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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,002,416 | OWR-12723-002 | Optimal Order of Multidimensional Point-Set Discrepancy | For $s\geq3$, is the sharp order of the minimum $L^\infty$ discrepancy of $N$-point sets in the unit half-open $s$-cube equal to $(\log N)^{s-1}/N$, and do the Chen–Skriganov and digital-net constructions discussed in the source attain that order? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917](https://doi.org/10.4171/owr/2013/49)
## Literature review (checked 2026-0... | 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-12723-002",
"literature-status:open",
"owr-year:2013"
] | No sharp construction matching the conjectured L-infinity discrepancy order has been established; current work continues to describe optimal deterministic star-discrepancy constructions as open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3380/OWR_2013_49.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach Report 49"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0885064X26000178",
"label": "Recent discrepancy research"
},
{
"url": "https://doi.org... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/49 | null | null | null | For $s\geq3$, is the sharp order of the minimum $L^\infty$ discrepancy of $N$-point sets in the unit half-open $s$-cube equal to $(\log N)^{s-1}/N$, and do the Chen–Skriganov and digital-net constructions discussed in the source attain that order? | Is the sharp order of the minimum L-infinity discrepancy of N-point sets in [0,1)^s equal to (log N)^{s-1}/N, and do the constructions in the cited works [4] and [6] attain this optimal order? | corrected_verified | The malformed half-open-cube delimiter was replaced by prose, and the source’s unnamed citation references were replaced by the families of constructions identified in the official report. | null | null | null | null | null | Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917 |
30,002,417 | OWR-12723-003 | Duplicate Halton–Kronecker Discrepancy Question | Does the discrepancy D_N of the two-dimensional sequence z_n=(phi_2(n),{n sqrt(2)}) for n at least 0 satisfy D_N=O((log N)^{2+epsilon}/N) for every epsilon>0? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917](https://doi.org/10.4171/owr/2013/49)
## Literature review (checked 2026-0... | 3 | open | null | 2,013 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (This record is the same Halton–Kronecker discrepancy problem represented canonically and with the missing definition of $\phi_2$ by OWR-1272) | [
"OWR-12723-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12723-003",
"literature-status:open",
"owr-year:2013"
] | For the Halton--Kronecker sequence with the indicated square-root parameter, known algebraic-parameter bounds do not yield the proposed logarithmic discrepancy estimate, which remains open. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/e7d12ca4-407e-4a07-80b5-234bad310c6b/download",
"label": "Oberwolfach Report 49"
},
{
"url": "https://arxiv.org/abs/1407.2380",
"label": "Larcher"
},
{
"url": "https://www.geometrie.tuwien.ac.at/drmota/haltonkronecker.pdf",
"label": "Drmo... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/49 | null | null | null | null | Does the discrepancy D_N of the two-dimensional sequence z_n=(phi_2(n),{n sqrt(2)}) for n at least 0 satisfy D_N=O((log N)^{2+epsilon}/N) for every epsilon>0? | unrecoverable | This record is the same Halton–Kronecker discrepancy problem represented canonically and with the missing definition of $\phi_2$ by OWR-12723-004. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917 |
30,002,418 | OWR-12723-004 | Sharp Bounds for Halton–Kronecker Sequence Discrepancy | Does the discrepancy $D_N$ of the two-dimensional Halton–Kronecker sequence
$$z_n=(\phi_2(n),\{n\sqrt2\}),\qquad n\geq0,$$
where $\phi_2$ is the base-$2$ van der Corput sequence, satisfy $D_N=O((\log N)^{2+\varepsilon}/N)$ for every $\varepsilon>0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917](https://doi.org/10.4171/owr/2013/49)
## Literature review (checked 2026-0... | 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... | [
"OWR-12723-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12723-004",
"literature-status:open",
"owr-year:2013"
] | The report poses the explicit discrepancy bound for the base-2 Halton--Kronecker sequence with\sqrt{2}; no proof or counterexample establishing the bound was found in the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2013/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/49 | null | null | null | Does the discrepancy $D_N$ of the two-dimensional Halton–Kronecker sequence
$$z_n=(\phi_2(n),\{n\sqrt2\}),\qquad n\geq0,$$
where $\phi_2$ is the base-$2$ van der Corput sequence, satisfy $D_N=O((\log N)^{2+\varepsilon}/N)$ for every $\varepsilon>0$? | Does the discrepancy D_N of the two-dimensional Halton-Kronecker sequence z_n=(phi_2(n),{n sqrt(2)}) for n at least 0, where phi_2 is the base-2 van der Corput sequence, satisfy D_N=O((log N)^{2+epsilon}/N) for every epsilon>0)? | 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 | Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917 |
30,002,419 | OWR-12723-005 | The Optimal Constant in One-Dimensional Sequence Discrepancy | Let $I=\{x\in\mathbb R:0\leq x<1\}$. Determine the optimal constant $c^*=\sup\{c:\text{every sequence }(x_n)\subset I\text{ satisfies }D_N\geq c(\log N)/N\text{ for infinitely many }N\}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917](https://doi.org/10.4171/owr/2013/49)
## Literature review (checked 2026-0... | 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 | {
"source_url": "https://doi.org/10.1515/udt-2016-0001",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved** (the source's request answered; c* open). G. Larcher (OWR 49/2013, p. 2871) considers c*, the supremum of the c such that every sequence in [0, 1) has D_N ≥ c log N / N for infinitely many N, recalls 0.06015… ≤ c* ≤ 0.222…, raises the lower bound to 0.0... | [
"owr",
"oberwolfach-reports",
"OWR-12723-005",
"literature-status:open",
"owr-year:2013"
] | The one-dimensional universal discrepancy constant remains bounded between known lower and upper estimates; the report's request to improve the lower estimate is not resolved by the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2013/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/49 | null | null | null | Let $I=\{x\in\mathbb R:0\leq x<1\}$. Determine the optimal constant $c^*=\sup\{c:\text{every sequence }(x_n)\subset I\text{ satisfies }D_N\geq c(\log N)/N\text{ for infinitely many }N\}$. | Determine the optimal constant c^{*}=\sup\{c: every sequence (x_n) in [0,1) satisfies D_N\ge c\log N/N for infinitely many N\}. | 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 | Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917 |
30,002,420 | OWR-12723-006 | Sample-Based Approximation of Ridge Functions | What algorithm can exploit the ridge structure of functions in $R_d^{\alpha,p}$ to approximate them efficiently from samples? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917](https://doi.org/10.4171/owr/2013/49)
## Literature review (checked 2026-0... | 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-12723-006",
"literature-status:partially-solved",
"owr-year:2013"
] | For the stated ridge-function classes, sampling-number bounds and tractability regimes are established, but the report's request for an effective algorithm exploiting ridge structure has no general optimal construction in the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2013/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/49 | null | null | null | What algorithm can exploit the ridge structure of functions in $R_d^{\alpha,p}$ to approximate them efficiently from samples? | What algorithm can exploit the ridge structure of functions in R_d^{\alpha,p} to approximate them efficiently from samples? | 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 | Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917 |
30,002,421 | OWR-12723-007 | Discrepancy Lower Bounds for Line Unions in Three Dimensions | For
$$A=\bigcup_{i=1}^N(\ell_i\cap[0,1]^3),\qquad \ell_i\subset\mathbb R^3,$$
and
$$D_N(A)=\sup_Q\left|\frac{H^1(A\cap Q)}{H^1(A)}-H^3(Q)\right|,$$
does there exist an absolute constant $c>0$ such that
$$D_N(A)\geq c\frac{\log H^1(A)}{H^1(A)}$$
for every such union of lines? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917](https://doi.org/10.4171/owr/2013/49)
## Literature review (checked 2026-0... | 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-12723-007",
"literature-status:open",
"owr-year:2013"
] | The proposed lower bound for the line-union discrepancy would extend Schmidt-type bounds beyond point sets, but the checked primary literature gives no proof or disproof of this inequality. | [
{
"url": "https://doi.org/10.4171/owr/2013/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/49 | null | null | null | For
$$A=\bigcup_{i=1}^N(\ell_i\cap[0,1]^3),\qquad \ell_i\subset\mathbb R^3,$$
and
$$D_N(A)=\sup_Q\left|\frac{H^1(A\cap Q)}{H^1(A)}-H^3(Q)\right|,$$
does there exist an absolute constant $c>0$ such that
$$D_N(A)\geq c\frac{\log H^1(A)}{H^1(A)}$$
for every such union of lines? | For A=\bigcup_{i=1}^{N}(\ell_i\cap[0,1]^3) with lines \ell_i\subset\mathbb R^3 and D_N(A)=\sup_Q\left|H^1(A\cap Q)/H^1(A)-H^3(Q)\right|, does an absolute c>0 exist such that D_N(A)\ge c\log H^1(A)/H^1(A)? | 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 | Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917 |
30,002,422 | OWR-12723-008 | Hexagonal Extremizers for a Geometric Uncertainty Principle | For a finite measurable partition $[0,1]^2=\bigcup_{i=1}^N\Omega_i$, define
$$\mathcal A(\Omega_i)=\inf_{|B|=|\Omega_i|}\frac{|\Omega_i\mathbin\triangle B|}{|\Omega_i|},\qquad \mathcal D(\Omega_i)=\frac{|\Omega_i|-\min_j|\Omega_j|}{|\Omega_i|},$$
where the infimum is over disks $B$. Is the minimum of
$$\sum_{i=1}^N|... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917](https://doi.org/10.4171/owr/2013/49)
## Literature review (checked 2026-0... | 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 | {
"source_url": "https://zenodo.org/records/23107228",
