12175-023",
"literature-status:open",
"owr-year:2012"
] | The no-character hypothesis alone is still insufficient for a known proof: the Dadarlat--Toms criterion requires a unital subhomogeneous algebra without characters inside the infinite tensor power. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3323/OWR_2012_52.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach report, Questions 10--11"
},
{
"url": "https://doi.org/10.1016/j.aim.2008.07.002",
"label": "Dadarlat--Toms, infinite tensor powers"
},
{
"url": "https://arxiv.o... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | If $F(A)$ has no characters, must it contain a unital copy of $\mathcal Z$? Does $\mathcal Z$ embed unitally into $\bigotimes_{n=1}^{\infty}D$ for every unital $C^*$-algebra $D$ without characters? | If F(A) has no characters, must it contain a unital copy of Z, and does Z embed unitally into \bigotimes_{n=1}^{\infty}D for every unital C*-algebra D without characters? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,229 | OWR-12175-024 | Subhomogeneous Character-Free Subalgebras of Infinite Tensor Powers | Let $B$ be a separable unital $C^*$-algebra without characters and with separating tracial states. Does $B\otimes_{\min}B\otimes_{\min}\cdots$ contain a subhomogeneous $C^*$-algebra without characters? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,012 | 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-12175-024",
"literature-status:open",
"owr-year:2012"
] | The question remains open in the stated generality: positive results require extra divisibility or subhomogeneous-subalgebra hypotheses, and the needed conclusion is not known even for broad simple non-elementary classes. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3323/OWR_2012_52.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach report, Question 13"
},
{
"url": "https://arxiv.org/abs/1106.5523",
"label": "Robert--Rordam, divisibility properties"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | Let $B$ be a separable unital $C^*$-algebra without characters and with separating tracial states. Does $B\otimes_{\min}B\otimes_{\min}\cdots$ contain a subhomogeneous $C^*$-algebra without characters? | Let B be a separable unital C*-algebra without characters and with separating tracial states. Does B\otimes_{\min}B\otimes_{\min}\cdots contain a subhomogeneous C*-algebra without characters? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,230 | OWR-12175-025 | Comparison Properties and Jiang–Su Absorption | For every nonelementary, stably finite, simple, separable, unital, nuclear $C^*$-algebra, are $\mathcal Z$-absorption, local weak comparison, and strict comparison equivalent? In particular, are local weak comparison and strict comparison equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 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-12175-025",
"literature-status:partially-solved",
"owr-year:2012"
] | For simple separable nuclear algebras, finite nuclear dimension and Z-stability are equivalent and Z-stability implies strict comparison; the converse from strict comparison to Z-stability remains open in full generality. | [
{
"url": "https://doi.org/10.1007/s00222-020-01013-1",
"label": "Castillejos--Evington--Tikuisis--White--Winter, nuclear dimension"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3323/OWR_2012_52.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach report, Toms--Winter question"
}... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | For every nonelementary, stably finite, simple, separable, unital, nuclear $C^*$-algebra, are $\mathcal Z$-absorption, local weak comparison, and strict comparison equivalent? In particular, are local weak comparison and strict comparison equivalent? | For every non-elementary, stably finite, simple, separable, unital, nuclear C*-algebra, are Z-absorption, local weak comparison, and strict comparison equivalent; in particular, are local weak comparison and strict comparison equivalent? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,231 | OWR-12175-027 | Nuclear Dimension after Jiang–Su Stabilization | Is $\operatorname{dim}_{\mathrm{nuc}}(A\otimes\mathcal Z)<\infty$ for every nuclear $C^*$-algebra $A$? What is the decomposition rank of $C(X)\subset C(X,M_n)$? Is it less than $\dim X$, or does dimension drop only after tensoring with a UHF algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,012 | 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-12175-027",
"literature-status:open",
"owr-year:2012"
] | The general non-simple assertion that every nuclear A has finite nuclear dimension after tensoring with Z remains unresolved; the equivalence is established for simple nuclear algebras and only under additional hypotheses for non-simple algebras. | [
{
"url": "https://arxiv.org/abs/1308.2941",
"label": "Robert--Tikuisis, non-simple nuclear dimension and Z-stability"
},
{
"url": "https://doi.org/10.1007/s00222-020-01013-1",
"label": "Castillejos--Evington--Tikuisis--White--Winter, simple case"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | Is $\operatorname{dim}_{\mathrm{nuc}}(A\otimes\mathcal Z)<\infty$ for every nuclear $C^*$-algebra $A$? What is the decomposition rank of $C(X)\subset C(X,M_n)$? Is it less than $\dim X$, or does dimension drop only after tensoring with a UHF algebra? | Is \operatorname{dim}_{\mathrm{nuc}}(A\otimes Z)<\infty for every nuclear C*-algebra A, and what is the decomposition rank of C(X)\subset C(X,M_n)? Is it less than \dim X, or does dimension drop only after tensoring with a UHF algebra? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,232 | OWR-12175-028 | Invariant Translation Approximation Property | Does every discrete group $\Gamma$ have the invariant translation approximation property, i.e., $C_r^*(\Gamma)=UC_r^*(\Gamma)^\Gamma$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,012 | 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-12175-028",
"literature-status:open",
"owr-year:2012"
] | ITAP is known for important classes such as amenable and finitely generated free groups, but the assertion that every discrete group has ITAP remains open. | [
{
"url": "https://doi.org/10.1090/S0002-9939-06-08191-3",
"label": "Zacharias, invariant translation approximation property"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3323/OWR_2012_52.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach report, current-at-publication status"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | Does every discrete group $\Gamma$ have the invariant translation approximation property, i.e., $C_r^*(\Gamma)=UC_r^*(\Gamma)^\Gamma$? | Does every discrete group \Gamma have the invariant translation approximation property, i.e. C_r^*(\Gamma)=UC_r^*(\Gamma)^\Gamma? | 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 | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,233 | OWR-12176-001 | Surjectivity on Component Groups of Semistable Curves | Let $f:X'\to X$ be a finite morphism of smooth, proper, geometrically connected curves over $K$, with induced map $f_*:\Phi_{X'}\to\Phi_X$. Is $f_*$ surjective when the minimal regular model of $X'$ consists of two rational components meeting transversally and $X$ is a Mumford curve of genus at least $2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Analytic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/53, pp. 3211--3265](https://doi.org/10.4171/owr/2012/53)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,012 | 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-12176-001",
"literature-status:open",
"owr-year:2012"
] | The extracted record is only the lead-in to Question 21 and contains no independently stated mathematical claim; under the required conservative rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/53",
"label": "Oberwolfach report, source context"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/53 | null | null | null | Let $f:X'\to X$ be a finite morphism of smooth, proper, geometrically connected curves over $K$, with induced map $f_*:\Phi_{X'}\to\Phi_X$. Is $f_*$ surjective when the minimal regular model of $X'$ consists of two rational components meeting transversally and $X$ is a Mumford curve of genus at least $2$? | Let f:X'\to X be a finite morphism of smooth, proper, geometrically connected curves over K, with induced f_*:\Phi_{X'}\to\Phi_X. Is f_* surjective when the minimal regular model of X' consists of two rational components meeting transversally and X is a Mumford curve of genus at least 2? | 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 | Non-Archimedean Analytic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/53, pp. 3211--3265 |
30,002,234 | OWR-12177-001 | Differential-Privacy Workshop Framing | What is the computational complexity of problems arising in differential privacy, including privately releasing statistical queries with useful accuracy? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304](https://doi.org/10.4171/owr/2012/54)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,012 | 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 | Unrecoverable OWR statement (The official report uses this broad complexity prompt as workshop framing and supplies no determinate claim distinct from the concrete high-) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12177-001",
"literature-status:open",
"owr-year:2012"
] | The extracted record is a survey-context paragraph about differential privacy rather than a definite mathematical problem, so no sharper resolution can be assigned. | [
{
"url": "https://doi.org/10.4171/owr/2012/54",
"label": "Oberwolfach report, source context"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/54 | null | null | null | null | What is the computational complexity of problems arising in differential privacy, including privately releasing statistical queries with useful accuracy? | unrecoverable | The official report uses this broad complexity prompt as workshop framing and supplies no determinate claim distinct from the concrete high-dimensional query problem retained later in the same report. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304 |
30,002,235 | OWR-12177-002 | Real $\tau$-Conjecture for Sparse Polynomial Sums and Products | Is the number of real roots of a sum of products of sparse univariate polynomials bounded polynomially in the size of that representation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304](https://doi.org/10.4171/owr/2012/54)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,012 | 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-12177-002",
"literature-status:partially-solved",
"owr-year:2012"
] | The full real tau-conjecture remains open, while Briquel--Burgisser prove the conjectured polynomial bound on average for Gaussian coefficients and earlier work handles restricted circuit forms. | [
{
"url": "https://doi.org/10.1002/rsa.20926",
"label": "Briquel--Burgisser, real tau-conjecture on average"
},
{
"url": "https://arxiv.org/abs/1107.1434",
"label": "Grenet--Koiran--Portier--Strozecki, restricted forms"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/54 | null | null | null | Is the number of real roots of a sum of products of sparse univariate polynomials bounded polynomially in the size of that representation? | Real Tau Conjecture: the number of real zeros of a polynomial computed by a depth-four arithmetic circuit is bounded by a polynomial in the size of the circuit. | corrected_verified | The official report states the real $\tau$-conjecture for sums of products of sparse univariate polynomials, not arbitrary depth-four circuits. | null | null | null | null | null | Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304 |
30,002,236 | OWR-12177-005 | Useful Differential-Privacy Framing | What is the complexity of ensuring differential privacy for useful statistical data analysis? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304](https://doi.org/10.4171/owr/2012/54)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,012 | 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 | Unrecoverable OWR statement (The official report uses this broad sentence as expository framing and does not pose it as a determinate problem separate from the explicit ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12177-005",
"literature-status:open",
"owr-year:2012"
] | The question is too broad to have one status without fixing the privacy definition, utility goal, data model, and computational task; substantial special-case theory exists, but the extracted problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/54",
"label": "Oberwolfach report, differential privacy problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/54 | null | null | null | null | What is the complexity of ensuring differential privacy for useful statistical data analysis? | unrecoverable | The official report uses this broad sentence as expository framing and does not pose it as a determinate problem separate from the explicit algorithmic question retained below. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304 |
30,002,237 | OWR-12177-006 | Private-Data-Analysis Framing | How can useful statistical analyses be enabled on a data set while protecting the privacy of the individuals whose data is analyzed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304](https://doi.org/10.4171/owr/2012/54)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,012 | 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 | Unrecoverable OWR statement (The official contribution uses this broad prompt to motivate differential privacy and then narrows it to the concrete high-dimensional runni) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12177-006",
"literature-status:open",
"owr-year:2012"
] | This is a broad research question rather than a specified theorem; many useful analyses have differential-privacy mechanisms, but no general resolution of the extracted problem is known. | [
{
"url": "https://doi.org/10.4171/owr/2012/54",
"label": "Oberwolfach report, source context"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/54 | null | null | null | null | How can useful statistical analyses be enabled on a data set while protecting the privacy of the individuals whose data is analyzed? | unrecoverable | The official contribution uses this broad prompt to motivate differential privacy and then narrows it to the concrete high-dimensional running-time question; it is not 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 | Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304 |
30,002,238 | OWR-12177-007 | Polynomial-Time Algorithms for High-Dimensional Private Queries | Can differentially private algorithms for answering many high-dimensional statistical queries achieve polynomial running time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304](https://doi.org/10.4171/owr/2012/54)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,012 | 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-12177-007",
"literature-status:open",
"owr-year:2012"
] | The extracted text is only an open-problems heading and the fragment Can we achieve a polynomial running time? without a specified computational problem, so it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/54",
"label": "Oberwolfach report, source context"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/54 | null | null | null | Can differentially private algorithms for answering many high-dimensional statistical queries achieve polynomial running time? | Can differentially private algorithms for answering many high-dimensional statistical queries achieve polynomial running time? | exact | The official report explicitly asks this polynomial-running-time question for many high-dimensional statistical queries. | null | null | null | null | null | Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304 |
30,002,239 | OWR-12177-008 | Polynomial Freiman–Ruzsa Conjecture over Binary Vector Spaces | If $A\subseteq\mathbb F_2^n$ satisfies $|A+A|\leq K|A|$, is there a subset $A^{\prime}\subseteq A$ with $|A^{\prime}|\geq |A|/\operatorname{poly}(K)$ and $|\operatorname{span}(A^{\prime})|\leq\operatorname{poly}(K)|A^{\prime}|$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304](https://doi.org/10.4171/owr/2012/54)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | solved | null | 2,012 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-27T00:00:00 | 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 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-27",
"kind": "resolution",
"evidence": "published"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12177-008",
"literature-status:open",
"owr-year:2012"
] | Gowers, Green, Manners and Tao prove the polynomial Freiman–Ruzsa conjecture in characteristic two (2023), covering the binary-vector-space formulation in this record.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://arxiv.org/abs/2311.05762",
"label": "Gowers, Green, Manners and Tao, On a conjecture of Marton"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follow-ups"
}
] | 2026-09-27T00:00:00 | Gowers, Green, Manners and Tao, On a conjecture of Marton: https://arxiv.org/abs/2311.05762 | https://doi.org/10.4171/owr/2012/54 | null | null | null | If $A\subseteq\mathbb F_2^n$ satisfies $|A+A|\leq K|A|$, is there a subset $A^{\prime}\subseteq A$ with $|A^{\prime}|\geq |A|/\operatorname{poly}(K)$ and $|\operatorname{span}(A^{\prime})|\leq\operatorname{poly}(K)|A^{\prime}|$? | Polynomial Freiman-Ruzsa conjecture: if A\subseteq\mathbb F_2^n satisfies |A+A|\leq K|A|, then there is A'\subseteq A with |A'|\geq |A|/\operatorname{poly}(K) and |\operatorname{span}(A')|\leq\operatorname{poly}(K)|A'|. | corrected_verified | The official report states this binary-vector-space form of the Polynomial Freiman–Ruzsa Conjecture. | null | null | null | null | null | Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304 |