"checked_at": "2026-10-02",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-02] I have released an unrefereed preprint, **The Sharp Hexagonal Constant in Steinerberger's Geometric Uncertainty Principle on the Square** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23107228) | [
"owr",
"oberwolfach-reports",
"OWR-12723-008",
"literature-status:open",
"owr-year:2013"
] | The hexagonal decomposition is presented only as a conjectural extremizer for the quantitative partition inequality; no matching optimality theorem was found. | [
{
"url": "https://doi.org/10.4171/owr/2013/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/49 | null | null | null | For a finite measurable partition $[0,1]^2=\bigcup_{i=1}^N\Omega_i$, define
$$\mathcal A(\Omega_i)=\inf_{|B|=|\Omega_i|}\frac{|\Omega_i\mathbin\triangle B|}{|\Omega_i|},\qquad \mathcal D(\Omega_i)=\frac{|\Omega_i|-\min_j|\Omega_j|}{|\Omega_i|},$$
where the infimum is over disks $B$. Is the minimum of
$$\sum_{i=1}^N|... | Is the extremal partition in the stated geometric uncertainty principle given by a decomposition of [0,1]^2 into hexagons, with the evident boundary modifications? | corrected_verified | The official report defines the Fraenkel asymmetry, relative size deviation, and weighted partition functional before asking whether hexagons are extremal. Those missing definitions were restored. | null | null | null | null | null | Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917 |
30,002,423 | OWR-12723-011 | Polynomial Tractability of Permutation-Invariant Integration | For integration over the permutation-invariant spaces $S_{I_d}(E_{d,\alpha})$, under what conditions on the coordinate sets $I_d$ is the information complexity $n(\varepsilon,d)$ polynomially bounded in $d$ and $\varepsilon^{-1}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917](https://doi.org/10.4171/owr/2013/49)
## Literature review (checked 2026-0... | 3 | open | null | 2,013 | 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-12723-011",
"literature-status:open",
"owr-year:2013"
] | The record asks for a full characterization of polynomial tractability for integration on permutation-invariant Korobov spaces; the cited lower bounds leave this general condition unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2013/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/49 | null | null | null | For integration over the permutation-invariant spaces $S_{I_d}(E_{d,\alpha})$, under what conditions on the coordinate sets $I_d$ is the information complexity $n(\varepsilon,d)$ polynomially bounded in $d$ and $\varepsilon^{-1}$? | For integration over the permutation-invariant spaces S_{I_d}(E_{d,\alpha}), under what conditions on the coordinate sets I_d is the information complexity n(\varepsilon,d) polynomially bounded in d and \varepsilon^{-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 | Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917 |
30,002,424 | OWR-12724-004 | Gottschalk Surjunctivity Problem | Is every countable discrete group $\Gamma$ surjunctive; that is, for every finite alphabet $A$, is every continuous injective $\Gamma$-equivariant map $A^\Gamma\to A^\Gamma$ necessarily surjective? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Sofic Entropy (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/50, pp. 2919--2961](https://doi.org/10.4171/owr/2013/50)
## Literature review (checked 2026-08-21)
**S... | 3 | open | null | 2,013 | 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-12724-004",
"literature-status:open",
"owr-year:2013"
] | Gottschalk surjunctivity and the corresponding all-groups form of Kaplansky's direct-finiteness problem remain unresolved in general, although they are proved for broad classes such as sofic groups. | [
{
"url": "https://doi.org/10.4171/owr/2013/50",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s00209-024-03589-3",
"label": "current surjunctivity literature"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/50 | null | null | null | Is every countable discrete group $\Gamma$ surjunctive; that is, for every finite alphabet $A$, is every continuous injective $\Gamma$-equivariant map $A^\Gamma\to A^\Gamma$ necessarily surjective? | Is every countable discrete group surjunctive, meaning that every continuous injective equivariant map A^\Gamma\to A^\Gamma for a finite alphabet A is surjective? This is Gottschalk's surjunctivity problem and is related to Kaplansky's direct-finiteness conjecture. | 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: Sofic Entropy (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/50, pp. 2919--2961 |
30,002,425 | OWR-12724-005 | Monotonicity of Sofic Model Counts | How does the cardinality of \operatorname{Map}_{\mu}(\alpha,F,\delta,\sigma_i) vary with the finite partition \alpha, finite set F\subset G, positive \delta, and sofic approximation \sigma_i? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Sofic Entropy (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/50, pp. 2919--2961](https://doi.org/10.4171/owr/2013/50)
## Literature review (checked 2026-08-21)
**S... | 3 | open | null | 2,013 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (answered in the source; not a research problem)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source; not a research problem)**. The record is an expository question in J. Wu's Arbeitsgemeinschaft talk (OWR 50/2013, p. 2932), answered in the next sentences: |Map_μ(α, F, δ, σ_i)| decreases as F grows or δ shrinks, and can move either way whe... | [
"owr",
"oberwolfach-reports",
"OWR-12724-005",
"literature-status:open",
"owr-year:2013"
] | The extracted question asks for the dependence of the sofic model-counting quantity on its parameters; the checked literature develops estimates and invariance results but no general quantitative classification. | [
{
"url": "https://doi.org/10.4171/owr/2013/50",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/50 | null | null | null | null | How does the cardinality of \operatorname{Map}_{\mu}(\alpha,F,\delta,\sigma_i) vary with the finite partition \alpha, finite set F\subset G, positive \delta, and sofic approximation \sigma_i? | unrecoverable | Checked against the official Oberwolfach report. The source immediately gives the basic parameter dependence of these model counts and then uses it to define entropy; the extraction is didactic exposition rather than a separate open problem. No separate clean statement is promoted; the original record remains publicly ... | null | null | null | null | null | Arbeitsgemeinschaft: Sofic Entropy (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/50, pp. 2919--2961 |
30,002,426 | OWR-12724-008 | Distal Actions with Negative Infinite Sofic Entropy | Does there exist a distal action whose sofic topological entropy is $-\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Sofic Entropy (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/50, pp. 2919--2961](https://doi.org/10.4171/owr/2013/50)
## Literature review (checked 2026-08-21)
**S... | 3 | open | null | 2,013 | 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-12724-008",
"literature-status:open",
"owr-year:2013"
] | The checked primary source still states that it is unknown whether a distal action can have sofic topological entropy minus infinity; no later resolution was located. | [
{
"url": "https://doi.org/10.4171/owr/2013/50",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/50 | null | null | null | Does there exist a distal action whose sofic topological entropy is $-\infty$? | Does there exist a distal action with sofic topological entropy -\infty? | 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: Sofic Entropy (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/50, pp. 2919--2961 |
30,002,427 | OWR-12725-001 | Rational Points on Cartan Modular Curves | Let $X_G$ be the modular curve of level $N$ attached to a subgroup $G\subseteq\operatorname{GL}_2(\mathbb Z/N\mathbb Z)$ with full determinant. Describe $X_G(\mathbb Q)$, especially when $N=p$ is prime and $G$ is a Borel subgroup or the normalizer of a split or nonsplit Cartan subgroup. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-001",
"literature-status:partially-solved",
"owr-year:2013"
] | Rational points on the split-Cartan and related Atkin--Lehner curves are classified in broad ranges and exceptional levels, including level 13, but the general rational-point problem forX_{\mathrm{ns}}^+(p) remains open. | [
{
"url": "https://doi.org/10.4007/annals.2011.173.1.13",
"label": "Bilu--Parent split-Cartan theorem"
},
{
"url": "https://doi.org/10.5802/aif.2781",
"label": "Bilu--Parent--Rebolledo rational points"
},
{
"url": "https://arxiv.org/abs/2101.01862",
"label": "quadratic Chabauty comput... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | Let $X_G$ be the modular curve of level $N$ attached to a subgroup $G\subseteq\operatorname{GL}_2(\mathbb Z/N\mathbb Z)$ with full determinant. Describe $X_G(\mathbb Q)$, especially when $N=p$ is prime and $G$ is a Borel subgroup or the normalizer of a split or nonsplit Cartan subgroup. | For the modular curve X_G of level N attached to G\subseteq\operatorname{GL}_2(\mathbb Z/N\mathbb Z) with full determinant, describe X_G(\mathbb Q), especially for prime N=p and G a Borel subgroup or the normalizer of a split or nonsplit Cartan subgroup. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,428 | OWR-12725-002 | Lang–Trotter Asymptotics for Fixed Frobenius Fields | Let $E/\mathbb Q$ be a non-CM elliptic curve and let $K$ be an imaginary quadratic field. Is
$$\Pi_E(K;x)\sim c(E,K)\frac{\sqrt{x}}{\log x}$$
for some $c(E,K)>0$, where $\Pi_E(K;x)$ counts ordinary primes of good reduction $p\leq x$ for which $\mathbb Q(\pi_p(E))\cong K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-002",
"literature-status:open",
"owr-year:2013"
] | The Lang--Trotter-type asymptotic for fixed Frobenius fields of a non-CM elliptic curve remains unproved in general; recent work gives substantial results for special families but not the conjectured asymptotic. | [
{
"url": "https://arxiv.org/abs/2608.17639",
"label": "Wang, fixed Frobenius fields"
},
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | Let $E/\mathbb Q$ be a non-CM elliptic curve and let $K$ be an imaginary quadratic field. Is
$$\Pi_E(K;x)\sim c(E,K)\frac{\sqrt{x}}{\log x}$$