30,002,240 | OWR-12177-009 | Unique Games Conjecture | Is Khot's Unique Games Conjecture true? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304](https://doi.org/10.4171/owr/2012/54)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,012 | 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 of canonical problem CS-001 | [
"CS-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12177-009",
"literature-status:open",
"owr-year:2012"
] | The extracted record concerns the Unique Games Conjecture. It remains a prominent open problem in current literature, despite major progress on restricted cases and its algorithmic consequences. | [
{
"url": "https://doi.org/10.1145/509907.510017",
"label": "Khot original formulation"
},
{
"url": "https://theoryofcomputing.org/articles/v021a010/v021a010.pdf",
"label": "current status survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/54 | null | null | null | Is Khot's Unique Games Conjecture true? | Is Khot's Unique Games Conjecture true? | exact | The official report explicitly names Khot’s Unique Games Conjecture as an open problem. | null | null | null | null | null | Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304 |
30,002,241 | OWR-12177-010 | Multicolored Sunflower Conjecture over Ternary Vector Spaces | Does there exist $c>0$ such that every $S\subseteq(\mathbb Z_3^n)^3$ with $|S|\geq3^{n(1-c)}$ and $x+y+z=0$ for every $(x,y,z)\in S$ contains three elements $(x_i,y_i,z_i)$ satisfying $x_1+y_2+z_3=0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304](https://doi.org/10.4171/owr/2012/54)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | solved | null | 2,012 | 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 | {
"source_url": "https://doi.org/10.1109/CCC.2012.26",
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (yes)**. C. Umans (OWR 54/2012, p. 3292, Conjecture 7) states the multicolored sunflower conjecture of Alon–Shpilka–Umans ([CCC 2012](https://doi.org/10.1109/CCC.2012.26), Conjecture 6). | [
"owr",
"oberwolfach-reports",
"OWR-12177-010",
"literature-status:open",
"owr-year:2012"
] | The record is a truncated fragment about multicolored sunflowers and related additive equations, so it does not state a uniquely triageable theorem. The cited sunflower-type conjectural direction has no unambiguous general resolution here. | [
{
"url": "https://doi.org/10.4171/owr/2012/54",
"label": "Oberwolfach report"
},
{
"url": "https://people.csail.mit.edu/virgi/6.890/papers/sunflowersmult.pdf",
"label": "sunflower and matrix multiplication paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/54 | null | null | null | Does there exist $c>0$ such that every $S\subseteq(\mathbb Z_3^n)^3$ with $|S|\geq3^{n(1-c)}$ and $x+y+z=0$ for every $(x,y,z)\in S$ contains three elements $(x_i,y_i,z_i)$ satisfying $x_1+y_2+z_3=0$? | Multicolored sunflower conjecture: there is a constant c>0 such that every S\subseteq(\mathbb Z_3^n)^3 with |S|\geq 3^{n(1-c)} and x+y+z=0 for every (x,y,z)\in S contains three elements (x_i,y_i,z_i) with x_1+y_2+z_3=0. | corrected_verified | The official report states this multicolored sunflower conjecture over $\mathbb Z_3^n$. | null | null | null | null | null | Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304 |
30,002,242 | OWR-12177-011 | Machine-Learning Algorithms Results Report | Machine-learning tasks are often computationally intractable, while practical algorithms lack provable guarantees on running time or solution quality. Can one develop algorithms for such tasks with provable running-time and solution-quality guarantees? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304](https://doi.org/10.4171/owr/2012/54)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,012 | 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 | Unrecoverable OWR statement (The official contribution asks rhetorically whether provable algorithms are possible and immediately answers yes by presenting three results) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12177-011",
"literature-status:open",
"owr-year:2012"
] | The extracted question is only the broad prompt whether the surveyed machine learning bounds can be improved, without a precise mathematical claim. No unique resolution can therefore be established, so it remains open under the stated triage rule. | [
{
"url": "https://doi.org/10.4171/owr/2012/54",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/54 | null | null | null | null | Machine-learning tasks are often computationally intractable, while practical algorithms lack provable guarantees on running time or solution quality. Can one develop algorithms for such tasks with provable running-time and solution-quality guarantees? | unrecoverable | The official contribution asks rhetorically whether provable algorithms are possible and immediately answers yes by presenting three results; the extraction is expository framing, not a residual open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenan... | null | null | null | null | null | Complexity Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/54, pp. 3267--3304 |
30,002,243 | OWR-12179-002 | Open Problems on Smoothed Laplace Periodograms | For smoothed Laplace periodograms and their rank-based variants, determine their asymptotic distributions, develop their use in signal detection, and extend the methods to locally stationary time series. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Frontiers in Quantile Regression (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/56, pp. 3339--3373](https://doi.org/10.4171/owr/2012/56)
## Literature review (checked 202... | 3 | partially_solved | null | 2,012 | 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-12179-002",
"literature-status:partially-solved",
"owr-year:2012"
] | Smoothed Laplace periodogram asymptotics, signal detection applications, and locally stationary extensions were subsequently developed, but the record lists a broad research program rather than a single completely closed theory. | [
{
"url": "https://arxiv.org/abs/1401.8104",
"label": "quantile spectral processes"
},
{
"url": "https://academic.oup.com/jrsssb/article/79/5/1619/7040912",
"label": "locally stationary quantile spectra"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC2650682/",
"label": "period... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/56 | null | null | null | For smoothed Laplace periodograms and their rank-based variants, determine their asymptotic distributions, develop their use in signal detection, and extend the methods to locally stationary time series. | For smoothed Laplace periodograms and their rank-based variants, determine the asymptotic distribution, analyze applications to signal detection, and extend the methods to locally stationary time series. | corrected_verified | The official report explicitly labels these three directions as interesting open questions currently under investigation. | null | null | null | null | null | Mini-Workshop: Frontiers in Quantile Regression (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/56, pp. 3339--3373 |
30,002,244 | OWR-12180-001 | Existence of Optimal Two-Phase Eigenvalue Configurations | Let $\Omega\subset\mathbb R^d$ be bounded, let $0<m<|\Omega|$, and let $A=\Omega\setminus B$ and $\sigma=\alpha\chi_A+\beta\chi_B$ with $0<\alpha<\beta$ and $|B|=m$. Does minimizing the first Dirichlet eigenvalue $\lambda(B)$ over measurable $B\subset\Omega$ with $|B|=m$ always have a solution? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Geometries, Shapes and Topologies in PDE-based Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/57, pp. 3375--3415](https://doi.org/10.4171/owr/2012/57)
## Lit... | 3 | solved | null | 2,012 | 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 | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no)**. A. Laurain (joint with C. Conca and R. Mahadevan; OWR 57/2012, p. 3407) calls open whether minimizing the first Dirichlet eigenvalue of −div((αχ_A + βχ_B)∇u), 0 < α < β, over B ⊂ Ω with |B| = m has a solution (it does for balls); the record asks if one "alw... | [
"owr",
"oberwolfach-reports",
"OWR-12180-001",
"literature-status:open",
"owr-year:2012"
] | The conjectured optimizer is false in general, but the extracted record separately states that existence of a minimizer for the unrestricted two phase problem remains open. The false conjecture does not resolve that existence question. | [
{
"url": "https://ems.press/content/serial-article-files/46428",
"label": "Oberwolfach report"
},
{
"url": "https://epubs.siam.org/doi/10.1137/110847822",
"label": "low contrast counterexample paper"
},
{
"url": "https://www.numdam.org/item/COCV_2014__20_2_362_0.pdf",
"label": "globa... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/57 | null | null | null | Let $\Omega\subset\mathbb R^d$ be bounded, let $0<m<|\Omega|$, and let $A=\Omega\setminus B$ and $\sigma=\alpha\chi_A+\beta\chi_B$ with $0<\alpha<\beta$ and $|B|=m$. Does minimizing the first Dirichlet eigenvalue $\lambda(B)$ over measurable $B\subset\Omega$ with $|B|=m$ always have a solution? | Let \Omega\subset\mathbb{R}^d be bounded, let 0<m<|\Omega|, and let A=\Omega\setminus B and \sigma=\alpha\chi_A+\beta\chi_B with 0<\alpha<\beta and |B|=m. Does minimizing the first Dirichlet eigenvalue \lambda(B) over measurable B\subset\Omega with |B|=m always have a solution? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Geometries, Shapes and Topologies in PDE-based Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/57, pp. 3375--3415 |
30,002,245 | OWR-12181-001 | Heterogeneous-Parameter Inversion in Atmospheric Chemistry | For atmospheric-chemistry data assimilation, can one formulate and solve the generalized inversion problem of estimating heterogeneous parameters, including emissions and initial values, with realistic multivariate and temporal error covariances? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical and Algorithmic Aspects of Atmosphere-Ocean Data Assimilation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/58, pp. 3417--3471](https://doi.org/10.4171/owr/2012/58)
## Lit... | 3 | open | null | 2,012 | 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-12181-001",
"literature-status:open",
"owr-year:2012"
] | The extracted item is a broad statement of open chemistry data assimilation challenges rather than a precise solved proposition. Current atmospheric chemistry assimilation literature still identifies model transport, transformations, observations, and efficient inversion as active challenges. | [
{
"url": "https://ems.press/content/serial-article-files/46429",
"label": "Oberwolfach report"
},
{
"url": "https://www.ecmwf.int/sites/default/files/elibrary/2006/74418-scientific-challenges-chemical-data-assimilation_0.pdf",
"label": "ECMWF chemistry assimilation challenges"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/58 | null | null | null | For atmospheric-chemistry data assimilation, can one formulate and solve the generalized inversion problem of estimating heterogeneous parameters, including emissions and initial values, with realistic multivariate and temporal error covariances? | For atmospheric-chemistry data assimilation, can one formulate and solve the generalized inversion problem of estimating heterogeneous parameters, including emissions and initial values, with realistic multivariate and temporal error covariances? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Mathematical and Algorithmic Aspects of Atmosphere-Ocean Data Assimilation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/58, pp. 3417--3471 |
30,002,246 | OWR-12181-002 | Efficient Covariance Models for Atmospheric-Chemistry Data Assimilation | Can the forecast-error covariance matrices for atmospheric chemistry, especially chemically consistent multivariate and temporal covariances, be treated efficiently in numerical data assimilation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical and Algorithmic Aspects of Atmosphere-Ocean Data Assimilation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/58, pp. 3417--3471](https://doi.org/10.4171/owr/2012/58)
## Lit... | 3 | open | null | 2,012 | 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-12181-002",
"literature-status:open",
"owr-year:2012"
] | Efficient numerical schemes and assimilation systems exist for selected atmospheric chemistry models, but the unrestricted efficient numerical treatment identified in the record remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46429?nt=1",
"label": "Oberwolfach report"
},
{
"url": "https://journals.rcsi.science/0002-3515/article/view/319554",
"label": "current atmospheric chemistry algorithms"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/58 | null | null | null | Can the forecast-error covariance matrices for atmospheric chemistry, especially chemically consistent multivariate and temporal covariances, be treated efficiently in numerical data assimilation? | Can the forecast-error covariance matrices for atmospheric chemistry, especially chemically consistent multivariate and temporal covariances, be treated efficiently in numerical data assimilation? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Mathematical and Algorithmic Aspects of Atmosphere-Ocean Data Assimilation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/58, pp. 3417--3471 |
30,002,247 | OWR-12182-002 | Variance Conjecture for Log-Concave Random Vectors | Does there exist an absolute constant $C$ such that every centered log-concave random vector $X\in\mathbb R^n$ satisfies $\operatorname{Var}(|X|^2)\leq C\lambda_X^2\mathbb E|X|^2$, where $\lambda_X$ is the largest eigenvalue of its covariance matrix? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548](https://doi.org/10.4171/owr/2012/59)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-12182-002",
"literature-status:open",
"owr-year:2012"
] | The extracted record contains only a methodological observation about lack of linear invariance, not a standalone mathematical question with a definite claim. No unique resolution can be assigned, so it is open under the stated rule. | [
{
"url": "https://ems.press/content/serial-article-files/46430",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/59 | null | null | null | Does there exist an absolute constant $C$ such that every centered log-concave random vector $X\in\mathbb R^n$ satisfies $\operatorname{Var}(|X|^2)\leq C\lambda_X^2\mathbb E|X|^2$, where $\lambda_X$ is the largest eigenvalue of its covariance matrix? | Does there exist an absolute constant C such that every centered log-concave random vector X in \mathbb{R}^n satisfies \operatorname{Var}|X|^2\le C\lambda_X^2\mathbb{E}|X|^2, where \lambda_X is the largest eigenvalue of its covariance matrix? | corrected_verified | The official report states this variance conjecture with the same covariance normalization. | null | null | null | null | null | Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548 |
30,002,248 | OWR-12182-003 | Convergence of Arbitrary Steiner-Symmetrization Sequences | For every compact set $K\subset\mathbb R^n$ and every sequence of directions $(u_m)\subset S^{n-1}$, do the iterated Steiner symmetrals $S_{u_m}\cdots S_{u_1}K$ always converge in shape, without any assumption on the directions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548](https://doi.org/10.4171/owr/2012/59)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-12182-003",
"literature-status:open",
"owr-year:2012"
] | The extracted text truncates the first of two open problems before stating the summation claim. Because the exact assertion is unavailable, its status is unresolved and therefore open. | [
{
"url": "https://ems.press/content/serial-article-files/46430",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/59 | null | null | null | For every compact set $K\subset\mathbb R^n$ and every sequence of directions $(u_m)\subset S^{n-1}$, do the iterated Steiner symmetrals $S_{u_m}\cdots S_{u_1}K$ always converge in shape, without any assumption on the directions? | For any compact set K\subset\mathbb{R}^n and any sequence of directions (u_m)\subset S^{n-1}, do the iterated Steiner symmetrals S_{u_m}\cdots S_{u_1}K always converge in shape, without assumptions on the directions? | corrected_verified | The official report states this as its fourth explicit problem. | null | null | null | null | null | Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548 |
30,002,249 | OWR-12182-004 | Uniqueness for Symmetric Cone-Volume Measures | For origin-symmetric convex bodies $K$ and $C$ with equal volume and cone-volume measures $V_K=V_C$, must there be direct-sum decompositions $K=K_1\oplus\cdots\oplus K_m$ and $C=C_1\oplus\cdots\oplus C_m$ with $K_i=\lambda_i C_i$ for some $\lambda_i>0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548](https://doi.org/10.4171/owr/2012/59)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-12182-004",
"literature-status:open",
"owr-year:2012"
] | Existence and several restricted cases for cone volume measures are known, but the stated global uniqueness and equality characterization for origin symmetric bodies remains an open logarithmic Brunn Minkowski type problem. | [
{
"url": "https://ems.press/content/serial-article-files/46430",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2104.12408",
"label": "Milman logarithmic Brunn Minkowski results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/59 | null | null | null | For origin-symmetric convex bodies $K$ and $C$ with equal volume and cone-volume measures $V_K=V_C$, must there be direct-sum decompositions $K=K_1\oplus\cdots\oplus K_m$ and $C=C_1\oplus\cdots\oplus C_m$ with $K_i=\lambda_i C_i$ for some $\lambda_i>0$? | For o-symmetric convex bodies K,C with equal volume and cone volume measures V_K=V_C, must K and C have dilated direct summands, namely K=K_1\oplus\cdots\oplus K_m, C=C_1\oplus\cdots\oplus C_m, and K_i=\lambda_i C_i with \lambda_i>0? | corrected_verified | The official report states this equality-case conjecture for cone-volume measures. | null | null | null | null | null | Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548 |