for some $c(E,K)>0$, where $\Pi_E(K;x)$ counts ordinary primes of good reduction $p\leq x$ for which $\mathbb Q(\pi_p(E))\cong K$? | Lang--Trotter conjecture: if E/\mathbb Q has no complex multiplication and K is imaginary quadratic, then \Pi_E(K;x)\sim c(E,K)\sqrt{x}/\log x for some c(E,K)>0, where \Pi_E(K;x) counts ordinary good-reduction primes p\le x with \mathbb Q(\pi_p(E))\cong K. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,429 | OWR-12725-003 | Gaussian Limits for Arithmetic Progressions Under Weaker Growth | Does the Gaussian limit theorem for normalized cusp-form and divisor-function values in arithmetic progressions remain valid when its auxiliary function is assumed only to satisfy $\Phi(x)=O_\varepsilon(x^{1-\varepsilon})$ for some $\varepsilon>0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-003",
"literature-status:open",
"owr-year:2013"
] | The Fouvry--Ganguly--Kowalski--Michel theorem proves the Gaussian law under\Phi(x)=O_\varepsilon(x^\varepsilon); the weakerO_\varepsilon(x^{1-\varepsilon}) extension stated in the record remains conjectural in the checked literature. | [
{
"url": "https://doi.org/10.4171/CMH/342",
"label": "Fouvry--Ganguly--Kowalski--Michel"
},
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | Does the Gaussian limit theorem for normalized cusp-form and divisor-function values in arithmetic progressions remain valid when its auxiliary function is assumed only to satisfy $\Phi(x)=O_\varepsilon(x^{1-\varepsilon})$ for some $\varepsilon>0$? | The Gaussian-limit theorem for normalized cusp-form and divisor-function values in arithmetic progressions should remain valid when its auxiliary function satisfies only \Phi(x)=O_{\varepsilon}(x^{1-\varepsilon}) for some \varepsilon>0. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,430 | OWR-12725-004 | Singular Locus Dimension of Nonsingular Form Systems | For a nonsingular system of $R$ homogeneous forms of the same degree, is the dimension $B$ of its singular locus always equal to $R-1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | solved | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (yes, for D ≥ 2)**, by a short standard argument. We found no reference that states the equality, so the combination below is ours. | [
"owr",
"oberwolfach-reports",
"OWR-12725-004",
"literature-status:open",
"owr-year:2013"
] | For nonsingular systems of equal-degree forms the known argument givesB\leq R-1, while equalityB=R-1 is still not established in the generality of the extracted question. | [
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | For a nonsingular system of $R$ homogeneous forms of the same degree, is the dimension $B$ of its singular locus always equal to $R-1$? | For a nonsingular system of R homogeneous forms of equal degree, with B the dimension of its singular locus, is it always true that B=R-1? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,431 | OWR-12725-006 | Polignac Conjecture for Consecutive Prime Gaps | Does every positive even integer occur infinitely often as a gap $p_{n+1}-p_n$ between consecutive primes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-006",
"literature-status:open",
"owr-year:2013"
] | Bounded-gap theorems prove that some even gap occurs infinitely often and give many Polignac numbers, but no prescribed positive integer is known to be a Polignac number in the full conjectured sense. | [
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1311.4600",
"label": "Maynard, small gaps between primes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | Does every positive even integer occur infinitely often as a gap $p_{n+1}-p_n$ between consecutive primes? | Polignac's conjecture: every positive integer m occurs infinitely often as a gap p_{n+1}-p_n between consecutive primes. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,432 | OWR-12725-007 | Squarefree Kernel Counts Outside the Established Range | Let $k(n)$ be the squarefree kernel of $n$ and
$$N(x,y)=\#\{n\leq x:k(n)\leq y\}.$$
Determine the asymptotic behavior of $N(x,y)$ outside
$$H_\varepsilon=\{(x,y):\exp((\log\log x)^\varepsilon)\leq y\leq x\},$$
apart from the known small-$y$ range. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-007",
"literature-status:open",
"owr-year:2013"
] | The record explicitly concerns the asymptotic behavior of the nuclear-number counting function outside the established domain; the checked literature supplies no general asymptotic there. | [
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | Let $k(n)$ be the squarefree kernel of $n$ and
$$N(x,y)=\#\{n\leq x:k(n)\leq y\}.$$
Determine the asymptotic behavior of $N(x,y)$ outside
$$H_\varepsilon=\{(x,y):\exp((\log\log x)^\varepsilon)\leq y\leq x\},$$
apart from the known small-$y$ range. | For N(x,y)=\#\{n\le x:k(n)\le y\}, where k(n) is the squarefree kernel, determine the asymptotic behavior of N(x,y) outside H_{\varepsilon}=\{(x,y):\exp((\log\log x)^{\varepsilon})\le y\le x\}, apart from the small-y range. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,433 | OWR-12725-008 | Independent-Kernel Heuristic for Refined abc Bounds | Heuristic for the refinement of the abc conjecture: for coprime positive integers a,b, the kernels k(a), k(b), and k(a+b) may be modeled as independent random variables. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (Checked against the official Oberwolfach report. The source explicitly labels independence of the three kernels as a heuristic assumption us) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-008",
"literature-status:open",
"owr-year:2013"
] | The extracted passage is an unfinished heuristic refinement of the abc conjecture and does not state a verified theorem; the underlying claim is unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | null | Heuristic for the refinement of the abc conjecture: for coprime positive integers a,b, the kernels k(a), k(b), and k(a+b) may be modeled as independent random variables. | unrecoverable | Checked against the official Oberwolfach report. The source explicitly labels independence of the three kernels as a heuristic assumption used to derive a proposed refinement, not as a mathematical question or conjecture in its own right. No separate clean statement is promoted; the original record remains publicly vis... | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,434 | OWR-12725-009 | Polynomial Asymptotics for Shifted Divisor Correlations | For $r\geq 3$ and fixed $h\neq 0$, is
$$D_r(X;h)=\sum_{n\leq X}d_r(n)d_r(n+h)\sim X P_{2(r-1)}(\log X;h),$$
where $P_{2(r-1)}(u;h)$ is a polynomial of degree $2(r-1)$ in $u$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-009",
"literature-status:open",
"owr-year:2013"
] | For shifted divisor correlations, ther=2 case is classical, whereas the conjectured polynomial asymptotic forr\geq3 remains open despite function-field analogues and later partial progress. | [
{
"url": "https://ems.press/content/serial-article-files/53325",
"label": "current additive-divisor literature"
},
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | For $r\geq 3$ and fixed $h\neq 0$, is
$$D_r(X;h)=\sum_{n\leq X}d_r(n)d_r(n+h)\sim X P_{2(r-1)}(\log X;h),$$
where $P_{2(r-1)}(u;h)$ is a polynomial of degree $2(r-1)$ in $u$? | For r\ge3 and fixed h\ne0, conjecture that D_r(X;h)=\sum_{n\le X}d_r(n)d_r(n+h)\sim X P_{2(r-1)}(\log X;h), where P_{2(r-1)}(u;h) is a degree-2(r-1) polynomial in u. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,435 | OWR-12725-010 | Polynomial Images of Subgroups and Function-Field Curve Points | For polynomials $f,g\in\mathbb F_p[X]$ and multiplicative subgroups $G,H\subseteq\mathbb F_p^*$, estimate $\#(f(G)\cap g(H))$. Separately, let $K=\mathbb F_q(T)$ and let $F\in K[X,Y]$ be absolutely irreducible of degree $d$. Bound the number of solutions to $F(x,y)=0$ with $x,y\in\mathbb F_q[T]$ of degree at most $n$ a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-010",
"literature-status:open",
"owr-year:2013"
] | Special cases have bounds, but the general two-polynomial two-subgroup intersection problem remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1401.0964",
"label": "Shparlinski polynomial values"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | For polynomials $f,g\in\mathbb F_p[X]$ and multiplicative subgroups $G,H\subseteq\mathbb F_p^*$, estimate $\#(f(G)\cap g(H))$. Separately, let $K=\mathbb F_q(T)$ and let $F\in K[X,Y]$ be absolutely irreducible of degree $d$. Bound the number of solutions to $F(x,y)=0$ with $x,y\in\mathbb F_q[T]$ of degree at most $n$ a... | Question 1: estimate \#(f(G)\cap g(H)) for f,g\in\mathbb F_p[X] and subgroups G,H\subseteq\mathbb F_p^{*}. Question 2: for K=\mathbb F_q(T) and absolutely irreducible F\in K[X,Y] of degree d, bound the number of polynomial solutions F(x,y)=0 with x,y\in\mathbb F_q[T] of degree at most n as n\to\infty. | 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 | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,436 | OWR-12725-013 | Consecutive Integers with Restricted Prime Divisors | Let $T$ be the set of positive integers all of whose prime divisors are not congruent to $1\pmod 4$. Does $T$ contain infinitely many pairs of consecutive integers? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-013",
"literature-status:open",
"owr-year:2013"
] | The source poses the consecutive-pair assertion as a question, and no primary proof or disproof was located in the current search. | [
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | Let $T$ be the set of positive integers all of whose prime divisors are not congruent to $1\pmod 4$. Does $T$ contain infinitely many pairs of consecutive integers? | Let T be the set of positive integers whose prime divisors are all congruent to neither 1 modulo 4; does T contain infinitely many pairs of consecutive integers? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,437 | OWR-12725-014 | Subpolynomial Bounds for an Additive Multiplicative Equation | Let $SP(n)$ be the number of positive-integer solutions to $abc+a+b+c=n$. For every $\varepsilon>0$, does there exist $C(\varepsilon)$ such that $SP(n)<C(\varepsilon)n^\varepsilon$ for all $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-014",
"literature-status:open",
"owr-year:2013"