30,002,250 | OWR-12182-007 | Generalized Wills-Polynomial Results Report | For convex bodies K,E\in\mathcal{K}^n and a nonnegative measure \mu on \mathbb{R}_{\ge0}, do the roots of the generalized Wills polynomial g_{K;E}^{\mu}(z)=\sum_{i=0}^{n}\binom{n}{i}W_i(K;E)m_i(\mu)z^i have common structural properties independent of \mu? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548](https://doi.org/10.4171/owr/2012/59)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,012 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official contribution introduces an interest in measure-independent root properties and then states the properties it proves; the extrac) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12182-007",
"literature-status:partially-solved",
"owr-year:2012"
] | Substantial measure independent structure of generalized Wills polynomial roots has been proved, including convex cone containment and monotonicity properties, but the broad request for all common properties is not a complete classification. | [
{
"url": "https://ems.press/content/serial-article-files/46430",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.4171/RMI/842",
"label": "Wills polynomial roots theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/59 | null | null | null | null | For convex bodies K,E\in\mathcal{K}^n and a nonnegative measure \mu on \mathbb{R}_{\ge0}, do the roots of the generalized Wills polynomial g_{K;E}^{\mu}(z)=\sum_{i=0}^{n}\binom{n}{i}W_i(K;E)m_i(\mu)z^i have common structural properties independent of \mu? | unrecoverable | The official contribution introduces an interest in measure-independent root properties and then states the properties it proves; the extraction is an answered research aim, not a separately posed open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for proven... | null | null | null | null | null | Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548 |
30,002,251 | OWR-12182-008 | Geometric-Comparison Stability Framework | Let f_K,f_L be geometric characteristics of origin-symmetric convex bodies K,L\subset\mathbb{R}^n. If f_K(\xi)\le f_L(\xi)+\varepsilon for every \xi\in S^{n-1}, does there exist an absolute constant c such that |K|^{(n-1)/n}\le |L|^{(n-1)/n}+c\varepsilon for every \varepsilon>0? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548](https://doi.org/10.4171/owr/2012/59)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official contribution presents this generic inequality as a framework before applying it to specified geometric characteristics; without) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12182-008",
"literature-status:open",
"owr-year:2012"
] | The extracted stability inequality omits the definitions of the geometric quantities and the body class, so its exact assertion cannot be identified. General volume comparison stability remains dependent on those missing hypotheses. | [
{
"url": "https://ems.press/content/serial-article-files/46430",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1207.6347",
"label": "volume comparison stability paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/59 | null | null | null | null | Let f_K,f_L be geometric characteristics of origin-symmetric convex bodies K,L\subset\mathbb{R}^n. If f_K(\xi)\le f_L(\xi)+\varepsilon for every \xi\in S^{n-1}, does there exist an absolute constant c such that |K|^{(n-1)/n}\le |L|^{(n-1)/n}+c\varepsilon for every \varepsilon>0? | unrecoverable | The official contribution presents this generic inequality as a framework before applying it to specified geometric characteristics; without naming the characteristic it is not a determinate standalone problem, and the reported applications supply results. No separate clean statement is promoted; the original record re... | null | null | null | null | null | Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548 |
30,002,252 | OWR-12182-009 | Geometric-Comparison Separation Framework | Let f_K,f_L be geometric characteristics of origin-symmetric convex bodies K,L\subset\mathbb{R}^n. If f_K(\xi)\le f_L(\xi)-\varepsilon for every \xi\in S^{n-1}, does there exist an absolute constant c>0 such that |K|^{(n-1)/n}\le |L|^{(n-1)/n}-c\varepsilon for every \varepsilon>0? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548](https://doi.org/10.4171/owr/2012/59)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official contribution presents this generic separation inequality as the companion framework to its proved applications; the extraction ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12182-009",
"literature-status:open",
"owr-year:2012"
] | This is the companion separation inequality with the same omitted geometric definitions and body class. Without those hypotheses no definitive status is available, so it remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46430",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1207.6347",
"label": "volume comparison stability paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/59 | null | null | null | null | Let f_K,f_L be geometric characteristics of origin-symmetric convex bodies K,L\subset\mathbb{R}^n. If f_K(\xi)\le f_L(\xi)-\varepsilon for every \xi\in S^{n-1}, does there exist an absolute constant c>0 such that |K|^{(n-1)/n}\le |L|^{(n-1)/n}-c\varepsilon for every \varepsilon>0? | unrecoverable | The official contribution presents this generic separation inequality as the companion framework to its proved applications; the extraction omits the choice of geometric characteristic and does not preserve a determinate open claim. No separate clean statement is promoted; the original record remains publicly visible a... | null | null | null | null | null | Convex Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/59, pp. 3473--3548 |
30,002,253 | OWR-12183-001 | Switching Ratios in Discretized Hysteresis Dynamics | For the discretized hysteresis equation $\dot u_n=(u_{n-1}-2u_n+u_{n+1})/h^2+\mathcal H(u_n)$ with $u_n(0)=-c(hn)^2$, $c>0$, and thresholds $H_1>0>H_{-1}$, is $\#\{\text{switched points}\}/\#\{\text{nonswitched points}\}\approx|H_1/H_{-1}|$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamics of Patterns (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/60, pp. 3549--3633](https://doi.org/10.4171/owr/2012/60)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,012 | 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-12183-001",
"literature-status:partially-solved",
"owr-year:2012"
] | Later analysis established the rattling mechanism, propagation behavior, and detailed one dimensional microstructure, but the exact switched point ratio conjecture and its multidimensional extension are not fully resolved. | [
{
"url": "https://doi.org/10.1137/16M106039X",
"label": "rattling primary paper"
},
{
"url": "https://www.numdam.org/articles/10.1016/j.anihpc.2017.09.006/",
"label": "spatially discrete hysteresis paper"
},
{
"url": "https://ems.press/content/serial-article-files/46431",
"label": "O... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/60 | null | null | null | For the discretized hysteresis equation $\dot u_n=(u_{n-1}-2u_n+u_{n+1})/h^2+\mathcal H(u_n)$ with $u_n(0)=-c(hn)^2$, $c>0$, and thresholds $H_1>0>H_{-1}$, is $\#\{\text{switched points}\}/\#\{\text{nonswitched points}\}\approx|H_1/H_{-1}|$? | For the discretized hysteresis equation \dot u_n=(u_{n-1}-2u_n+u_{n+1})/h^2+H(u_n) with quadratic initial data u_n(0)=-c(hn)^2 and thresholds H_1>0,H_{-1}<0, is the conjectured ratio \#\mathrm{switched\ points}/\#\mathrm{not\ switched\ points}\approx H_1/H_{-1}? | corrected_verified | The official report states this conjectured switching ratio; the absolute value missing from the extraction is essential because the lower threshold is negative. | null | null | null | null | null | Dynamics of Patterns (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/60, pp. 3549--3633 |
30,002,254 | OWR-12183-002 | Stable Label Patterns on Graphs | For a graph-based pattern system with stable vertex labels in $\{+,-,0\}$, which graphs support a stable pattern, and can one graph support several stable patterns not related by the stated trivial symmetries? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamics of Patterns (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/60, pp. 3549--3633](https://doi.org/10.4171/owr/2012/60)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 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-12183-002",
"literature-status:open",
"owr-year:2012"
] | The report gives examples such as stars but leaves both graph classification and multiplicity questions open; no later general solution was located. | [
{
"url": "https://doi.org/10.4171/owr/2012/60",
"label": "Dynamics of Patterns, Oberwolfach Report 60/2012"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/60 | null | null | null | For a graph-based pattern system with stable vertex labels in $\{+,-,0\}$, which graphs support a stable pattern, and can one graph support several stable patterns not related by the stated trivial symmetries? | For a graph-based pattern system with stable vertex labels in \{+,−,0\}, which graphs support such stable patterns, and can a graph support several stable patterns not related by trivial symmetries? | corrected_verified | The official report explicitly poses both the existence/classification and nontrivial-multiplicity questions. | null | null | null | null | null | Dynamics of Patterns (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/60, pp. 3549--3633 |
30,002,255 | OWR-12329-001 | Borel Cardinalities of Lascar Equivalence Relations | For the level-$\alpha$ Lascar equivalence relation $\equiv_L^\alpha$ in a complete first-order theory, which Borel cardinalities can it have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66](https://doi.org/10.4171/owr/2013/01)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,013 | 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-12329-001",
"literature-status:partially-solved",
"owr-year:2013"
] | Kaplan, Miller, and Simon prove non-smoothness whenever the Lascar relation on a KP strong type is nontrivial, but this does not classify all possible Borel cardinalities. | [
{
"url": "https://doi.org/10.1112/jlms/jdu041",
"label": "The Borel Cardinality of Lascar Strong Types"
},
{
"url": "https://doi.org/10.4171/owr/2013/01",
"label": "Model Theory, Oberwolfach Report 01/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/01 | null | null | null | For the level-$\alpha$ Lascar equivalence relation $\equiv_L^\alpha$ in a complete first-order theory, which Borel cardinalities can it have? | For the level-\alpha Lascar equivalence relation \equiv_L^\alpha in a complete first-order theory, what Borel cardinalities can the equivalence relation have? | corrected_verified | The official report poses this as its fifth explicit descriptive-set-theoretic problem. | null | null | null | null | null | Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66 |
30,002,256 | OWR-12329-004 | Extendable Outer Automorphisms of Subgroup Inclusions | Given a subgroup $H\leq G$, let $\operatorname{Out}(H\hookrightarrow G)$ be the outer automorphisms of $H$ that extend to $G$. What elements can this group contain, and is it finitely generated or finitely presented? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66](https://doi.org/10.4171/owr/2013/01)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,013 | 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-12329-004",
"literature-status:partially-solved",
"owr-year:2013"
] | Guirardel and Levitt describe the extendable subgroup and prove finite-index McCool and finite-presentation results for malnormal quasiconvex and relatively hyperbolic cases, but not for arbitrary subgroup inclusions. | [
{
"url": "https://arxiv.org/abs/1212.1434",
"label": "Splittings and Automorphisms of Relatively Hyperbolic Groups"
},
{
"url": "https://doi.org/10.4171/owr/2013/01",
"label": "Model Theory, Oberwolfach Report 01/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/01 | null | null | null | Given a subgroup $H\leq G$, let $\operatorname{Out}(H\hookrightarrow G)$ be the outer automorphisms of $H$ that extend to $G$. What elements can this group contain, and is it finitely generated or finitely presented? | Given a subgroup H\le G, let \operatorname{Out}(H\hookrightarrow G) be the outer automorphisms of H that extend to G. What does this group contain, and is it finitely generated or finitely presented? | corrected_verified | The official report states this general question with the same extendability definition and finiteness alternatives. | null | null | null | null | null | Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66 |
30,002,257 | OWR-12329-005 | Higher-Arity VC-Density Bounds in NIP Theories | Assume a theory $T$ has NIP and every formula $\varphi(x;y)$ with $|x|=1$ satisfies $\operatorname{vc}^*(\varphi)\leq k$. For every $n$, does there exist a bound $k(n)$ such that $\operatorname{vc}^*(\varphi(x;y))\leq k(|x|)$ for every formula with $|x|=n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66](https://doi.org/10.4171/owr/2013/01)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,013 | 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-12329-005",
"literature-status:partially-solved",
"owr-year:2013"
] | The general NIP unary-to-arbitrary-arity VC-density bound remains open; established bounds cover restricted classes such as weakly o-minimal and finite-rank theories. | [
{
"url": "https://doi.org/10.4171/owr/2013/01",
"label": "Model Theory, Oberwolfach Report 01/2013"
},
{
"url": "https://chernikov.umd.edu/FHP.pdf",
"label": "Fractional Helly Property and Forking in NTP2 Theories"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/01 | null | null | null | Assume a theory $T$ has NIP and every formula $\varphi(x;y)$ with $|x|=1$ satisfies $\operatorname{vc}^*(\varphi)\leq k$. For every $n$, does there exist a bound $k(n)$ such that $\operatorname{vc}^*(\varphi(x;y))\leq k(|x|)$ for every formula with $|x|=n$? | Assume T has NIP and that every formula \phi(x;y) with \ell(x)=1 satisfies \operatorname{vc}^{*}(\phi)\le k. Does there exist, for every n, a bound k(n) such that \operatorname{vc}^{*}(\phi(x;y))\le k(\ell(x)) for all formulas? | corrected_verified | The official report asks whether the unary VC-density bound extends uniformly to each higher tuple arity. | null | null | null | null | null | Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66 |
30,002,258 | OWR-12329-007 | Nearly-Lie Quotients of Automorphism Groups in NIP Theories | Given a saturated model $M$ of an NIP theory $T$ and a formula $\varphi(x,y)$, does there exist a homomorphism $h:\operatorname{Aut}(M)\to G$ into a nearly Lie group $G$ whose kernel fixes every $\varphi$-type over $M$ that does not fork over $\varnothing$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66](https://doi.org/10.4171/owr/2013/01)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,013 | 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-12329-007",
"literature-status:partially-solved",
"owr-year:2013"
] | The report proves nearly-Lie quotients for definable groups with generically stable measures, while the proposed automorphism-group homomorphism with the stated kernel is not established in general. | [
{
"url": "https://doi.org/10.4171/owr/2013/01",
"label": "Model Theory, Oberwolfach Report 01/2013"
},
{
"url": "https://ora.ox.ac.uk/objects/uuid:d079a1e5-75e9-49c2-bb91-89da02759474",
"label": "Approximate Equivalence Relations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/01 | null | null | null | Given a saturated model $M$ of an NIP theory $T$ and a formula $\varphi(x,y)$, does there exist a homomorphism $h:\operatorname{Aut}(M)\to G$ into a nearly Lie group $G$ whose kernel fixes every $\varphi$-type over $M$ that does not fork over $\varnothing$? | Given a saturated model M of an NIP theory T and a formula \phi(x,y), does there exist a homomorphism h:\operatorname{Aut}(M)\to G into a nearly-Lie group G whose kernel fixes all \phi-types over M that do not fork over \varnothing? | corrected_verified | The official report states this automorphism-group question with the nonforking type condition. | null | null | null | null | null | Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66 |
30,002,259 | OWR-12329-008 | Bad Groups of Finite Morley Rank | Does there exist a simple group of finite Morley rank that is not isomorphic to $G(F)$ for any algebraic group $G$ over an algebraically closed field $F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66](https://doi.org/10.4171/owr/2013/01)
## Literature review (checked 2026-0... | 3 | open | null | 2,013 | 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-12329-008",
"literature-status:open",
"owr-year:2013"
] | The existence of a bad group of finite Morley rank remains a conjectural problem; the report proposes analytic constructions but supplies neither a construction nor a disproof. | [
{
"url": "https://doi.org/10.4171/owr/2013/01",
"label": "Model Theory, Oberwolfach Report 01/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/01 | null | null | null | Does there exist a simple group of finite Morley rank that is not isomorphic to $G(F)$ for any algebraic group $G$ over an algebraically closed field $F$? | Does there exist a simple group of finite Morley rank that is not isomorphic to G(F) for an algebraic group G over an algebraically closed field F, namely a bad group? | corrected_verified | The official report describes the existence of such a bad group as an open belief rather than a known example. | null | null | null | null | null | Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66 |
30,002,260 | OWR-12329-009 | Model-Theoretic Connected-Component Quotients | Let $G$ be a group definable in a first-order structure $M$, let $M^*$ be a saturated elementary extension, and for a small parameter set $A$ let $G_A^{*00}$ and $G_A^{*000}$ denote the model-theoretic connected components of $G(M^*)$ (the smallest $A$-type-definable subgroup of bounded index and the smallest $A$-invar... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66](https://doi.org/10.4171/owr/2013/01)
## Literature review (checked 2026-0... | 3 | open | null | 2,013 | 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-12329-009",
"literature-status:open",
"owr-year:2013"
] | The quotient question remains unresolved in general; work on definable connected components gives structural cases but does not classify possible quotients or decide non-abelianity. | [
{
"url": "https://doi.org/10.4171/owr/2013/01",
"label": "Model Theory, Oberwolfach Report 01/2013"
},
{
"url": "https://arxiv.org/abs/1201.5221",
"label": "Model-Theoretic Connected Components in Group Extensions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/01 | null | null | null | Let $G$ be a group definable in a first-order structure $M$, let $M^*$ be a saturated elementary extension, and for a small parameter set $A$ let $G_A^{*00}$ and $G_A^{*000}$ denote the model-theoretic connected components of $G(M^*)$ (the smallest $A$-type-definable subgroup of bounded index and the smallest $A$-invar... | For the model-theoretic quotient G_A^{*00}/G_A^{*000}, can it be non-abelian, and what groups can occur as such quotients? | corrected_verified | The official report asks both whether the quotient can be nonabelian and which groups occur, but the same contribution then constructs nonabelian examples; only the classification question remains open. | null | null | null | null | null | Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66 |
30,002,261 | OWR-12329-010 | Quasiminimal Complex Exponentiation and Abelian Regular Groups | Is the complex exponential field $(\mathbb C,+,\cdot,0,1,\exp)$ quasiminimal, as conjectured by Zilber, and is every regular group abelian? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66](https://doi.org/10.4171/owr/2013/01)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,013 | 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-12329-010",
"literature-status:partially-solved",
"owr-year:2013"
] | Minimal groups are abelian and substantial results hold for quasi-minimal and generically stable settings, but the assertion that every regular group is abelian remains open. | [
{
"url": "https://doi.org/10.4171/owr/2013/01",
"label": "Model Theory, Oberwolfach Report 01/2013"
},
{
"url": "https://doi.org/10.4064/fm222-2-4",
"label": "Around Podewski's Conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/01 | null | null | null | Is the complex exponential field $(\mathbb C,+,\cdot,0,1,\exp)$ quasiminimal, as conjectured by Zilber, and is every regular group abelian? | Is the complex exponential field (\mathbb{C},+,\cdot,0,1,\exp) quasi-minimal, as conjectured by Zilber, and is every regular group abelian? | corrected_verified | The official report poses both questions in the same model-theory discussion. | null | null | null | null | null | Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66 |
30,002,262 | OWR-12329-011 | Algebraic Closure and Orderability of Minimal Fields | Is every minimal field algebraically closed, as asserted by Podewski’s conjecture, and can a minimal ordered field of characteristic zero exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66](https://doi.org/10.4171/owr/2013/01)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,013 | 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-12329-011",
"literature-status:partially-solved",
"owr-year:2013"
] | Generic stability proves algebraic closedness for regular fields and resolves broad special cases, but the constructed group and the remaining minimal and quasi-minimal questions are not fully settled. | [
{
"url": "https://doi.org/10.4171/owr/2013/01",
"label": "Model Theory, Oberwolfach Report 01/2013"
},
{
"url": "https://doi.org/10.4064/fm222-2-4",
"label": "Around Podewski's Conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/01 | null | null | null | Is every minimal field algebraically closed, as asserted by Podewski’s conjecture, and can a minimal ordered field of characteristic zero exist? | Is the constructed group quasi-minimal, or at least regular? Are all minimal fields algebraically closed, as in Podewski's conjecture, and are there no minimal ordered fields of characteristic zero? | corrected_verified | The official report separately poses these two self-contained field questions; the extraction’s additional “constructed group” lacks enough defining context to publish safely. | null | null | null | null | null | Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66 |
30,002,263 | OWR-12329-012 | Minimal Ordered Structures Beyond Almost Linearity | Does there exist a minimal ordered structure, in particular a minimal ordered group, that is not almost linear? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66](https://doi.org/10.4171/owr/2013/01)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,013 | 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-12329-012",
"literature-status:partially-solved",
"owr-year:2013"
] | The almost-linear case is classified and no almost-linear minimal field exists, but the existence of a minimal ordered structure that is not almost linear remains unresolved. | [
{
"url": "https://doi.org/10.4064/fm222-2-4",
"label": "Around Podewski's Conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2013/01",
"label": "Model Theory, Oberwolfach Report 01/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/01 | null | null | null | Does there exist a minimal ordered structure, in particular a minimal ordered group, that is not almost linear? | Does there exist a minimal ordered structure, in particular a minimal ordered group, that is not almost linear? | exact | The official report states this existence question explicitly and retains it as open after the almost-linear classification. | null | null | null | null | null | Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66 |
30,002,264 | OWR-12329-013 | Duplicate Minimal Ordered-Structure Question | Does there exist a minimal ordered structure or group that is not almost linear? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66](https://doi.org/10.4171/owr/2013/01)
## Literature review (checked 2026-0... | 3 | open | null | 2,013 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report contains one existence question beyond almost linearity, and this extraction duplicates the preceding canonical record f) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12329-013",
"literature-status:open",
"owr-year:2013"
] | The published treatment proves the almost-linear classification and records this existence question as open; no later proof or counterexample was located. | [
{
"url": "https://doi.org/10.4064/fm222-2-4",
"label": "Around Podewski's Conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2013/01",
"label": "Model Theory, Oberwolfach Report 01/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/01 | null | null | null | null | Does there exist a minimal ordered structure or group that is not almost linear? | unrecoverable | The official report contains one existence question beyond almost linearity, and this extraction duplicates the preceding canonical record from the same report. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Model Theory: Groups, Geometry, and Combinatorics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/01, pp. 5--66 |
30,002,265 | OWR-12330-006 | Maximum Simplices in Euclidean Diameter Graphs | Fix $d\neq3$ and $n\geq d+1$, and let $D$ be the diameter graph of $n$ points in $\mathbb R^d$ whose maximum pairwise distance is $1$. Is the maximum possible number of $(d-1)$-dimensional simplices in $D$ equal to $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** partially solved... | 3 | partially_solved | null | 2,013 | 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-12330-006",
"literature-status:partially-solved",
"owr-year:2013"
] | Schur's diameter-simplex conjecture is proved for dimension three, while the report states it open for all other dimensions and gives only conditional results. | [
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "Graph Theory, Oberwolfach Report 02/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | Fix $d\neq3$ and $n\geq d+1$, and let $D$ be the diameter graph of $n$ points in $\mathbb R^d$ whose maximum pairwise distance is $1$. Is the maximum possible number of $(d-1)$-dimensional simplices in $D$ equal to $n$? | Given n points in \mathbb{R}^d with maximum pairwise distance 1, form the diameter graph by joining pairs at distance 1. For every n\ge d+1, is the maximum number of (d-1)-dimensional simplices in this graph equal to n? | corrected_verified | The official report states Schur’s conjecture and notes that it is proved for dimension three but open for all other dimensions. The clean statement isolates the unresolved range and names the diameter graph to avoid a dangling reference. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,266 | OWR-12330-007 | Disjoint-Edge Bounds for Simple Topological Graphs | Is it true that every simple topological graph with $n$ vertices and no $k$ pairwise disjoint edges has at most $O(kn)$ edges? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** partially solved... | 3 | partially_solved | null | 2,013 | 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-12330-007",
"literature-status:partially-solved",
"owr-year:2013"
] | The desired O(kn) bound remains open for simple topological graphs; primary work gives only polylogarithmic upper bounds, with linear bounds in geometric and special subclasses. | [
{
"url": "https://www.cs.bme.hu/~geza/disjoint.pdf",
"label": "Disjoint Edges in Topological Graphs"
},
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "Graph Theory, Oberwolfach Report 02/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | Is it true that every simple topological graph with $n$ vertices and no $k$ pairwise disjoint edges has at most $O(kn)$ edges? | Is it true that every simple topological graph with n vertices and no k pairwise disjoint edges has at most O(kn) edges? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,267 | OWR-12330-009 | Edge-Disjoint Connected Spanning Subgraphs | For $a_1,a_2\geq1$, does every $(a_1+a_2+2)$-edge-connected graph $G$ have edge-disjoint spanning subgraphs $G_1,G_2$ such that $G_j$ is $a_j$-edge-connected for $j=1,2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** partially solved... | 3 | partially_solved | null | 2,013 | 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-12330-009",
"literature-status:partially-solved",
"owr-year:2013"
] | The first open case with parameters one and two is proved, but the general a1,a2 partitioning conjecture remains open; tree packing supplies only the weaker 2(a1+a2) connectivity condition. | [
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "Graph Theory, Oberwolfach Report 02/2013"
},
{
"url": "https://www.sfu.ca/~mdevos/papers/courteous.pdf",
"label": "Cut Coloring and Circuit Covering"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | For $a_1,a_2\geq1$, does every $(a_1+a_2+2)$-edge-connected graph $G$ have edge-disjoint spanning subgraphs $G_1,G_2$ such that $G_j$ is $a_j$-edge-connected for $j=1,2$? | For a_1,a_2\geq 1, does every (a_1+a_2+2)-edge-connected graph G have edge-disjoint spanning subgraphs G_1,G_2 such that G_j is a_j-edge-connected for j=1,2? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,268 | OWR-12330-010 | Reed’s Chromatic Number Conjecture | Does every graph $G$ satisfy Reed's conjectured bound? Specifically, must
$$\chi(G)\leq\left\lceil\frac12\bigl(\Delta(G)+1+\omega(G)\bigr)\right\rceil$$
hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** partially solved... | 3 | partially_solved | null | 2,013 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | 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 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12330-010",
"literature-status:partially-solved",
"owr-year:2013"
] | Restored the ceiling signs printed in Conjectures 3–6 of OWR 02/2013, pp. 103–104. Without rounding, the five-cycle is an immediate counterexample, so the unrounded transcription is not the intended conjecture.
**What remains.** The corrected integer-colouring conjecture retains its previous unresolved status; the fra... | [
{
"url": "https://doi.org/10.1016/j.jctb.2022.01.009",
"label": "Colouring Graphs with Sparse Neighbourhoods"
},
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "Graph Theory, Oberwolfach Report 02/2013"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussion... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | Does every graph $G$ satisfy Reed's conjectured bound? Specifically, must
$$\chi(G)\leq\left\lceil\frac12\bigl(\Delta(G)+1+\omega(G)\bigr)\right\rceil$$
hold? | Reed's conjecture: every graph G satisfies \chi(G)\leq\tfrac12\bigl(\Delta(G)+1+\omega(G)\bigr). | corrected_verified | Reviewed against the cited source on 2026-09-28; the correction and its scope are explained in the current literature review. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,269 | OWR-12330-011 | Local Clique-Weighted Chromatic Bounds | Does there exist a universal constant $\varepsilon>0$ for which
$$\chi(G)\leq\max_{v\in V(G)}\left\lceil(1-\varepsilon)(d(v)+1)+\varepsilon\omega(G[\widetilde N(v)])\right\rceil$$
holds for every graph $G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** partially solved... | 3 | partially_solved | null | 2,013 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | 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 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12330-011",
"literature-status:partially-solved",
"owr-year:2013"
] | Restored the ceiling signs printed in Conjectures 3–6 of OWR 02/2013, pp. 103–104. Without rounding, the five-cycle is an immediate counterexample, so the unrounded transcription is not the intended conjecture.
**What remains.** The corrected integer-colouring conjecture retains its previous unresolved status; the fra... | [
{
"url": "https://arxiv.org/abs/1109.2112",
"label": "A Local Strengthening of Reed's Conjecture for Quasi-Line Graphs"
},
{
"url": "https://arxiv.org/abs/1208.5188",
"label": "A Superlocal Version of Reed's Conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "Gra... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | Does there exist a universal constant $\varepsilon>0$ for which
$$\chi(G)\leq\max_{v\in V(G)}\left\lceil(1-\varepsilon)(d(v)+1)+\varepsilon\omega(G[\widetilde N(v)])\right\rceil$$
holds for every graph $G$? | Does there exist a universal constant \varepsilon>0 such that every graph G satisfies \chi(G)\leq\max_{v\in V(G)}\bigl((1-\varepsilon)(d(v)+1)+\varepsilon\omega(G[\widetilde N(v)])\bigr)? | corrected_verified | Reviewed against the cited source on 2026-09-28; the correction and its scope are explained in the current literature review. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,270 | OWR-12330-012 | Local and Edgewise Reed Bounds | Conjecturally, every graph $G$ satisfies both
$$\chi(G)\leq\max_{v\in V(G)}\left\lceil\frac12\bigl(d(v)+1+\omega(G[\widetilde N(v)])\bigr)\right\rceil$$
and
$$\chi(G)\leq\max_{uv\in E(G)}\left\lceil\frac12\bigl(\gamma_\ell(u)+\gamma_\ell(v)\bigr)\right\rceil,$$
where $\gamma_\ell(v)=\frac12\bigl(d(v)+1+\omega(G[\wi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,013 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | 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 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12330-012",
"literature-status:open",
"owr-year:2013"
] | Restored the ceiling signs printed in Conjectures 3–6 of OWR 02/2013, pp. 103–104. Without rounding, the five-cycle is an immediate counterexample, so the unrounded transcription is not the intended conjecture.
**What remains.** The corrected integer-colouring conjecture retains its previous unresolved status; the fra... | [
{
"url": "https://doi.org/10.37236/2666",
"label": "Edwards--King, A superlocal version of Reed's conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128"
},
{
"url": "https://huggingface.co/d... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | Conjecturally, every graph $G$ satisfies both
$$\chi(G)\leq\max_{v\in V(G)}\left\lceil\frac12\bigl(d(v)+1+\omega(G[\widetilde N(v)])\bigr)\right\rceil$$
and
$$\chi(G)\leq\max_{uv\in E(G)}\left\lceil\frac12\bigl(\gamma_\ell(u)+\gamma_\ell(v)\bigr)\right\rceil,$$
where $\gamma_\ell(v)=\frac12\bigl(d(v)+1+\omega(G[\wi... | Conjecturally, every graph G satisfies both \chi(G)\leq\max_{v\in V(G)}\tfrac12\bigl(d(v)+1+\omega(G[\widetilde N(v)])\bigr) and \chi(G)\leq\max_{uv\in E(G)}\tfrac12\bigl(\gamma_\ell(u)+\gamma_\ell(v)\bigr), where \gamma_\ell(v)=\tfrac12\bigl(d(v)+1+\omega(G[\widetilde N(v)])\bigr). | corrected_verified | Reviewed against the cited source on 2026-09-28; the correction and its scope are explained in the current literature review. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,271 | OWR-12330-013 | Counterexamples to Averaged Local Fractional-Coloring Bounds | Can
$$\chi_f(G)>\max_{u\in V(G)}\frac{\sum_{v\in\widetilde N(u)}\gamma_\ell(v)}{d(u)+1}$$
hold for some graph $G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | solved | null | 2,013 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | 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 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "resolution",
"evidence": "source_report"
} | Already answered in the original Oberwolfach workshop report (not an open problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12330-013",
"literature-status:open",
"owr-year:2013"
] | The original report answers this question affirmatively on p. 105. Attach $k$ pendant vertices to each vertex of $K_k$. The fractional chromatic number is $k$, while the maximum closed-neighbourhood average in the question is $3k/4+1$, smaller than $k$ for $k\ge5$.