] | The sum-product bound remains a conjectural problem in the authoritative source, with no verified primary resolution located. | [
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | Let $SP(n)$ be the number of positive-integer solutions to $abc+a+b+c=n$. For every $\varepsilon>0$, does there exist $C(\varepsilon)$ such that $SP(n)<C(\varepsilon)n^\varepsilon$ for all $n$? | If SP(n) counts positive-integer solutions of abc+a+b+c=n, is it true that for every \varepsilon>0 there is C(\varepsilon) such that SP(n)<C(\varepsilon)n^{\varepsilon}? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,438 | OWR-12725-015 | Uniform Lattice-Point Bounds on Short Circle Arcs | Let $A$ be an arc of length $R^\theta$ on a circle of radius $R$. If $\theta<1$, is the number of lattice points on $A$ bounded by a constant $C(\theta)$ independent of $R$ and $A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-015",
"literature-status:partially-solved",
"owr-year:2013"
] | The lattice-point assertion is proved below the square-root scale, but the full range below the radius scale remains open. | [
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1090/S0002-9939-1992-1089403-8",
"label": "Cilleruelo and Cordoba"
},
{
"url": "https://doi.org/10.4064/aa143-3-1",
"label": "Ramana conic arc bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | Let $A$ be an arc of length $R^\theta$ on a circle of radius $R$. If $\theta<1$, is the number of lattice points on $A$ bounded by a constant $C(\theta)$ independent of $R$ and $A$? | If A is an arc of length R^{\theta} on a circle of radius R, does \theta<1 imply that A contains at most C(\theta) lattice points for some constant C(\theta)? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,439 | OWR-12725-016 | Height Counts for Closed Projective Immersions | Let $f:\mathbb P^n\to\mathbb P^m$ be a degree-$d$ morphism induced by degree-$d$ forms with no common zero, and suppose that $f$ is a closed immersion. Does
$$n_f(B)=O_{d,n,\varepsilon}\!\left(B^{(n+1)/d+\varepsilon}\right),$$
where $n_f(B)=\#\{x\in\mathbb P^n(\mathbb Q):H(f(x))\leq B\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037](https://doi.org/10.4171/owr/2013/51)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12725-016",
"literature-status:open",
"owr-year:2013"
] | The sharper closed-immersion height exponent is still presented as a conjecture and no general proof was found. | [
{
"url": "https://doi.org/10.4171/owr/2013/51",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.ansens.2004.10.005",
"label": "Salberger rational point bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/51 | null | null | null | Let $f:\mathbb P^n\to\mathbb P^m$ be a degree-$d$ morphism induced by degree-$d$ forms with no common zero, and suppose that $f$ is a closed immersion. Does
$$n_f(B)=O_{d,n,\varepsilon}\!\left(B^{(n+1)/d+\varepsilon}\right),$$
where $n_f(B)=\#\{x\in\mathbb P^n(\mathbb Q):H(f(x))\leq B\}$? | For a degree-d morphism f:\mathbb P^n\to\mathbb P^m induced by degree-d forms with no common zero, if f is a closed immersion, does n_f(B)=O_{d,n,\varepsilon}(B^{(n+1)/d+\varepsilon}) hold for n_f(B)=\#\{x\in\mathbb P^n(\mathbb Q):H(f(x))\le B\}? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analytic Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/51, pp. 2963--3037 |
30,002,440 | OWR-12726-001 | Quenched Central Limit Theorem for Small-Disorder Random Walks | For $d\geq3$, does there exist $\varepsilon(d)>0$ such that, under the i.i.d. small-disorder assumptions,
$$n^{-1/2}(X_n-na(\mu))$$
converges in law, almost surely in the environment, to $N(0,\Sigma(\mu))$, with $\Sigma(\mu)$ positive definite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/52, pp. 3039--3113](https://doi.org/10.4171/owr/2013/52)
## Literature review (checked 2026-08-21)
**Stat... | 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-12726-001",
"literature-status:open",
"owr-year:2013"
] | The multidimensional perturbative central limit theorem is still described as beyond current techniques, with later results covering only restricted regimes. | [
{
"url": "https://doi.org/10.4171/owr/2013/52",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/52 | null | null | null | For $d\geq3$, does there exist $\varepsilon(d)>0$ such that, under the i.i.d. small-disorder assumptions,
$$n^{-1/2}(X_n-na(\mu))$$
converges in law, almost surely in the environment, to $N(0,\Sigma(\mu))$, with $\Sigma(\mu)$ positive definite? | For d\ge3, does there exist \varepsilon(d)>0 such that under the i.i.d. small-disorder assumptions, n^{-1/2}(X_n-na(\mu)) converges in law, almost surely in the environment, to N(0,\Sigma(\mu)) with \Sigma(\mu) positive definite? | 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 | Large Scale Stochastic Dynamics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/52, pp. 3039--3113 |
30,002,441 | OWR-12726-003 | Quenched Invariance Principles for Random Conductance Models | For a stationary ergodic random conductance model on $\mathbb Z^d$ with $0<\omega(e)<\infty$ almost surely and finite mean conductance, does finiteness of $\mathbb E[1/\omega(e)]$ for every edge suffice for a quenched functional central limit theorem with deterministic nondegenerate covariance $\Sigma^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/52, pp. 3039--3113](https://doi.org/10.4171/owr/2013/52)
## Literature review (checked 2026-08-21)
**Stat... | 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-12726-003",
"literature-status:partially-solved",
"owr-year:2013"
] | The first-moment quenched invariance principle is proved in dimension two and in stronger-moment settings, but the stated general conjecture in dimensions at least three remains open. | [
{
"url": "https://doi.org/10.4171/owr/2013/52",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1214/19-AOP1361",
"label": "Bella and Schaeffer invariance principle"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/52 | null | null | null | For a stationary ergodic random conductance model on $\mathbb Z^d$ with $0<\omega(e)<\infty$ almost surely and finite mean conductance, does finiteness of $\mathbb E[1/\omega(e)]$ for every edge suffice for a quenched functional central limit theorem with deterministic nondegenerate covariance $\Sigma^2$? | For a stationary ergodic random conductance model on \mathbb Z^d with 0<\omega(e)<\infty almost surely and finite mean conductance, does finite E[1/\omega(e)] for every edge suffice for a quenched functional central limit theorem with deterministic nondegenerate covariance \Sigma^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 | Large Scale Stochastic Dynamics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/52, pp. 3039--3113 |
30,002,442 | OWR-12727-001 | Homogeneity of Fano Contact Manifolds | Is every Fano contact manifold homogeneous? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Quaternion Kähler Structures in Riemannian and Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/53, pp. 3115--3145](https://doi.org/10.4171/owr/2013/53)
... | 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"
} | {
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"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-12727-001",
"literature-status:open",
"owr-year:2013"
] | The Fano-contact homogeneity conjecture remains open in general; substantial results cover low dimensions and extra automorphism hypotheses. | [
{
"url": "https://doi.org/10.4171/owr/2013/53",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1802.05002",
"label": "Buczynski Wisniewski and Weber"
},
{
"url": "https://arxiv.org/abs/2004.05971",
"label": "Occhetta and collaborators"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/53 | null | null | null | Is every Fano contact manifold homogeneous? | Every Fano contact manifold is conjectured to be homogeneous; moreover, a Fano contact manifold admitting a K\~{a}hler--Einstein metric should be the twistor space of a positive quaternion--K\~{a}hler manifold. | corrected_verified | The official report presents homogeneity as the open conjecture. The Kähler–Einstein/twistor-space assertion included by the extraction is stated there as a theorem, so it was removed. | null | null | null | null | null | Mini-Workshop: Quaternion Kähler Structures in Riemannian and Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/53, pp. 3115--3145 |
30,002,443 | OWR-12727-002 | Answered Reconstruction of Contact Structures from Contact Lines | For a Fano contact manifold X with b_2(X)=1, is the contact structure uniquely determined by its rational contact lines, equivalently by the variety of minimal rational tangents? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Quaternion Kähler Structures in Riemannian and Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/53, pp. 3115--3145](https://doi.org/10.4171/owr/2013/53)
... | 3 | open | null | 2,013 | 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"
} | {
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (yes, if X is not projective space; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes, if X is not projective space; answered in the source)**. S. Kebekus (OWR 53/2013, pp. 3127–3128) explains that on a Fano contact manifold X with b₂ = 1 other than projective space, the tangent directions of contact lines through a general point span the conta... | [
"owr",
"oberwolfach-reports",
"OWR-12727-002",
"literature-status:open",
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] | The extracted text is only a fragment saying that a question was answered, so the mathematical claim cannot be identified; the unresolved record is therefore open. | [
{
"url": "https://doi.org/10.4171/owr/2013/53",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/53 | null | null | null | null | For a Fano contact manifold X with b_2(X)=1, is the contact structure uniquely determined by its rational contact lines, equivalently by the variety of minimal rational tangents? | unrecoverable | The official report proves that contact lines generate the contact distribution and says explicitly that this answers the motivating question. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Quaternion Kähler Structures in Riemannian and Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/53, pp. 3115--3145 |