**What remains.** The different clique-averaged conje... | [
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and foll... | 2026-09-28T00:00:00 | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128: https://doi.org/10.4171/owr/2013/02 | https://doi.org/10.4171/owr/2013/02 | null | null | null | Can
$$\chi_f(G)>\max_{u\in V(G)}\frac{\sum_{v\in\widetilde N(u)}\gamma_\ell(v)}{d(u)+1}$$
hold for some graph $G$? | Is there a graph G for which \chi_f(G)>\max_{u\in V(G)}\frac{\sum_{v\in\widetilde N(u)}\gamma_\ell(v)}{d(u)+1}? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,272 | OWR-12330-014 | Color Bounds for Weight-Modified Reed Fractional Coloring | Does the weight-modified Reed fractional-coloring algorithm always use at most $\max_{v\in V(G)}\gamma_\ell(v)$ colors, and can one prove better bounds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,013 | 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-12330-015"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12330-014",
"literature-status:open",
"owr-year:2013"
] | The clique-averaged fractional inequality is stated as Conjecture 7; the report gives no proof and no general resolution was found. | [
{
"url": "https://doi.org/10.37236/2666",
"label": "Edwards--King, clique-averaged conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | Does the weight-modified Reed fractional-coloring algorithm always use at most $\max_{v\in V(G)}\gamma_\ell(v)$ colors, and can one prove better bounds? | Does the weight-modified Reed fractional-colouring algorithm always use at most \max_{v\in V(G)}\gamma_\ell(v) colours, and can one prove better bounds? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,273 | OWR-12330-015 | Duplicate Weight-Modified Reed Coloring Question | Does the weight-modified Reed fractional-colouring algorithm always use at most \max_{v\in V(G)}\gamma_\ell(v) colours, and can one prove better bounds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,013 | 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 record exactly repeats the same-report fractional-coloring question represented canonically by OWR-12330-014. No separate clean stateme) | [
"OWR-12330-014"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12330-015",
"literature-status:open",
"owr-year:2013"
] | Question 2 remains explicitly unanswered in the primary report; the pendant-clique example only rules out a stronger neighborhood-average bound. | [
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.37236/2666",
"label": "Edwards--King, fractional coloring framework"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | null | Does the weight-modified Reed fractional-colouring algorithm always use at most \max_{v\in V(G)}\gamma_\ell(v) colours, and can one prove better bounds? | unrecoverable | This record exactly repeats the same-report fractional-coloring question represented canonically by OWR-12330-014. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,274 | OWR-12330-017 | Structural Invariants for Very Large Graphs | What kinds of numerical data or invariants should be extracted from very large graphs, such as protein-interaction graphs, to describe useful structural information? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,013 | 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-12330-017",
"literature-status:open",
"owr-year:2013"
] | The record is an open-ended methodological question and supplies no definite numeric invariant or proposition that can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | What kinds of numerical data or invariants should be extracted from very large graphs, such as protein-interaction graphs, to describe useful structural information? | What kinds of numerical data or invariants should be extracted from very large graphs, such as protein-interaction graphs, to describe useful structural information? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,275 | OWR-12330-018 | Fork Graphs and Directed Cycle Double Covers | How numerous are fork graphs, and is the directed cycle double cover conjecture as hard for fork graphs as for general cubic bridgeless graphs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,013 | 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-12330-018",
"literature-status:open",
"owr-year:2013"
] | The primary paper proves Jaeger's conjecture only for lean fork-graphs; the general fork-graph claim and directed cycle double cover conjecture remain unresolved. | [
{
"url": "https://arxiv.org/abs/1310.5539",
"label": "Jiménez--Loebl, directed cycle double cover conjecture for fork graphs"
},
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | How numerous are fork graphs, and is the directed cycle double cover conjecture as hard for fork graphs as for general cubic bridgeless graphs? | How rich is the class of fork graphs, and is the directed cycle double cover conjecture as hard for fork graphs as for general cubic bridgeless graphs? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,276 | OWR-12330-019 | The Caccetta–Häggkvist Directed-Cycle Conjecture | Does every $n$-vertex digraph with minimum outdegree at least $r$ contain a directed cycle of length at most $\lceil n/r\rceil$, as conjectured by Caccetta and Häggkvist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128](https://doi.org/10.4171/owr/2013/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,013 | 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-12330-019",
"literature-status:open",
"owr-year:2013"
] | The r=n/3 directed-triangle case remains unresolved; published work provides bounds strictly above 1/3 rather than a proof of the conjectured threshold. | [
{
"url": "https://doi.org/10.1006/jctb.1998.1839",
"label": "Shen, directed triangles in digraphs"
},
{
"url": "https://doi.org/10.4171/owr/2013/02",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/02 | null | null | null | Does every $n$-vertex digraph with minimum outdegree at least $r$ contain a directed cycle of length at most $\lceil n/r\rceil$, as conjectured by Caccetta and Häggkvist? | Caccetta--H\"aggkvist conjecture: every n-vertex digraph with minimum outdegree at least r contains a directed cycle of length at most \lceil n/r\rceil. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Graph Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/02, pp. 67--128 |
30,002,277 | OWR-12331-001 | Optimal SVD-Based Space–Time Focusing Signals | For a two-dimensional acoustic medium containing unknown point scatterers and an array of transducers, let $\phi_{\mathrm{sym}}(\omega)$ be the phase selected by a symmetric singular-value decomposition of the frequency-domain scattering operator for a simple singular value. Does the associated superposition of time-ha... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Electromagnetism and Acoustics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/03, pp. 129--237](https://doi.org/10.4171/owr/2013/03)
## Literature review (checked 2026-08-... | 3 | open | null | 2,013 | 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-12331-001",
"literature-status:open",
"owr-year:2013"
] | The primary report states that no mathematical focusing functional was found, so optimality of the proposed signal is not established. | [
{
"url": "https://www.fresnel.fr/perso/cassier/papers/Oberwolfach-report-2013.pdf",
"label": "Cassier, selective focusing for time-dependent waves"
},
{
"url": "https://doi.org/10.4171/owr/2013/03",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/03 | null | null | null | For a two-dimensional acoustic medium containing unknown point scatterers and an array of transducers, let $\phi_{\mathrm{sym}}(\omega)$ be the phase selected by a symmetric singular-value decomposition of the frequency-domain scattering operator for a simple singular value. Does the associated superposition of time-ha... | For the phase choice \phi_{\mathrm{sym}}(\omega) obtained from the symmetric SVD of the scattering operator, does the resulting time-harmonic superposition yield an optimal spatial and temporal focusing signal? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Computational Electromagnetism and Acoustics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/03, pp. 129--237 |
30,002,278 | OWR-12331-002 | Lyapunov Functions for Three-Dimensional Acoustic PML Systems | For the three-dimensional acoustic perfectly matched layer system with spatially varying damping coefficients, construct a Lyapunov function that is nonincreasing and uniformly controls the acoustic energy; in particular, control the terms created by spatial variation of the damping. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Electromagnetism and Acoustics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/03, pp. 129--237](https://doi.org/10.4171/owr/2013/03)
## Literature review (checked 2026-08-... | 3 | open | null | 2,013 | 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-12331-002",
"literature-status:open",
"owr-year:2013"
] | The report states that spatially varying conductivity creates an uncontrolled term; no general resolution of this problem was located. | [
{
"url": "https://doi.org/10.4171/owr/2013/03",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/03 | null | null | null | For the three-dimensional acoustic perfectly matched layer system with spatially varying damping coefficients, construct a Lyapunov function that is nonincreasing and uniformly controls the acoustic energy; in particular, control the terms created by spatial variation of the damping. | Can the parameters defining the Lyapunov function \eta be chosen so that the energy is bounded by a fixed multiple of \eta? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Computational Electromagnetism and Acoustics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/03, pp. 129--237 |
30,002,279 | OWR-12331-003 | Sign-Definite Variational Formulations of Helmholtz Impedance Problems | Are there other known sign-definite variational formulations of the Helmholtz impedance boundary-value problem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Electromagnetism and Acoustics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/03, pp. 129--237](https://doi.org/10.4171/owr/2013/03)
## Literature review (checked 2026-08-... | 3 | open | null | 2,013 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report asks for other sign-definite formulations and immediately supplies examples and a general transformation, so the extract) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12331-003",
"literature-status:open",
"owr-year:2013"
] | This is an open-ended request for alternative sign-definite formulations, with no uniquely specified proposition or complete canonical answer. | [
{
"url": "https://doi.org/10.4171/owr/2013/03",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/03 | null | null | null | null | Are there other known sign-definite variational formulations of the Helmholtz impedance boundary-value problem? | unrecoverable | The official report asks for other sign-definite formulations and immediately supplies examples and a general transformation, so the extracted sentence is an expository transition rather than a standalone open problem. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Computational Electromagnetism and Acoustics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/03, pp. 129--237 |
30,002,280 | OWR-12333-001 | Kinematic Formulas for DC-Boundary Sets | Do kinematic formulas hold for sets whose boundaries are described by differences of convex functions and for which normal cycles can be constructed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Integral Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/05, pp. 295--342](https://doi.org/10.4171/owr/2013/05)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,013 | 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-12333-001",
"literature-status:open",
"owr-year:2013"
] | The kinematic-formula claim is explicitly presented as a conjecture for a class of sets, while the record omits the class definition and no general proof was found. | [
{
"url": "https://doi.org/10.4171/owr/2013/05",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/05 | null | null | null | Do kinematic formulas hold for sets whose boundaries are described by differences of convex functions and for which normal cycles can be constructed? | Conjecture: kinematic formulas are valid for sets whose boundaries are described by differences of convex functions, for which normal cycles can be constructed. | 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 | Integral Geometry and its Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/05, pp. 295--342 |
30,002,281 | OWR-12334-004 | Motivic Stabilization of Symmetric Powers | Motivic stabilization conjecture: If $X$ is geometrically irreducible, then
$$\frac{[\operatorname{Sym}^nX]}{\mathbb L^{n\dim X}}$$
tends to a limit as $n\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli Spaces in Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/06, pp. 343--392](https://doi.org/10.4171/owr/2013/06)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,013 | 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-12334-004",
"literature-status:open",
"owr-year:2013"
] | The Vakil--Wood motivic stabilization conjecture remains unresolved in general; related nonstabilization results do not settle this exact normalized limit. | [
{
"url": "https://arxiv.org/abs/1208.3166",
"label": "Vakil--Wood, discriminants in the Grothendieck ring"
},
{
"url": "https://arxiv.org/abs/1209.4708",
"label": "Litt, symmetric powers do not stabilize"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/06 | null | null | null | Motivic stabilization conjecture: If $X$ is geometrically irreducible, then
$$\frac{[\operatorname{Sym}^nX]}{\mathbb L^{n\dim X}}$$
tends to a limit as $n\to\infty$. | Motivic stabilization conjecture: if X is geometrically irreducible, then [\operatorname{Sym}^n X]/\mathbb L^{n\dim X} tends to a limit as n\to\infty. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Moduli Spaces in Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/06, pp. 343--392 |
30,002,282 | OWR-12334-005 | Dual-Graph Generation of Tautological Relations | Let $\mathcal S_{g,n}$ be the strata algebra and let $\mathcal R\subset\mathcal S_{g,n}$ be the ideal generated by pullbacks and pushforwards of the dual-graph relations $R(g,n,r)$. Is $\mathcal R$ exactly the kernel of the natural surjection $\mathcal S_{g,n}\to R^*(\overline{\mathcal M}_{g,n})$? Do the analogous comp... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli Spaces in Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/06, pp. 343--392](https://doi.org/10.4171/owr/2013/06)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,013 | 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-12334-005",
"literature-status:partially-solved",
"owr-year:2013"
] | Janda proves Pixton's conjectural relations are tautological Chow relations, but whether they generate all tautological relations remains open. | [
{
"url": "https://doi.org/10.14231/AG-2017-018",
"label": "Janda, relations via equivariant Gromov--Witten theory"
},
{
"url": "https://websites.umich.edu/~pixton/papers/conjrel.pdf",
"label": "Pixton, conjectural tautological relations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/06 | null | null | null | Let $\mathcal S_{g,n}$ be the strata algebra and let $\mathcal R\subset\mathcal S_{g,n}$ be the ideal generated by pullbacks and pushforwards of the dual-graph relations $R(g,n,r)$. Is $\mathcal R$ exactly the kernel of the natural surjection $\mathcal S_{g,n}\to R^*(\overline{\mathcal M}_{g,n})$? Do the analogous comp... | Conjecture: the ideal R generated by the stated dual-graph contributions is the ideal of tautological relations on \mathcal M_{g,n}; its restrictions give analogous conjectures, and all known relations are linear combinations of these. | corrected_verified | The official report defines the strata algebra and the ideal generated by the dual-graph relations before conjecturing that the ideal gives all tautological relations. Those missing definitions and the natural kernel formulation were restored. | null | null | null | null | null | Moduli Spaces in Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/06, pp. 343--392 |
30,002,283 | OWR-12334-007 | Classification Problems for Del Pezzo Fibrations | For del Pezzo fibrations, are there fibrations with square-free discriminant of height two and with height six and maximal monodromy; are those of a given height irreducible; how can one characterize their Prym varieties; and, in the height-twelve example $X\to\mathbb P^1$, are there sections other than the canonical s... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli Spaces in Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/06, pp. 343--392](https://doi.org/10.4171/owr/2013/06)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,013 | 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-12334-007",
"literature-status:open",
"owr-year:2013"
] | Later work classifies many heights and components of quartic del Pezzo fibrations, but the extracted multi-part question, especially the Prym-variety characterization, is not fully resolved. | [
{
"url": "https://doi.org/10.4171/owr/2013/06",
"label": "Oberwolfach Report 2013"
},
{
"url": "https://arxiv.org/abs/1301.7270",
"label": "Hassett--Tschinkel, Quartic del Pezzo surfaces"
},
{
"url": "https://math.nyu.edu/~tschinke/papers/yuri/13noheighttwo/noheighttwo16.pdf",
"label... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/06 | null | null | null | For del Pezzo fibrations, are there fibrations with square-free discriminant of height two and with height six and maximal monodromy; are those of a given height irreducible; how can one characterize their Prym varieties; and, in the height-twelve example $X\to\mathbb P^1$, are there sections other than the canonical s... | For del Pezzo fibrations, are there fibrations with square-free discriminant of height two and with height six and maximal monodromy; are those of a given height irreducible; how can one characterize their Prym varieties; and, in the height-twelve example X\to\mathbb P^1, are there sections other than the canonical sec... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Moduli Spaces in Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/06, pp. 343--392 |
30,002,284 | OWR-12334-010 | Global Quotient Presentations of Algebraic Stacks | Which algebraic stacks are global quotient stacks, and in particular is every separated Deligne–Mumford stack a global quotient stack? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli Spaces in Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/06, pp. 343--392](https://doi.org/10.4171/owr/2013/06)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,013 | 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-12334-010",
"literature-status:open",
"owr-year:2013"
] | The extracted text is contextual prose rather than a complete mathematical assertion; it does not identify a falsifiable claim whose resolution can be verified, so it remains open under the queue rule for unclear statements. | [
{
"url": "https://doi.org/10.4171/owr/2013/06",
"label": "Oberwolfach Report 2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/06 | null | null | null | Which algebraic stacks are global quotient stacks, and in particular is every separated Deligne–Mumford stack a global quotient stack? | Which algebraic stacks are global quotient stacks, and in particular is every separated Deligne--Mumford stack a global quotient stack? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Moduli Spaces in Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/06, pp. 343--392 |
30,002,285 | OWR-12334-013 | Cohomological Stability for Moduli of Curves with Group Actions | Fix a finite group $G$ and a topological action type $\rho$ on curves, and let $g'$ denote the genus of the quotient curve. Do the cohomology groups of the corresponding moduli spaces $\mathcal M_{g,G,\rho}$ stabilize as $g'\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli Spaces in Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/06, pp. 343--392](https://doi.org/10.4171/owr/2013/06)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,013 | 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-12334-013",
"literature-status:open",
"owr-year:2013"
] | Component stabilization is known, and recent work proves homology stabilization only for a framed variant with at most one branch point; the general cohomology-stabilization conjecture remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2013/06",
"label": "Oberwolfach Report 2013"
},
{
"url": "https://arxiv.org/abs/2508.10199",
"label": "Catanese--Loenne--Perroni, Genus stabilization"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/06 | null | null | null | Fix a finite group $G$ and a topological action type $\rho$ on curves, and let $g'$ denote the genus of the quotient curve. Do the cohomology groups of the corresponding moduli spaces $\mathcal M_{g,G,\rho}$ stabilize as $g'\to\infty$? | Conjecture: for sufficiently large g', the cohomology groups of the moduli spaces \mathcal M_{g,G,\rho} stabilize. | corrected_verified | The official report identifies the moduli spaces as those of curves with a fixed finite-group action type and identifies the stabilization parameter as the quotient-curve genus. That context was restored and the extracted conjecture label was removed. | null | null | null | null | null | Moduli Spaces in Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/06, pp. 343--392 |
30,002,286 | OWR-12336-001 | Coincidence of Supports and Maxima in Infinity-Eigenvalue Limits | For the limiting infinity-eigenvalue and optimal-transport problem, is $\operatorname{spt}(f_\infty)=\operatorname*{argmax}u_\infty=\operatorname*{argmax}d_\Omega$, rather than merely $\operatorname{spt}(f_\infty)\subseteq\operatorname*{argmax}u_\infty\subseteq\operatorname*{argmax}d_\Omega$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The p-Laplacian Operator and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/08, pp. 433--482](https://doi.org/10.4171/owr/2013/08)
## Literature review (chec... | 3 | open | null | 2,013 | 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-12336-001",
"literature-status:open",
"owr-year:2013"
] | The extracted record contains only an announcement that an open problem follows and no complete mathematical assertion; it is therefore unresolved under the queue rule for unclear statements. | [
{
"url": "https://doi.org/10.4171/owr/2013/08",
"label": "Oberwolfach Report 2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/08 | null | null | null | For the limiting infinity-eigenvalue and optimal-transport problem, is $\operatorname{spt}(f_\infty)=\operatorname*{argmax}u_\infty=\operatorname*{argmax}d_\Omega$, rather than merely $\operatorname{spt}(f_\infty)\subseteq\operatorname*{argmax}u_\infty\subseteq\operatorname*{argmax}d_\Omega$? | For the limiting infinity-eigenvalue/optimal-transport problem, prove that spt(f_{\infty})=argmax u_{\infty}=argmax d_{\Omega}, rather than only the inclusions spt(f_{\infty})\subseteq argmax u_{\infty}\subseteq argmax d_{\Omega}. | corrected_verified | The official report concludes the contribution by explicitly asking whether both displayed inclusions are equalities. | null | null | null | null | null | Mini-Workshop: The p-Laplacian Operator and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/08, pp. 433--482 |
30,002,287 | OWR-12336-003 | Discreteness of the Dirichlet $p$-Laplacian Spectrum | Is the spectrum of the Dirichlet $p$-Laplacian on a bounded domain discrete? In particular, do higher eigenvalues have finite multiplicity, and is there at least one number above the second eigenvalue that is not an eigenvalue? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The p-Laplacian Operator and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/08, pp. 433--482](https://doi.org/10.4171/owr/2013/08)
## Literature review (chec... | 3 | open | null | 2,013 | 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-12336-003",
"literature-status:open",
"owr-year:2013"
] | The standard Dirichlet p-Laplacian spectrum is still not known to be discrete on general bounded domains; the known non-discrete example concerns the distinct (p,q)-problem with q<p. | [
{
"url": "https://doi.org/10.4171/owr/2013/08",
"label": "Oberwolfach Report 2013"
},
{
"url": "https://doi.org/10.1016/j.na.2005.05.056",
"label": "Le, Eigenvalue problems for the p-Laplacian"
},
{
"url": "https://arxiv.org/abs/1707.00867",
"label": "Brasco--Franzina, non-discrete (... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/08 | null | null | null | Is the spectrum of the Dirichlet $p$-Laplacian on a bounded domain discrete? In particular, do higher eigenvalues have finite multiplicity, and is there at least one number above the second eigenvalue that is not an eigenvalue? | Determine whether the spectrum of the Dirichlet p-Laplacian on a bounded domain is discrete; in particular, determine whether higher eigenvalues have finite multiplicity and whether some numbers above the second eigenvalue are not eigenvalues. | corrected_verified | The official report calls discreteness the main open problem and explicitly records both weaker unknown consequences. | null | null | null | null | null | Mini-Workshop: The p-Laplacian Operator and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/08, pp. 433--482 |
30,002,288 | OWR-12336-004 | Representation and Limits of Fractional Infinity Eigenfunctions | For the fractional infinity-eigenvalue problem, does $u(x)=\delta(x)^\alpha/(\delta(x)^\alpha+\varrho_1(x)^\alpha)$ produce every first eigenfunction when $\varrho_1(x)=\operatorname{dist}(x,\Gamma_1)$ and $\Gamma_1\subseteq\Gamma$? Is the maximal solution, with $\Gamma_1=\Gamma$, the limit of the fractional $p$-eigenf... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The p-Laplacian Operator and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/08, pp. 433--482](https://doi.org/10.4171/owr/2013/08)
## Literature review (chec... | 3 | open | null | 2,013 | 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-12336-004",
"literature-status:open",
"owr-year:2013"
] | Lindgren--Lindqvist explicitly leave open both completeness of the \Gamma_1-representation of first infinity eigenfunctions and convergence of fractional p-eigenfunctions to the maximal solution. | [
{
"url": "https://doi.org/10.4171/owr/2013/08",
"label": "Oberwolfach Report 2013"
},
{
"url": "https://doi.org/10.1007/s00526-013-0600-1",
"label": "Lindgren--Lindqvist, Fractional Eigenvalues"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/08 | null | null | null | For the fractional infinity-eigenvalue problem, does $u(x)=\delta(x)^\alpha/(\delta(x)^\alpha+\varrho_1(x)^\alpha)$ produce every first eigenfunction when $\varrho_1(x)=\operatorname{dist}(x,\Gamma_1)$ and $\Gamma_1\subseteq\Gamma$? Is the maximal solution, with $\Gamma_1=\Gamma$, the limit of the fractional $p$-eigenf... | For the fractional infinity-eigenvalue problem, determine whether the formula u(x)=\delta(x)^\alpha/(\delta(x)^\alpha+\rho_1(x)^\alpha) produces all first eigenfunctions, and whether the maximal solution with \Gamma_1=\Gamma is the limit of the fractional p-eigenfunctions as p\to\infty. | corrected_verified | The official report explicitly poses both questions and supplies the definitions of the high-ridge subset and its distance function. | null | null | null | null | null | Mini-Workshop: The p-Laplacian Operator and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/08, pp. 433--482 |
30,002,289 | OWR-12336-007 | Endpoint Regularity for $p$-Laplacian Gradients | For $p$-harmonic functions in dimensions $n\geq3$, can one construct higher-dimensional analogues of the planar least-regular examples and determine their optimal gradient regularity? In particular, does $V(\nabla u)=|\nabla u|^{(p-2)/2}\nabla u$ belong locally to $C^{1/2}$ in every dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The p-Laplacian Operator and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/08, pp. 433--482](https://doi.org/10.4171/owr/2013/08)
## Literature review (chec... | 3 | open | null | 2,013 | 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-12336-007",
"literature-status:open",
"owr-year:2013"
] | The planar optimal exponent is known, but the sharp gradient Holder exponent and matching higher-dimensional extremals for n\ge3 remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2013/08",
"label": "Oberwolfach Report 2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/08 | null | null | null | For $p$-harmonic functions in dimensions $n\geq3$, can one construct higher-dimensional analogues of the planar least-regular examples and determine their optimal gradient regularity? In particular, does $V(\nabla u)=|\nabla u|^{(p-2)/2}\nabla u$ belong locally to $C^{1/2}$ in every dimension? | Determine the endpoint and finer regularity of p-Laplacian solutions as q\to\infty, including whether V(\nabla u)=|\nabla u|^{(p-2)/2}\nabla u belongs locally to C^{1/2} in every dimension. | corrected_verified | The official open-problem session asks for higher-dimensional analogues of the planar construction and explicitly conjectures local $C^{1/2}$ regularity of $V(\nabla u)$. | null | null | null | null | null | Mini-Workshop: The p-Laplacian Operator and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/08, pp. 433--482 |
30,002,290 | OWR-12337-001 | The Hyperplane Slicing Conjecture | Hyperplane slicing conjecture: There exists a universal constant $c>0$ such that every convex body $K\subset\mathbb R^n$ of volume $1$ has a hyperplane section of $(n-1)$-dimensional volume at least $c$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Ito Chaos Expansions and Stochastic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/09,... | 3 | solved | null | 2,013 | 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": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] - **Replace both literature notes**; that of `OWR-12337-001` wrongly calls the statement a fragment. | [
"owr",
"oberwolfach-reports",
"OWR-12337-001",
"literature-status:open",
"owr-year:2013"
] | The extracted record is only the fragment conjecture and does not state a falsifiable mathematical claim; it remains open under the queue rule for unclear statements. | [
{
"url": "https://doi.org/10.4171/owr/2013/09",
"label": "Oberwolfach Report 2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/09 | null | null | null | Hyperplane slicing conjecture: There exists a universal constant $c>0$ such that every convex body $K\subset\mathbb R^n$ of volume $1$ has a hyperplane section of $(n-1)$-dimensional volume at least $c$. | Hyperplane (slicing) conjecture: prove that there is a universal c>0 such that every convex body K\subset\mathbb{R}^n of volume 1 has a hyperplane section of (n-1)-volume at least c. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Ito Chaos Expansions and Stochastic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/09, pp. 483--520 |
30,002,291 | OWR-12337-002 | Variation Limits for Pure-Jump Semimartingales | Let
$$X_t=X_0+\int_{-\infty}^t g(t-s)\,dL_s,$$
where $L$ is a pure-jump Lévy process, $g(x)=x^\alpha f(x)$ with $0<\alpha<1/2$, and $f$ is smooth with exponential decay and $f(0)\neq0$. For
$$V_t^n(X)=\sum_{i=1}^{\lfloor t/\Delta_n\rfloor}|X_{i\Delta_n}-X_{(i-1)\Delta_n}|^2,$$
the compound-Poisson case satisfies
$... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Ito Chaos Expansions and Stochastic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/09,... | 3 | open | null | 2,013 | 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-12337-002",
"literature-status:open",
"owr-year:2013"
] | Subsequent work proves limit theorems for broad Levy-driven moving-average classes, but not the stated result for a general pure-jump semimartingale driver; the conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2013/09",
"label": "Oberwolfach Report 2013"
},
{
"url": "https://arxiv.org/abs/1506.06679",
"label": "Basse-O'Connor--Lachieze-Rey--Podolskij, Levy-driven moving averages"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/09 | null | null | null | Let
$$X_t=X_0+\int_{-\infty}^t g(t-s)\,dL_s,$$
where $L$ is a pure-jump Lévy process, $g(x)=x^\alpha f(x)$ with $0<\alpha<1/2$, and $f$ is smooth with exponential decay and $f(0)\neq0$. For
$$V_t^n(X)=\sum_{i=1}^{\lfloor t/\Delta_n\rfloor}|X_{i\Delta_n}-X_{(i-1)\Delta_n}|^2,$$
the compound-Poisson case satisfies
$... | Prove that the displayed jump-driven asymptotic limit for the variation statistic remains valid for a sufficiently general pure-jump semimartingale driver under suitable hypotheses. | corrected_verified | The official report supplies the omitted variation statistic, moving-average hypotheses, and compound-Poisson stable limit before conjecturing its extension to general pure-jump semimartingale drivers. The full source formula was restored. | null | null | null | null | null | Mini-Workshop: Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Ito Chaos Expansions and Stochastic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/09, pp. 483--520 |
30,002,292 | OWR-12338-001 | Finite-Time Perfect Mixing Under Power Constraints | Determine whether finite-time perfect mixing can occur for a two-dimensional incompressible flow subject to a finite power constraint. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geophysical Fluid Dynamics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/10, pp. 521--577](https://doi.org/10.4171/owr/2013/10)
## Literature review (checked 2026-08-21)
**Status:** o... | 3 | solved | null | 2,013 | 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 | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no)**. E. Lunasin (OWR 10/2013, p. 550) calls finite-time perfect mixing by 2D incompressible stirring under finite power (enstrophy) open; Lunasin–Lin–Novikov–Mazzucato–Doering (2012) conjecture an exponential lower bound on the H⁻¹ mix-norm. | [
"owr",
"oberwolfach-reports",
"OWR-12338-001",
"literature-status:open",
"owr-year:2013"
] | The finite-power exponential lower-bound problem remains a conjecture; later instantaneous optimization results under related constraints do not prove the global finite-power statement. | [
{
"url": "https://doi.org/10.4171/owr/2013/10",
"label": "Oberwolfach Report 2013"
},
{
"url": "https://doi.org/10.1063/1.4752098",
"label": "Lunasin--Lin--Novikov--Mazzucato--Doering, Optimal mixing and stirring"
},
{
"url": "https://arxiv.org/abs/2401.05684",
"label": "Zhu et al., ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/10 | null | null | null | Determine whether finite-time perfect mixing can occur for a two-dimensional incompressible flow subject to a finite power constraint. | Determine whether finite-time perfect mixing can occur for a two-dimensional incompressible flow subject to a finite power constraint. | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geophysical Fluid Dynamics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/10, pp. 521--577 |
30,002,293 | OWR-12338-002 | Long-Time Navier–Stokes Flow in Exterior Domains | Clarify the large-time behavior of solutions of the Navier–Stokes initial-value problem in a two-dimensional exterior domain, including the associated Oseen evolution. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geophysical Fluid Dynamics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/10, pp. 521--577](https://doi.org/10.4171/owr/2013/10)
## Literature review (checked 2026-08-21)
**Status:** o... | 3 | open | null | 2,013 | 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-12338-002",
"literature-status:open",
"owr-year:2013"
] | The large-time behavior of the two-dimensional exterior-domain Oseen/Navier--Stokes initial-value problem is still explicitly described as open, including for sufficiently small nonzero Oseen parameter. | [
{
"url": "https://doi.org/10.4171/owr/2013/10",
"label": "Oberwolfach Report 2013"
},
{
"url": "https://eprints.lib.hokudai.ac.jp/repo/huscap/all/68077/tech153.pdf",