30,002,444 | OWR-12727-003 | Homogeneity from Legendrian Varieties of Minimal Rational Tangents | Let $X$ be a Fano manifold with $b_2(X)=1$. If its variety of minimal rational tangents at a general point is a connected nonlinear Legendrian submanifold of the contact projective space, must $X$ be homogeneous, or at least quasi-homogeneous? Likewise, if the variety is a nonlinear smooth hypersurface, must $X$ be hom... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Quaternion Kähler Structures in Riemannian and Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/53, pp. 3115--3145](https://doi.org/10.4171/owr/2013/53)
... | 3 | partially_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"
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"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"
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"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-12727-003",
"literature-status:partially-solved",
"owr-year:2013"
] | The weaker hypersurface version was settled, while the connected nonlinear Legendrian version in the record remains open. | [
{
"url": "https://doi.org/10.4171/owr/2013/53",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/53 | null | null | null | Let $X$ be a Fano manifold with $b_2(X)=1$. If its variety of minimal rational tangents at a general point is a connected nonlinear Legendrian submanifold of the contact projective space, must $X$ be homogeneous, or at least quasi-homogeneous? Likewise, if the variety is a nonlinear smooth hypersurface, must $X$ be hom... | If X is a Fano manifold with b_2(X)=1 and its general VMRT is a connected nonlinear Legendrean submanifold of the contact projectivization, then X is conjectured to be homogeneous; the weaker conclusion is quasi-homogeneity. Likewise, a nonlinear smooth hypersurface VMRT is conjectured to imply homogeneity, with quasi-... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Quaternion Kähler Structures in Riemannian and Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/53, pp. 3115--3145 |
30,002,445 | OWR-12728-002 | Rigid Elasticity as a Variational Limit | Can rigid-elasticity models be obtained as a variational limit of models whose elastic constants tend to infinity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Inelastic and Non-equilibrium Material Behavior: from Atomistic Structure to Macroscopic Constitutive Relations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/54, pp. 3147... | 3 | partially_solved | null | 2,013 | 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-12728-002",
"literature-status:partially-solved",
"owr-year:2013"
] | Gamma convergence from finite elastic constants to rigid-elastic single-slip models is proved in two and three dimensions, but no general theorem covers all models described in the record. | [
{
"url": "https://doi.org/10.4171/owr/2013/54",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1137/100810320",
"label": "Conti Dolzmann and Kreisbeck"
},
{
"url": "https://doi.org/10.3934/dcdss.2013.6.1",
"label": "finite crystal plasticity Gamma convergence"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/54 | null | null | null | Can rigid-elasticity models be obtained as a variational limit of models whose elastic constants tend to infinity? | Can the rigid-elasticity models be obtained as a variational limit, such as Gamma-convergence, of models with elastic constants tending to infinity? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Inelastic and Non-equilibrium Material Behavior: from Atomistic Structure to Macroscopic Constitutive Relations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/54, pp. 3147--3188 |
30,002,446 | OWR-12729-001 | Scalable Sequential Monte Carlo for Pathogen Sequences | Can fundamental algorithmic developments enable sequential Monte Carlo models with about 1000 observed sequences and 20 parameters? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Design and Analysis of Infectious Disease Studies (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/55, pp. 3189--3219](https://doi.org/10.4171/owr/2013/55)
## Literature review (checked 2... | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"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-12729-001",
"literature-status:open",
"owr-year:2013"
] | No general primary result establishes the requested algorithmic scaling to very large sequence and parameter counts or proves a definitive barrier. | [
{
"url": "https://doi.org/10.4171/owr/2013/55",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/55 | null | null | null | Can fundamental algorithmic developments enable sequential Monte Carlo models with about 1000 observed sequences and 20 parameters? | Can fundamental algorithmic developments enable sequential Monte Carlo models with about 1000 observed sequences and 20 parameters? | 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 | Design and Analysis of Infectious Disease Studies (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/55, pp. 3189--3219 |
30,002,447 | OWR-12730-001 | Reliability of Numerically Computed PDE Eigenvalues | How many numerical eigenvalues from finite-difference or finite-element approximations of PDE eigenvalue problems are reliable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Numerical Solution of PDE Eigenvalue Problems (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/56, pp. 3221--3304](https://doi.org/10.4171/owr/2013/56)
## Literature review (checked 2026-... | 3 | partially_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"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"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-12730-001",
"literature-status:partially-solved",
"owr-year:2013"
] | Quantitative trusted-eigenvalue counts are known for standard elliptic finite element and finite difference models, but there is no method-independent answer and spectral pollution remains possible. | [
{
"url": "https://doi.org/10.4171/owr/2013/56",
"label": "original OWR report"
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{
"url": "https://doi.org/10.1007/s10915-014-9971-5",
"label": "Zhang trusted eigenvalues"
},
{
"url": "https://doi.org/10.1016/j.apnum.2015.08.007",
"label": "spectral pollution and bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/56 | null | null | null | How many numerical eigenvalues from finite-difference or finite-element approximations of PDE eigenvalue problems are reliable? | How many numerical eigenvalues from finite-difference or finite-element approximations of PDE eigenvalue problems are reliable? | 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 | Numerical Solution of PDE Eigenvalue Problems (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/56, pp. 3221--3304 |
30,002,448 | OWR-12730-002 | Low-Rank Tensor Methods for High-Dimensional Eigenproblems | Can low-rank tensor methods overcome the curse of dimensionality when computing the $p$ smallest eigenvalues of $-\Delta u+V(x)u=\lambda u$ on $(a,b)^d$ with Dirichlet boundary conditions, including for very large $d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Numerical Solution of PDE Eigenvalue Problems (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/56, pp. 3221--3304](https://doi.org/10.4171/owr/2013/56)
## Literature review (checked 2026-... | 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-12730-002",
"literature-status:open",
"owr-year:2013"
] | The extracted record is a model and motivation for low-rank tensor eigensolvers rather than a precise theorem or yes-no claim; general guarantees therefore remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2013/56",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/56 | null | null | null | Can low-rank tensor methods overcome the curse of dimensionality when computing the $p$ smallest eigenvalues of $-\Delta u+V(x)u=\lambda u$ on $(a,b)^d$ with Dirichlet boundary conditions, including for very large $d$? | Can low-rank tensor methods overcome the curse of dimensionality for the p smallest eigenvalues of -Delta u+V(x)u=lambda u on (a,b)^d with Dirichlet boundary conditions, including very large d? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Numerical Solution of PDE Eigenvalue Problems (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/56, pp. 3221--3304 |
30,002,449 | OWR-12732-001 | Algebras with Natural Cluster Structures | Which algebras carry natural cluster algebra structures? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432](https://doi.org/10.4171/owr/2013/58)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,013 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
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"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"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-12732-001",
"literature-status:open",
"owr-year:2013"
] | Natural cluster structures are known for many important algebras, but the general classification requested by the extracted question is not complete. | [
{
"url": "https://doi.org/10.4171/owr/2013/58",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/58 | null | null | null | Which algebras carry natural cluster algebra structures? | Which algebras carry natural cluster algebra structures? | 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 | Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432 |
30,002,450 | OWR-12732-002 | Potentials for Quivers from Twice-Punctured Surfaces | For quivers arising from triangulations of closed positive-genus surfaces with exactly two punctures, does there exist a unique non-degenerate potential up to weak right equivalence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432](https://doi.org/10.4171/owr/2013/58)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,013 | 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"
} | {
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"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-12732-002",
"literature-status:open",
"owr-year:2013"
] | Uniqueness is proved for many mutation classes, but closed positive-genus surfaces with exactly two punctures remain an unresolved classification case. | [
{
"url": "https://doi.org/10.4171/owr/2013/58",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.aim.2015.09.038",
"label": "Geiss Labardini-Fragoso and Schroer"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/58 | null | null | null | For quivers arising from triangulations of closed positive-genus surfaces with exactly two punctures, does there exist a unique non-degenerate potential up to weak right equivalence? | For quivers arising from triangulations of closed positive-genus surfaces with exactly two punctures, does there exist a unique non-degenerate potential up to weak right equivalence? | 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 | Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432 |
30,002,451 | OWR-12732-003 | Cluster Structures for Belavin–Drinfeld Data | Let $G$ be a simple complex Lie group and let $T=(\Gamma_1,\Gamma_2,\gamma)$ be a Belavin–Drinfeld triple, with associated class $R_T$ of classical $R$-matrices. Does there exist a cluster structure $\mathcal C_T$ on $G$ that is compatible with the Poisson bracket for every $r\in R_T$ and whose upper cluster algebra is... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432](https://doi.org/10.4171/owr/2013/58)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,013 | 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-12732-003",
"literature-status:partially-solved",
"owr-year:2013"
] | The conjecture is verified for standard data and broad classes of type A data, with isolated further examples, but the all-groups all-triples classification remains open. | [
{
"url": "https://doi.org/10.4171/owr/2013/58",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1902.02902",
"label": "Gekhtman Shapiro and Vainshtein"
},
{
"url": "https://doi.org/10.1080/00927872.2025.2450036",
"label": "Zhang SO3 cluster structures"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/58 | null | null | null | Let $G$ be a simple complex Lie group and let $T=(\Gamma_1,\Gamma_2,\gamma)$ be a Belavin–Drinfeld triple, with associated class $R_T$ of classical $R$-matrices. Does there exist a cluster structure $\mathcal C_T$ on $G$ that is compatible with the Poisson bracket for every $r\in R_T$ and whose upper cluster algebra is... | For every Belavin--Drinfeld triple T, does there exist a classification of regular cluster structures on G completely parallel to the Belavin--Drinfeld classification? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432 |
30,002,452 | OWR-12732-004 | Generalized Cluster Structures on Poisson–Lie Doubles | For every Belavin–Drinfeld triple $T$, does the double $D(G)$ admit a generalized cluster structure compatible with the corresponding Poisson–Lie structure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432](https://doi.org/10.4171/owr/2013/58)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,013 | 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-12732-004",
"literature-status:partially-solved",
"owr-year:2013"
] | The construction is proved for trivial and Cremmer-Gervais data and later isolated groups, but existence for every Belavin-Drinfeld triple remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2013/58",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1080/00927872.2025.2450036",
"label": "Zhang generalized double"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/58 | null | null | null | For every Belavin–Drinfeld triple $T$, does the double $D(G)$ admit a generalized cluster structure compatible with the corresponding Poisson–Lie structure? | For every Belavin--Drinfeld triple T, does there exist a generalized cluster structure on D(G) compatible with the corresponding Poisson--Lie structure? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432 |
30,002,453 | OWR-12732-005 | Recovery of Support $\tau$-Tilting Orders from $g$-Vectors | For a basic finite-dimensional $k$-algebra $\Lambda$, do the $g$-vectors determine the partial order on $\mathrm{s}\tau\text{-}\mathrm{tilt}\,\Lambda$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432](https://doi.org/10.4171/owr/2013/58)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,013 | 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-12732-005",
"literature-status:partially-solved",
"owr-year:2013"
] | The g-vector cones determine the support tau-tilting order for tau-tilting finite algebras, while the arbitrary finite-dimensional algebra case remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2013/58",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1503.00285",
"label": "tau-tilting finite algebras and g-vectors"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/58 | null | null | null | For a basic finite-dimensional $k$-algebra $\Lambda$, do the $g$-vectors determine the partial order on $\mathrm{s}\tau\text{-}\mathrm{tilt}\,\Lambda$? | Do g-vectors determine the partial order on s-tau-tilt Lambda? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432 |
30,002,454 | OWR-12732-006 | Spectral Coordinates for Grassmannian Cluster Structures | For the affine cone over $\operatorname{Gr}(k,n)$, viewed through decorated $\operatorname{GL}(k)$-connections, do spectral coordinates recover the cluster structure on its homogeneous coordinate ring, with a spectral network corresponding to every cluster? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432](https://doi.org/10.4171/owr/2013/58)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,013 | 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-12732-006",
"literature-status:open",
"owr-year:2013"
] | The spectral-coordinate and cluster-coordinate identification is still presented as conjectural; later work gives examples and partial Grassmannian results, not a general proof. | [
{
"url": "https://doi.org/10.4171/owr/2013/58",
"label": "Original OWR record"
},
{
"url": "https://arxiv.org/abs/1204.4824",
"label": "Gaiotto Moore Neitzke"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/58 | null | null | null | For the affine cone over $\operatorname{Gr}(k,n)$, viewed through decorated $\operatorname{GL}(k)$-connections, do spectral coordinates recover the cluster structure on its homogeneous coordinate ring, with a spectral network corresponding to every cluster? | For the Grassmannian case, do spectral coordinates recover the cluster structure on the homogeneous coordinate ring, with a spectral network corresponding to each cluster? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432 |
30,002,455 | OWR-12732-007 | Linear Independence of Cluster Monomials | For a cluster algebra $\mathcal A$ over a coefficient semifield $\mathbb P$, are the cluster monomials linearly independent over $\mathbb Z\mathbb P$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432](https://doi.org/10.4171/owr/2013/58)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,013 | 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-12732-007",
"literature-status:partially-solved",
"owr-year:2013"
] | The cited primary proof establishes linear independence for all skew-symmetric cluster algebras, while the extracted formulation allows arbitrary coefficient semifields; the full stated generality is not established by that result. | [
{
"url": "https://doi.org/10.4171/owr/2013/58",
"label": "Original OWR record"
},
{
"url": "https://arxiv.org/abs/1203.1307",
"label": "Cerulli Irelli Keller Labardini Fragoso Plamondon"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/58 | null | null | null | For a cluster algebra $\mathcal A$ over a coefficient semifield $\mathbb P$, are the cluster monomials linearly independent over $\mathbb Z\mathbb P$? | For a cluster algebra A over a coefficient semifield P, are the cluster monomials linearly independent over ZP? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Cluster Algebras and Related Topics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/58, pp. 3379--3432 |
30,002,456 | OWR-12733-001 | Mechanisms Maintaining Flat Plant Leaves | Which growth-coordination and mechanical-feedback mechanisms explain why most plant leaves remain approximately flat despite heterogeneous cellular growth? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Material Theories (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/59, pp. 3433--3485](https://doi.org/10.4171/owr/2013/59)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,013 | 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-12733-001",
"literature-status:open",
"owr-year:2013"
] | The extracted question is broad; primary mechanics work identifies growth coordination constraints and model behavior but does not give a general biological explanation for leaf flatness. | [
{
"url": "https://doi.org/10.4171/owr/2013/59",
"label": "Original OWR record"
},
{
"url": "https://ems.press/content/serial-article-files/46487",
"label": "Primary leaf growth mechanics study"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/59 | null | null | null | Which growth-coordination and mechanical-feedback mechanisms explain why most plant leaves remain approximately flat despite heterogeneous cellular growth? | Why are plant leaves generally flat? | 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 | Material Theories (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/59, pp. 3433--3485 |
30,002,457 | OWR-12733-002 | Cellular Response to Mechanical Stress | How do cells react to mechanical stress? In the reported model, stress induces cellular reinforcement and slows growth in the direction of greatest principal stress. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Material Theories (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/59, pp. 3433--3485](https://doi.org/10.4171/owr/2013/59)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 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 | Unrecoverable OWR statement (Checked against the official Oberwolfach report. The source poses this as a rhetorical question and immediately reports an experimental and ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12733-002",
"literature-status:open",
"owr-year:2013"
] | The record asks a broad mechanobiology question; experiments and models identify several cellular responses, but no complete general mechanism is established. | [
{
"url": "https://doi.org/10.4171/owr/2013/59",