"label": "Hishida, Decay estimates of the Oseen flow"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/10 | null | null | null | Clarify the large-time behavior of solutions of the Navier–Stokes initial-value problem in a two-dimensional exterior domain, including the associated Oseen evolution. | Clarify the large-time behavior of solutions of the Navier--Stokes initial-value problem in a two-dimensional exterior domain, including the associated Oseen evolution. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geophysical Fluid Dynamics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/10, pp. 521--577 |
30,002,294 | OWR-12338-003 | Duplicate Einstein-Type Fluid-Dynamics Question | Determine whether an Einstein-type mass--energy relation can be obtained for localized objects in fluid dynamics. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geophysical Fluid Dynamics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/10, pp. 521--577](https://doi.org/10.4171/owr/2013/10)
## Literature review (checked 2026-08-21)
**Status:** o... | 3 | open | null | 2,013 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report poses one question about deriving an Einstein-type law for localized fluid-mechanical objects and then cites concentrati) | [
"OWR-12338-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12338-003",
"literature-status:open",
"owr-year:2013"
] | The record asks a broad Einstein-type law for localized fluid objects, without specifying a theorem or precise model; the cited Klein--Gordon analogue does not resolve this fluid-mechanics question. | [
{
"url": "https://doi.org/10.4171/owr/2013/10",
"label": "Oberwolfach Report 2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/10 | null | null | null | null | Determine whether an Einstein-type mass--energy relation can be obtained for localized objects in fluid dynamics. | unrecoverable | The official report poses one question about deriving an Einstein-type law for localized fluid-mechanical objects and then cites concentrating two- and three-dimensional Euler flows as illustrations. This record is the less specific restatement of OWR-12338-004. No separate clean statement is promoted; the original rec... | null | null | null | null | null | Geophysical Fluid Dynamics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/10, pp. 521--577 |
30,002,295 | OWR-12338-004 | Einstein-Type Dynamics for Concentrated Euler Flows | Derive an analogue of Einstein's formula for the dynamics of localized objects in a fluid-mechanics framework, for example through concentrating solutions of the Euler equations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geophysical Fluid Dynamics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/10, pp. 521--577](https://doi.org/10.4171/owr/2013/10)
## Literature review (checked 2026-08-21)
**Status:** o... | 3 | open | null | 2,013 | 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... | [
"OWR-12338-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12338-004",
"literature-status:open",
"owr-year:2013"
] | No general derivation of an Einstein-type effective inertial relation for localized objects in fluid mechanics was identified; the question remains open as posed. | [
{
"url": "https://doi.org/10.4171/owr/2013/10",
"label": "Oberwolfach Report 2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/10 | null | null | null | Derive an analogue of Einstein's formula for the dynamics of localized objects in a fluid-mechanics framework, for example through concentrating solutions of the Euler equations. | Derive an analogue of Einstein's formula for the dynamics of localized objects in a fluid-mechanics framework, for example through concentrating solutions of the Euler equations. | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geophysical Fluid Dynamics (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/10, pp. 521--577 |
30,002,296 | OWR-12339-001 | Generator Bounds for Multivariate Tight Wavelet Frames | Obtain estimates for the number of generators needed by multivariate tight wavelet frames. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655](https://doi.org/10.4171/owr/2013/11)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,013 | 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-12339-001",
"literature-status:partially-solved",
"owr-year:2013"
] | Charina--Putinar--Scheiderer--Stockler solve the bivariate UEP existence question, while later work improves upper bounds and constructions for generator counts without providing a complete multivariate estimate. | [
{
"url": "https://doi.org/10.4171/owr/2013/11",
"label": "Oberwolfach Report 2013"
},
{
"url": "https://doi.org/10.1007/s00365-013-9191-5",
"label": "Charina--Putinar--Scheiderer--Stockler, Multivariate tight wavelet frames"
},
{
"url": "https://doi.org/10.1016/j.acha.2014.09.003",
"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/11 | null | null | null | Obtain estimates for the number of generators needed by multivariate tight wavelet frames. | Obtain estimates for the number of generators needed by multivariate tight wavelet frames. | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655 |
30,002,297 | OWR-12339-003 | Frame Property of the Gaussian Gabor System on $\Lambda_3$ | Let $g$ be the normalized Gaussian on $\mathbb R^2$, let
$$A_3=\begin{pmatrix}1&2/5\\0&\sqrt{21}/5\end{pmatrix},\qquad \Lambda_3=A_3(\mathbb Z+i\mathbb Z)^2,$$
and let $G(g,\Lambda_3)$ be the associated Gabor system. Is $G(g,\Lambda_3)$ a frame for $L^2(\mathbb R^2)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655](https://doi.org/10.4171/owr/2013/11)
## Literature review (checked 2026-08-... | 3 | open | null | 2,013 | 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-12339-003",
"literature-status:open",
"owr-year:2013"
] | The specific two-dimensional complex-lattice Gaussian system G(g,\Lambda_3) was conjectured to be a frame in the report, and no reliable proof or counterexample for that exact lattice was found. | [
{
"url": "https://doi.org/10.4171/owr/2013/11",
"label": "Oberwolfach Report 2013"
},
{
"url": "https://ems.press/content/serial-article-files/46446",
"label": "Structured Function Systems and Applications"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/11 | null | null | null | Let $g$ be the normalized Gaussian on $\mathbb R^2$, let
$$A_3=\begin{pmatrix}1&2/5\\0&\sqrt{21}/5\end{pmatrix},\qquad \Lambda_3=A_3(\mathbb Z+i\mathbb Z)^2,$$
and let $G(g,\Lambda_3)$ be the associated Gabor system. Is $G(g,\Lambda_3)$ a frame for $L^2(\mathbb R^2)$? | Prove or disprove that the Gabor system G(g,\Lambda_3) is a frame. | corrected_verified | The normalized Gaussian, generating matrix, complex lattice, and ambient Hilbert space omitted by the extraction were restored from the official report. | null | null | null | null | null | Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655 |
30,002,298 | OWR-12339-004 | Polyhedra with Vertex-Factored Fantappiè Denominators | Give a geometric characterization of compact polyhedra $P$ whose Fantappiè-transform denominator is $\Omega(u)=\prod_{v\in V(P)}(1-\langle v,u\rangle)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655](https://doi.org/10.4171/owr/2013/11)
## Literature review (checked 2026-08-... | 3 | open | null | 2,013 | 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-12339-004",
"literature-status:open",
"owr-year:2013"
] | The extracted record asks for a geometric characterization of a moment-generating-function case and supplies contextual polyhedral observations, but no complete characterization is stated or verified. | [
{
"url": "https://doi.org/10.4171/owr/2013/11",
"label": "Oberwolfach Report 2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/11 | null | null | null | Give a geometric characterization of compact polyhedra $P$ whose Fantappiè-transform denominator is $\Omega(u)=\prod_{v\in V(P)}(1-\langle v,u\rangle)$. | Give a geometric characterization of compact polyhedra P for which the Fantappiè-transform denominator satisfies \Omega(u)=\prod_{v\in V(P)}(1-\langle v,u\rangle). | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655 |
30,002,299 | OWR-12339-005 | Coefficients in Signed Simplex Decompositions | For the signed simplex decomposition of the uniform measure on $P$, is every nonzero coefficient $\alpha_T$ always $\pm1$? If not, characterize the possible coefficients. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655](https://doi.org/10.4171/owr/2013/11)
## Literature review (checked 2026-08-... | 3 | open | null | 2,013 | 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-12339-005",
"literature-status:open",
"owr-year:2013"
] | The extracted question is the report's Question 2 about whether all nonzero simplex coefficients in the signed polyhedral measure decomposition are always\ \pm 1; the report gives no proof, counterexample, or later resolution found in the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2013/11",
"label": "Oberwolfach Report 11/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/11 | null | null | null | For the signed simplex decomposition of the uniform measure on $P$, is every nonzero coefficient $\alpha_T$ always $\pm1$? If not, characterize the possible coefficients. | For the signed simplex decomposition of the uniform measure on P, determine whether every nonzero coefficient \alpha_T is always \pm1; if not, characterize the possible coefficients. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655 |
30,002,300 | OWR-12339-006 | Weakening General Position in Signed Simplex Representations | Can the requirement that every $(d+2)$-subset of the vertex set $V$ affinely span $\mathbb R^d$ be removed or weakened while retaining a signed representation of a compact polyhedron’s uniform measure by uniform measures on $(d+1)$-vertex simplices? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655](https://doi.org/10.4171/owr/2013/11)
## Literature review (checked 2026-08-... | 3 | open | null | 2,013 | 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-12339-006",
"literature-status:open",
"owr-year:2013"
] | The report poses removal or weakening of the affine spanning hypothesis as an explicit unresolved question; subsequent checked sources establish related positive and negative sum-of-squares results but do not settle this formulation. | [
{
"url": "https://doi.org/10.4171/owr/2013/11",
"label": "Oberwolfach Report 11/2013"
},
{
"url": "https://doi.org/10.1007/s00229-006-0630-5",
"label": "Scheiderer 2006"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/11 | null | null | null | Can the requirement that every $(d+2)$-subset of the vertex set $V$ affinely span $\mathbb R^d$ be removed or weakened while retaining a signed representation of a compact polyhedron’s uniform measure by uniform measures on $(d+1)$-vertex simplices? | Determine whether the condition that every (d+2)-subset of V affinely spans \mathbb{R}^d can be removed or weakened in the signed simplex representation theorem. | corrected_verified | The official report supplies the signed simplex representation to which the extracted theorem reference pointed. The clean statement restores the conclusion while preserving the source’s question about weakening its general-position hypothesis. | null | null | null | null | null | Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655 |
30,002,301 | OWR-12339-007 | Dual-Frame Completion of Bessel Wavelet Systems | Given two Bessel dyadic wavelet systems generated by $\psi_1$ and $\widetilde\psi_1$, can $\psi_2$ and $\widetilde\psi_2$ always be chosen so that the two two-generator systems are dual frames? Equivalently, does Han's conjectured tight-frame completion hold for every sufficiently large bound $K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655](https://doi.org/10.4171/owr/2013/11)
## Literature review (checked 2026-08-... | 3 | open | null | 2,013 | 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-12339-007",
"literature-status:open",
"owr-year:2013"
] | The unrestricted extension of arbitrary wavelet Bessel sequences to dual wavelet frames remains open; later work proves restricted extensions, especially under Fourier support or multiresolution hypotheses, not the stated general claim. | [
{
"url": "https://doi.org/10.1016/j.indag.2018.01.009",
"label": "Bessel sequences, wavelet frames, duals and extensions"
},
{
"url": "https://doi.org/10.4153/CMB-2013-015-9",
"label": "On Parseval wavelet frames with two or three generators"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/11 | null | null | null | Given two Bessel dyadic wavelet systems generated by $\psi_1$ and $\widetilde\psi_1$, can $\psi_2$ and $\widetilde\psi_2$ always be chosen so that the two two-generator systems are dual frames? Equivalently, does Han's conjectured tight-frame completion hold for every sufficiently large bound $K$? | Given two Bessel dyadic wavelet systems generated by \psi_1 and \widetilde{\psi}_1, determine whether \psi_2 and \widetilde{\psi}_2 can always be chosen so the two two-generator systems are dual frames; equivalently, test Han's conjectured tight-frame completion for every sufficiently large bound K. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655 |
30,002,302 | OWR-12339-008 | Trigonometric Factorization of Positive Matrix Polynomials | For every positive-semidefinite symmetric $m\times m$ trigonometric matrix polynomial $M$ on the two-dimensional torus, is $M=S^{\mathsf T}S$ for some trigonometric matrix polynomial $S$? The case $d=2$ and $m\geq2$ is open. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655](https://doi.org/10.4171/owr/2013/11)
## Literature review (checked 2026-08-... | 3 | open | null | 2,013 | 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-12339-008",
"literature-status:open",
"owr-year:2013"
] | Fejer--Riesz factorization is known in one variable and in the scalar two-variable case, while the matrix-valued two-dimensional case with matrix size at least two remains unresolved in the checked primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2013/11",
"label": "Oberwolfach Report 11/2013"
},
{
"url": "https://doi.org/10.1090/S0002-9947-99-02522-2",
"label": "Scheiderer 1999"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/11 | null | null | null | For every positive-semidefinite symmetric $m\times m$ trigonometric matrix polynomial $M$ on the two-dimensional torus, is $M=S^{\mathsf T}S$ for some trigonometric matrix polynomial $S$? The case $d=2$ and $m\geq2$ is open. | For every positive-semidefinite symmetric m\times m trigonometric matrix polynomial M on the two-dimensional torus, determine whether M=S^{\mathsf T}S for some trigonometric matrix polynomial S; the case d=2 and m\ge2 is open. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655 |
30,002,303 | OWR-12339-009 | Muckenhoupt Thresholds for Integer-Translate Schauder Bases | Let $\psi\in L^2(\mathbb R)$, let $B_\psi=\{\psi(\cdot-k):k\in\mathbb Z\}$ be a Schauder basis for its closed linear span, and set
$$p_\psi(\xi)=\sum_{k\in\mathbb Z}|\widehat\psi(\xi+k)|^2,\qquad q_\psi=\inf\{p>1:p_\psi\text{ is an }A_p\text{-weight}\}.$$
For each $q$ with $1\leq q<2$, which properties of $B_\psi$ ch... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655](https://doi.org/10.4171/owr/2013/11)
## Literature review (checked 2026-08-... | 3 | open | null | 2,013 | 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-12339-009",
"literature-status:open",
"owr-year:2013"
] | For translate Schauder bases the quantity q subscript psi is controlled by an A sub 2 weight, but no characterization of bases realizing each prescribed q in the interval from 1 to 2 was found. | [
{
"url": "https://doi.org/10.4171/owr/2013/11",
"label": "Oberwolfach Report 11/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/11 | null | null | null | Let $\psi\in L^2(\mathbb R)$, let $B_\psi=\{\psi(\cdot-k):k\in\mathbb Z\}$ be a Schauder basis for its closed linear span, and set
$$p_\psi(\xi)=\sum_{k\in\mathbb Z}|\widehat\psi(\xi+k)|^2,\qquad q_\psi=\inf\{p>1:p_\psi\text{ is an }A_p\text{-weight}\}.$$
For each $q$ with $1\leq q<2$, which properties of $B_\psi$ ch... | For a Schauder basis of integer translates B_\psi with q_\psi=\inf\{p\ge1:p_\psi is an A_p-weight\}, characterize the properties of B_\psi that realize each q\in[1,2). | corrected_verified | The official report defines the translate system, its closed span, the periodized Fourier weight, and the strict inequality in the infimum. The clean statement restores those definitions and removes the malformed half-open interval notation. | null | null | null | null | null | Structured Function Systems and Applications (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/11, pp. 579--655 |
30,002,304 | OWR-12340-001 | Historical Foundations of Mathematical Classification | Explain how the classificatory scheme for mathematics developed, and whether MSC 2010's pure/applied distinction reflects a natural historical organization of mathematical branches. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733](https://doi.org/10.4... | 3 | open | null | 2,013 | 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 | Early-Modern Mixed Mathematics workshop report (16th-century historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12340-001",
"literature-status:open",
"owr-year:2013"
] | This is a historiographical research question about the development of classification schemes and the pure--applied distinction; the checked literature provides competing historical analyses, not a completed explanatory account. | [
{
"url": "https://doi.org/10.4171/owr/2013/12",
"label": "Oberwolfach Report 12/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/12 | null | null | null | Explain how the classificatory scheme for mathematics developed, and whether MSC 2010's pure/applied distinction reflects a natural historical organization of mathematical branches. | Explain how the classificatory scheme for mathematics developed, and whether MSC 2010's pure/applied distinction reflects a natural historical organization of mathematical branches. | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733 |