"label": "Original OWR record"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/59 | null | null | null | null | How do cells react to mechanical stress? In the reported model, stress induces cellular reinforcement and slows growth in the direction of greatest principal stress. | unrecoverable | Checked against the official Oberwolfach report. The source poses this as a rhetorical question and immediately reports an experimental and mechanical answer, so it is not a separate unresolved problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Material Theories (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/59, pp. 3433--3485 |
30,002,458 | OWR-12861-001 | Existence of Combinatorial Designs at Admissible Orders | For integers $q>r\geq1$ and $\lambda\geq1$, an $(n,q,r,\lambda)$-design is a collection of $q$-subsets of an $n$-element set in which every $r$-subset occurs in exactly $\lambda$ blocks. Characterize the orders $n$ for which such a design exists. The necessary divisibility conditions are
$$\binom{q-i}{r-i}\mid\lambda\b... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** partially solved
... | 3 | partially_solved | null | 2,014 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-001",
"literature-status:partially-solved",
"owr-year:2014"
] | Keevash proved the existence conjecture asymptotically for fixed parameters and all sufficiently large admissible orders, but exact existence for every finite parameter set is not completely classified. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
},
{
"url": "https://arxiv.org/abs/1401.3665",
"label": "Keevash existence theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | For integers $q>r\geq1$ and $\lambda\geq1$, an $(n,q,r,\lambda)$-design is a collection of $q$-subsets of an $n$-element set in which every $r$-subset occurs in exactly $\lambda$ blocks. Characterize the orders $n$ for which such a design exists. The necessary divisibility conditions are
$$\binom{q-i}{r-i}\mid\lambda\b... | For fixed q, r, and lambda, are the necessary divisibility conditions sufficient, apart from finitely many exceptional n, for the existence of a design, and hence of a Steiner system when lambda=1? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,459 | OWR-12861-004 | Sidorenko's Inequality for Bipartite Graphs | For every bipartite graph $H$ and graph $G$, does Sidorenko's inequality
$$t_H(G)\geq t_{K_2}(G)^{|E(H)|}$$
hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-004",
"literature-status:open",
"owr-year:2014"
] | The referenced claim reduces to Sidorenko's conjecture; many graph families are now known, but the conjecture for all bipartite graphs remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
},
{
"url": "https://doi.org/10.1007/BF02988307",
"label": "Sidorenko's original paper"
},
{
"url": "https://arxiv.org/abs/2307.04588",
"label": "Current Sidorenko survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | For every bipartite graph $H$ and graph $G$, does Sidorenko's inequality
$$t_H(G)\geq t_{K_2}(G)^{|E(H)|}$$
hold? | For every bipartite graph H and graph G, does the Sidorenko inequality t_H(G) >= t_{K_2}(G)^{|E(H)|} hold? | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,460 | OWR-12861-005 | Linear Cycle-and-Edge Decompositions of Graphs | Does every graph on $n$ vertices decompose into $O(n)$ cycles and edges? This is known for random graphs and for graphs with linear minimum degree. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** partially solved
... | 3 | partially_solved | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-005",
"literature-status:partially-solved",
"owr-year:2014"
] | The extracted results settle random graphs and graphs of linear minimum degree, but the full Erdős Gallai linear-size cycle and edge decomposition conjecture for arbitrary graphs remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
},
{
"url": "https://arxiv.org/abs/1404.3306",
"label": "Conlon Fox Sudakov decomposition paper"
},
{
"url": "https://doi.org/10.1016/j.aim.2023.109434",
"label": "Bucic Montgomery decomposition bounds"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | Does every graph on $n$ vertices decompose into $O(n)$ cycles and edges? This is known for random graphs and for graphs with linear minimum degree. | Every graph on n vertices is conjectured to decompose into O(n) cycles and edges; the random-graph and linear-minimum-degree cases are established special cases. | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,461 | OWR-12861-009 | Thresholds for Spanning Combs and Bounded-Degree Trees | Is the threshold for a spanning comb $\operatorname{Comb}_n$ in $G(n,p)$ of order $(\log n)/n$? More generally, is this the threshold for every $n$-vertex tree of bounded degree? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | solved | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1002/cpa.21613",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. E. Lubetzky (joint with J. Kahn and N. Wormald; OWR 1/2014, pp. 42–43) states the Comb Conjecture, that the threshold for a spanning comb Comb_n in G(n, p) has order (log n)/n, and the more general conjecture (Kahn's) for every n-vertex tree of bounded deg... | [
"owr",
"oberwolfach-reports",
"OWR-12861-009",
"literature-status:open",
"owr-year:2014"
] | Subsequent work characterizes special cases such as three-profiles and tree profiles, but the general realization and local-to-global questions for arbitrary profiles remain open. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
},
{
"url": "https://arxiv.org/abs/1211.3106",
"label": "Three-local profiles of graphs"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | Is the threshold for a spanning comb $\operatorname{Comb}_n$ in $G(n,p)$ of order $(\log n)/n$? More generally, is this the threshold for every $n$-vertex tree of bounded degree? | The threshold for a spanning comb Combn in G(n,p) is conjectured to have order (log n)/n; more generally, the same threshold is conjectured for every n-vertex tree of bounded degree. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,462 | OWR-12861-010 | Realizability and Consequences of Graph Profiles | Which probability distributions on the set $\mathcal H_k$ of isomorphism types of $k$-vertex graphs occur as the $k$-profile $\pi_k(G)$ of a graph $G$? Which global properties of $G$ can be deduced from $\pi_k(G)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-010",
"literature-status:open",
"owr-year:2014"
] | The bounded-degree Ramsey growth conjecture remains open in general; bounded-chromatic and other special classes are known. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
},
{
"url": "https://arxiv.org/abs/1002.0045",
"label": "Conlon Fox Sudakov Ramsey bounds"
},
{
"url": "https://www.its.caltech.edu/~dconlon/GraphRamsey.pdf",
"label": "Current graph Ramsey survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | Which probability distributions on the set $\mathcal H_k$ of isomorphism types of $k$-vertex graphs occur as the $k$-profile $\pi_k(G)$ of a graph $G$? Which global properties of $G$ can be deduced from $\pi_k(G)$? | Which probability distributions on the set H_k of k-vertex graph isomorphism types can occur as the k-profile of a graph, and which global conclusions about G can be drawn from its distribution pi_k(G)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,463 | OWR-12861-011 | Structural Determinants of Graph Ramsey Numbers | Which structural properties of a graph $H$ approximately determine its Ramsey number? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-011",
"literature-status:open",
"owr-year:2014"
] | The lower bound and constant-chromatic and bipartite cases are known, but the claimed order estimate remains open for general graphs. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
},
{
"url": "https://arxiv.org/abs/1002.0045",
"label": "Conlon Fox Sudakov Ramsey bounds"
},
{
"url": "https://www.n.ethz.ch/~ywigderson/math/static/RamseyTheory2024LectureNotes.pdf",
"label": "Recent Ram... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | Which structural properties of a graph $H$ approximately determine its Ramsey number? | What properties of a graph H roughly determine its Ramsey number? | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,464 | OWR-12861-012 | Ramsey Numbers in Terms of Degeneracy | For every graph $H$ on $n$ vertices, is
$$\log r(H)=\Theta(d(H)+\log n),$$
where $d(H)$ is the degeneracy of $H$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-012",
"literature-status:open",
"owr-year:2014"
] | The exact record explicitly identifies the general non-bipartite case as open; later special cases do not resolve the general statement. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | For every graph $H$ on $n$ vertices, is
$$\log r(H)=\Theta(d(H)+\log n),$$
where $d(H)$ is the degeneracy of $H$? | For every graph H on n vertices, is log r(H) = Theta(d(H)+log n), where d(H) is the degeneracy of H? | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,465 | OWR-12861-013 | Sparse Random Graphs Avoiding Non-Bipartite Subgraphs | For a nonbipartite graph $H$, determine the density thresholds and typical structure of uniformly random $H$-free graphs with $m$ edges. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-013",
"literature-status:open",
"owr-year:2014"
] | Known exact formulas cover several loose and linear path and cycle families, but the broad pair of extremal-number questions in the record is not resolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0097316514001204",
"label": "Turán problems for paths and cycles"
},
{
"url": "https://arxiv.org/abs/1302.2387",
"label": "Linear hypergraph ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | For a nonbipartite graph $H$, determine the density thresholds and typical structure of uniformly random $H$-free graphs with $m$ edges. | Determine the density thresholds and typical structure of uniformly random H-free graphs with m edges when H is a general non-bipartite graph. | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,466 | OWR-12861-017 | Unit Distances in Rational Directions | For every $\varepsilon>0$, is the number of unit-distance pairs among any $n$ planar points whose connecting line makes a rational multiple of $\pi$ with the $x$-axis less than $n^{1+\varepsilon}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 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 | Answered in the source or not an open problem (solved (a theorem, answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (a theorem, answered in the source)**. J. Solymosi (joint with R. Schwartz; OWR 1/2014, p. 74, Theorem 2) states the bound as a theorem of Schwartz–Solymosi–de Zeeuw, [Mathematika 58 (2012)](https://doi.org/10.1112/S0025579311001847): n points in the plane determin... | [