30,002,305 | OWR-12340-002 | From Pure and Mixed to Pure and Applied Mathematics | Determine the conceptual framework that made the pure/mixed or pure/applied oppositions plausible, and explain how one opposition came to replace the other. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733](https://doi.org/10.4... | 3 | open | null | 2,013 | 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 | Early-Modern Mixed Mathematics workshop report (16th-century historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12340-002",
"literature-status:open",
"owr-year:2013"
] | The conceptual history of the pure, mixed, and applied oppositions remains an interpretive research problem rather than a theorem with a settled answer. | [
{
"url": "https://doi.org/10.4171/owr/2013/12",
"label": "Oberwolfach Report 12/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/12 | null | null | null | Determine the conceptual framework that made the pure/mixed or pure/applied oppositions plausible, and explain how one opposition came to replace the other. | Determine the conceptual framework that made the pure/mixed or pure/applied oppositions plausible, and explain how one opposition came to replace the other. | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733 |
30,002,306 | OWR-12340-003 | Mathematical Modelling as Scientific Knowledge Production | Determine the function and status of mathematical modelling in producing scientific knowledge, including how models are built, validated, negotiated across disciplines, and used to generate mathematical knowledge. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733](https://doi.org/10.4... | 3 | open | null | 2,013 | 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 | Early-Modern Mixed Mathematics workshop report (16th-century historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12340-003",
"literature-status:open",
"owr-year:2013"
] | The question asks for a general account of how mathematical models produce and negotiate knowledge across disciplines; current modeling literature gives domain-specific frameworks but no complete theory answering all listed aspects. | [
{
"url": "https://doi.org/10.4171/owr/2013/12",
"label": "Oberwolfach Report 12/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/12 | null | null | null | Determine the function and status of mathematical modelling in producing scientific knowledge, including how models are built, validated, negotiated across disciplines, and used to generate mathematical knowledge. | Determine the function and status of mathematical modelling in producing scientific knowledge, including how models are built, validated, negotiated across disciplines, and used to generate mathematical knowledge. | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733 |
30,002,307 | OWR-12340-005 | Mathematics in Early-Modern Landscape Design | For early-modern landscape design and gardening, determine who codified the relevant mathematical knowledge, why and how it was communicated, and what role mathematical sciences, instruments, and technology played in practice and fed back into those sciences. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733](https://doi.org/10.4... | 3 | open | null | 2,013 | 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 | Early-Modern Mixed Mathematics workshop report (16th-century historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12340-005",
"literature-status:open",
"owr-year:2013"
] | The report frames communication, mathematical sciences, instruments, and technology in early-modern landscape design as a substantial research agenda; the checked literature does not provide the requested comprehensive historical analysis. | [
{
"url": "https://doi.org/10.4171/owr/2013/12",
"label": "Oberwolfach Report 12/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/12 | null | null | null | For early-modern landscape design and gardening, determine who codified the relevant mathematical knowledge, why and how it was communicated, and what role mathematical sciences, instruments, and technology played in practice and fed back into those sciences. | For early-modern landscape design and gardening, determine who codified the relevant mathematical knowledge, why and how it was communicated, and what role mathematical sciences, instruments, and technology played in practice and fed back into those sciences. | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733 |
30,002,308 | OWR-12340-006 | Mixed Mathematics in Sixteenth-Century Practice | Determine how relevant the category of mixed mathematics is to sixteenth-century mathematical practice, especially where the term is absent from the surviving sources. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733](https://doi.org/10.4... | 3 | open | null | 2,013 | 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 | Early-Modern Mixed Mathematics workshop report (16th-century historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12340-006",
"literature-status:open",
"owr-year:2013"
] | The relevance of mixed mathematics to the sixteenth century remains dependent on unresolved historical comparisons of disciplinary practice and terminology; no definitive synthesis was found. | [
{
"url": "https://doi.org/10.4171/owr/2013/12",
"label": "Oberwolfach Report 12/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/12 | null | null | null | Determine how relevant the category of mixed mathematics is to sixteenth-century mathematical practice, especially where the term is absent from the surviving sources. | Determine how relevant the category of mixed mathematics is to sixteenth-century mathematical practice, especially where the term is absent from the surviving sources. | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733 |
30,002,309 | OWR-12340-007 | Practice-Based Histories of Applied Mathematics | Develop a historical analysis of applied mathematics based on what mathematicians do, including the transmission of knowledge and the formation of canonical texts and disciplines. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733](https://doi.org/10.4... | 3 | open | null | 2,013 | 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 | Early-Modern Mixed Mathematics workshop report (16th-century historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12340-007",
"literature-status:open",
"owr-year:2013"
] | The proposed move from a present-day impression to an evidence-based history of mathematicians' practices is a methodological research question, not a claim shown settled by the checked historiography. | [
{
"url": "https://doi.org/10.4171/owr/2013/12",
"label": "Oberwolfach Report 12/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/12 | null | null | null | Develop a historical analysis of applied mathematics based on what mathematicians do, including the transmission of knowledge and the formation of canonical texts and disciplines. | Develop a historical analysis of applied mathematics based on what mathematicians do, including the transmission of knowledge and the formation of canonical texts and disciplines. | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/12, pp. 657--733 |
30,002,310 | OWR-12341-001 | Open Problems in Geometric Nonlinear Quantum Dynamics | Develop a theory of densely defined vector fields on Hilbert manifolds that generate flows, generalizing Stone’s theorem. What are the best special-relativistic and general-relativistic analogues of the diffeomorphism group’s role in quantum mechanics? Develop nonlinear gauge transformations that may leave Hilbert spac... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Lie Groups and Supergroups (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/13, pp. 735--799](https://doi.org/10.4171/owr/2013/13)
## Literature review (checked 2026-08... | 3 | open | null | 2,013 | 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-12341-001",
"literature-status:open",
"owr-year:2013"
] | The extracted passage combines unresolved questions on flows of densely defined Hilbert-manifold vector fields, relativistic extensions, nonlinear gauge transformations, and composite-system evolution; later nonlinear-quantum literature still treats general well-posed and no-signaling extensions as open. | [
{
"url": "https://doi.org/10.4171/owr/2013/13",
"label": "Oberwolfach Report 13/2013"
},
{
"url": "https://doi.org/10.1134/S1063778808050177",
"label": "Goldin 2008"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/13 | null | null | null | Develop a theory of densely defined vector fields on Hilbert manifolds that generate flows, generalizing Stone’s theorem. What are the best special-relativistic and general-relativistic analogues of the diffeomorphism group’s role in quantum mechanics? Develop nonlinear gauge transformations that may leave Hilbert spac... | Develop a general theory of densely defined vector fields on Hilbert manifolds that generate flows, generalizing Stone's theorem; determine the best special and general relativistic analogues of the diffeomorphism group's role in quantum mechanics; develop nonlinear gauge transformations that may leave Hilbert space; e... | corrected_verified | The official report explicitly lists these items as parts of a six-item agenda of open problems and needed developments. | null | null | null | null | null | Representations of Lie Groups and Supergroups (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/13, pp. 735--799 |
30,002,311 | OWR-12342-001 | Intermediate Distributions in Stochastic Numerical Homogenization | For a multiscale numerical approximation $u_\varepsilon^h$ of a stochastic heterogeneous partial differential equation and the corresponding numerical homogenized solution $u_0^h$, determine the limiting distribution of the appropriately normalized fluctuation $u_\varepsilon^h-u_0^h$ as $\varepsilon\to0$ with coarse sc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/14, pp. 801--865](https://doi.org/10.4171/owr/2013/14)
##... | 3 | partially_solved | null | 2,013 | 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-12342-001",
"literature-status:partially-solved",
"owr-year:2013"
] | For the stated heterogeneous numerical homogenization models, the workshop literature identifies an intermediate limit depending on discretization and correlation regime, but no universal intermediate distribution for the full question is established. | [
{
"url": "https://doi.org/10.4171/owr/2013/14",
"label": "Oberwolfach Report 14/2013"
},
{
"url": "https://arxiv.org/abs/1409.1157",
"label": "arXiv:1409.1157"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/14 | null | null | null | For a multiscale numerical approximation $u_\varepsilon^h$ of a stochastic heterogeneous partial differential equation and the corresponding numerical homogenized solution $u_0^h$, determine the limiting distribution of the appropriately normalized fluctuation $u_\varepsilon^h-u_0^h$ as $\varepsilon\to0$ with coarse sc... | As epsilon tends to zero with the coarse scale h fixed, what is the resulting intermediate distribution, and does it converge to the distribution predicted by corrector theory as h tends to zero? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/14, pp. 801--865 |
30,002,312 | OWR-12342-002 | Homogenization of Nonlinear Plasticity | Why is homogenization of the nonlinear plasticity problem difficult, particularly for its differential inclusion and the limited regularity of two-scale solutions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/14, pp. 801--865](https://doi.org/10.4171/owr/2013/14)
##... | 3 | partially_solved | null | 2,013 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report immediately answers this explanatory question by identifying the nonlinear equations, differential inclusion, and insuff) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12342-002",
"literature-status:partially-solved",
"owr-year:2013"
] | Rigorous homogenization has been proved for important plasticity models, including stochastic hardening systems, but the nonlinear differential inclusion and insufficient two-scale regularity continue to obstruct a general theory. | [
{
"url": "https://doi.org/10.4171/owr/2013/14",
"label": "Oberwolfach Report 14/2013"
},
{
"url": "https://arxiv.org/abs/1604.02291",
"label": "arXiv:1604.02291"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/14 | null | null | null | null | Why is homogenization of the nonlinear plasticity problem difficult, particularly for its differential inclusion and the limited regularity of two-scale solutions? | unrecoverable | The official report immediately answers this explanatory question by identifying the nonlinear equations, differential inclusion, and insufficient regularity, then describes a finite-element workaround. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization (2013), Oberwolfach Reports, DOI 10.4171/owr/2013/14, pp. 801--865 |
30,002,313 | OWR-12479-004 | Minimum Graph Homomorphism Counts at Fixed Density | For a fixed finite graph $F$ and an $n$-vertex graph $G$ with at least $\rho n^2/2$ edges, determine the minimum possible number of graph homomorphisms $F\to G$, where homomorphisms need not be injective and need not preserve nonedges. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Limits of Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/16, pp. 963--1024](https://doi.org/10.4171/owr/2013/16)
## Literature review (checked 2026-08-21... | 3 | partially_solved | null | 2,013 | 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-12479-004",
"literature-status:partially-solved",
"owr-year:2013"
] | The minimum homomorphism-density function is known for substantial classes of graphs and has many general lower-bound results, but no formula for arbitrary F is known. | [
{
"url": "https://doi.org/10.4171/owr/2013/16",
"label": "Oberwolfach Report 16/2013"
},
{
"url": "https://arxiv.org/abs/2307.04588",
"label": "arXiv:2307.04588"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/16 | null | null | null | For a fixed finite graph $F$ and an $n$-vertex graph $G$ with at least $\rho n^2/2$ edges, determine the minimum possible number of graph homomorphisms $F\to G$, where homomorphisms need not be injective and need not preserve nonedges. | For a fixed small graph F and a graph G on n vertices with at least rho n squared over 2 edges, what is the minimum possible number of homomorphisms from F to G, where homomorphisms need not be injective or preserve non-edges? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Arbeitsgemeinschaft: Limits of Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/16, pp. 963--1024 |
30,002,314 | OWR-12479-006 | Li–Szegedy Smooth-Retract Conjecture | Let $T$ be an induced subtree of a bipartite graph $H$. If $H$ retracts onto $T$, meaning that there is a graph homomorphism $H\to T$ whose restriction to $T$ is the identity, then $T$ is smooth in $H$ in the sense of Li and Szegedy. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Limits of Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/16, pp. 963--1024](https://doi.org/10.4171/owr/2013/16)
## Literature review (checked 2026-08-21... | 3 | open | null | 2,013 | 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-12479-006",
"literature-status:open",
"owr-year:2013"
] | Li--Szegedy's converse that an induced subtree retracting from H must be smooth in H has known special cases, but the checked primary literature still presents the general statement as a conjecture. | [
{
"url": "https://arxiv.org/abs/1107.1153",
"label": "arXiv:1107.1153"
},
{
"url": "https://doi.org/10.4171/owr/2013/16",
"label": "Oberwolfach Report 16/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/16 | null | null | null | Let $T$ be an induced subtree of a bipartite graph $H$. If $H$ retracts onto $T$, meaning that there is a graph homomorphism $H\to T$ whose restriction to $T$ is the identity, then $T$ is smooth in $H$ in the sense of Li and Szegedy. | Li--Szegedy conjecture: if T is an induced subtree of a bipartite graph H and H retracts to T, meaning there is a graph homomorphism H to T restricting to the identity on T, then T is smooth in H in the Li--Szegedy sense. | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Arbeitsgemeinschaft: Limits of Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/16, pp. 963--1024 |
30,002,315 | OWR-12479-008 | Strict Graph-Invariant Bounds and Farber-Chain Rank Gradients | Let $\mathcal G=(G_n)$ be a sequence of connected graphs of uniformly bounded degree. For a field $K$, let $C_K(G)$ be the cycle space of $G$, let $C_K^q(G)$ be the subspace generated by cycles of length less than $q$, and define
$$s_K^q(\mathcal G)=\liminf_{n\to\infty}\frac{|E(G_n)|-\dim_K C_K^q(G_n)-|V(G_n)|}{|V(G_n... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Limits of Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/16, pp. 963--1024](https://doi.org/10.4171/owr/2013/16)
## Literature review (checked 2026-08-21... | 3 | open | null | 2,013 | 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-12479-008",
"literature-status:open",
"owr-year:2013"
] | The extracted record contains strictness questions for finite beta-invariant inequalities; the checked literature develops these invariants and related bounds but does not settle either strictness question in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2013/16",
"label": "Oberwolfach Report 16/2013"
},
{
"url": "https://www.numdam.org/item/10.5802/ahl.102.pdf",
"label": "Annales Henri Lebesgue"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/16 | null | null | null | Let $\mathcal G=(G_n)$ be a sequence of connected graphs of uniformly bounded degree. For a field $K$, let $C_K(G)$ be the cycle space of $G$, let $C_K^q(G)$ be the subspace generated by cycles of length less than $q$, and define
$$s_K^q(\mathcal G)=\liminf_{n\to\infty}\frac{|E(G_n)|-\dim_K C_K^q(G_n)-|V(G_n)|}{|V(G_n... | For graph sequences, can the inequality beta_Q(G) greater than or equal to beta_{F_p}(G) be strict; can the cost bound beta_K(G)+1 less than or equal to c(G) be strict; and for a finitely generated residually finite group with a Farber chain, does the rank gradient depend on the chain or only on the group? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Arbeitsgemeinschaft: Limits of Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/16, pp. 963--1024 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.