"owr",
"oberwolfach-reports",
"OWR-12861-017",
"literature-status:open",
"owr-year:2014"
] | The extracted record is a truncated theorem and conjecture fragment; although the rational-angle unit-distance bound is proved, no complete underlying conjecture is stated for verification. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
},
{
"url": "https://doi.org/10.1112/S0025579311001847",
"label": "Rational-angle unit-distance paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | For every $\varepsilon>0$, is the number of unit-distance pairs among any $n$ planar points whose connecting line makes a rational multiple of $\pi$ with the $x$-axis less than $n^{1+\varepsilon}$? | For every \epsilon>0, given n points in the plane, the number of unit-distance pairs whose connecting line makes a rational multiple of \pi with the x-axis is less than n^{1+\epsilon}. | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,467 | OWR-12861-018 | Extremal Numbers of Tight Hypergraph Paths and Cycles | For a $k$-uniform tight path $P_{\ell}^{k}$ and tight cycle $C_{\ell}^{k}$, what are the extremal numbers $\operatorname{ex}(n;P_{\ell}^{k})$ and $\operatorname{ex}(n;C_{\ell}^{k})$ when $k$ divides $\ell$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-018",
"literature-status:open",
"owr-year:2014"
] | Primary work settles important fixed-uniformity path and cycle families, but the general extremal-number questions posed in the record remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0097316514001204",
"label": "Turán problems for paths and cycles"
},
{
"url": "https://arxiv.org/abs/1302.2387",
"label": "Linear hypergraph ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | For a $k$-uniform tight path $P_{\ell}^{k}$ and tight cycle $C_{\ell}^{k}$, what are the extremal numbers $\operatorname{ex}(n;P_{\ell}^{k})$ and $\operatorname{ex}(n;C_{\ell}^{k})$ when $k$ divides $\ell$? | For a k-uniform tight path P_{\ell}^{k} and tight cycle C_{\ell}^{k}, what are the extremal numbers ex(n;P_{\ell}^{k}) and ex(n;C_{\ell}^{k}) when k divides \ell? | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,468 | OWR-12861-019 | Biclique Partition Numbers of Random Graphs | Let $\tau(G)$ be the minimum number of pairwise edge-disjoint complete bipartite subgraphs partitioning $E(G)$, and let $\beta(G)$ be the largest order of an induced complete bipartite subgraph. For $G\sim G(n,0.5)$, is $\tau(G)=n-\beta(G)+1$ with high probability? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | solved | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **solved (no)**; the dataset currently labels it open. N. Alon, OWR 1/2014, p. 80 (also Conjecture 4.1 of arXiv:1402.6466v1): for G = G(n, 1/2), is τ(G) = n − β(G) + 1 with high probability (whp), τ the least number of edge-disjoint complete bipartite subgraphs covering all... | [
"owr",
"oberwolfach-reports",
"OWR-12861-019",
"literature-status:open",
"owr-year:2014"
] | The revised random-graph conjecture remains a conjecture: available primary work states it as plausible and does not prove or disprove it. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Original OWR record"
},
{
"url": "https://www.tau.ac.il/~nogaa/PDFS/bipdec2.pdf",
"label": "Alon bipartite decomposition paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | Let $\tau(G)$ be the minimum number of pairwise edge-disjoint complete bipartite subgraphs partitioning $E(G)$, and let $\beta(G)$ be the largest order of an induced complete bipartite subgraph. For $G\sim G(n,0.5)$, is $\tau(G)=n-\beta(G)+1$ with high probability? | Let \tau(G) be the minimum number of pairwise edge-disjoint complete bipartite subgraphs partitioning E(G), and let \beta(G) be the largest order of an induced complete bipartite subgraph. For G\sim G(n,0.5), is \tau(G)=n-\beta(G)+1 with high probability? | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,469 | OWR-12861-020 | Graph Blocks and Coset Partition Refinements | Which properties force a graph $G$ to contain a $k$-block, meaning a maximal set of at least $k$ vertices no two of which can be separated by fewer than $k$ other vertices? How does
$$\beta(G)=\max\{k:G\text{ has a }k\text{-block}\}$$
relate to other graph invariants? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** partially solved
... | 3 | open | null | 2,014 | 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-12861-020",
"literature-status:partially-solved",
"owr-year:2014"
] | Removed the unrelated Hou–Yin Hamilton-generation note. It concerns Heinig’s Question 1, not either question in this record. The Friedgut coset-partition clause is represented by OWR-12481-012 and is now recorded there as disproved; this record retains Diestel’s k-block questions.
**What remains.** The structural k-bl... | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follo... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | Which properties force a graph $G$ to contain a $k$-block, meaning a maximal set of at least $k$ vertices no two of which can be separated by fewer than $k$ other vertices? How does
$$\beta(G)=\max\{k:G\text{ has a }k\text{-block}\}$$
relate to other graph invariants? | What properties force a graph G to contain a k-block, where a k-block is a maximal set of at least k vertices no two of which can be separated by fewer than k other vertices, and how does \beta(G)=\max\{k:G has a k-block\} relate to other graph invariants? Also, is every partition of S_n into t-cosets a refinement of a... | corrected_verified | Separated the adjacent Diestel and Friedgut questions in OWR 01/2014, p. 81. Friedgut’s question is retained at OWR-12481-012; the Hou–Yin note belongs to Heinig’s different question. | null | null | null | null | null | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,470 | OWR-12861-021 | Spanning Near-Squares of Odd Cycles | For every odd $n\geq7$, does every $n$-vertex graph with minimum degree at least $\lceil n/2\rceil$ contain a spanning graph formed from the square of an $n$-cycle by deleting alternate peripheral edges until exactly three consecutive vertices have degree $4$ and the remaining $n-3$ vertices have degree $3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** partially solved
... | 3 | partially_solved | null | 2,014 | 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": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-021",
"literature-status:partially-solved",
"owr-year:2014"
] | Negative answer to Heinig’s spanning-near-square question. Ferudun gives counterexamples for odd $n\ge7$. Independently checked the $n=9$ example $K_{4,4,1}$: its minimum degree is 5, and none of the 315 partitions of the cycle-square vertices into parts of sizes 4,4,1 can be made independent by deleting a matching of ... | [
{
"url": "https://doi.org/10.5281/zenodo.23004012",
"label": "Alper Ferudun (2026), Dirac Graphs Without a Spanning Near-Square of an Odd Cycle — unrefereed preprint"
},
{
"url": "https://eulersolve.org/papers/owr-12861-021/",
"label": "EulerSolve manuscript, source, and verification materials"
... | 2026-09-28T00:00:00 | Alper Ferudun (2026), Dirac Graphs Without a Spanning Near-Square of an Odd Cycle — unrefereed preprint: https://doi.org/10.5281/zenodo.23004012
EulerSolve manuscript, source, and verification materials: https://eulersolve.org/papers/owr-12861-021/
Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp.... | https://doi.org/10.4171/owr/2014/01 | null | null | null | For every odd $n\geq7$, does every $n$-vertex graph with minimum degree at least $\lceil n/2\rceil$ contain a spanning graph formed from the square of an $n$-cycle by deleting alternate peripheral edges until exactly three consecutive vertices have degree $4$ and the remaining $n-3$ vertices have degree $3$? | For every odd n\ge 7, does every n-vertex graph with minimum degree at least \lceil n/2\rceil contain a spanning copy of the graph obtained from the square of an n-cycle by deleting alternate peripheral edges until exactly three consecutive vertices have degree 4, with the other n-3 vertices having degree 3? | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,471 | OWR-12861-022 | Chromatic Uniqueness of Nonrepresentable Matroids | Does there exist a matroid whose chromatic polynomial is not the chromatic polynomial of any matroid representable over a field; does there exist a matroid not representable over any field that is chromatically unique; and how small can such a matroid be? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-022",
"literature-status:open",
"owr-year:2014"
] | The questions ask for nonrepresentable matroids with prescribed characteristic-polynomial behavior; modern Hodge results address log-concavity, not these existence and minimality questions, which remain open. | [
{
"url": "https://ems.press/content/serial-article-files/46491",
"label": "Oberwolfach combinatorics report"
},
{
"url": "https://arxiv.org/abs/1705.07960",
"label": "Baker, Hodge theory in combinatorics"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | Does there exist a matroid whose chromatic polynomial is not the chromatic polynomial of any matroid representable over a field; does there exist a matroid not representable over any field that is chromatically unique; and how small can such a matroid be? | Does there exist a matroid whose chromatic polynomial is not the chromatic polynomial of any matroid representable over a field; does there exist a matroid not representable over any field that is chromatically unique; and how small can such a matroid be? | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,472 | OWR-12861-023 | Existential Completeness in Triangle-Free Graphs | A triangle-free graph is $k$-existentially complete if, for every independent set $A$ and disjoint set $B$ with $|A|+|B|\leq k$, there is a vertex adjacent to every vertex of $A$ and to no vertex of $B$. Is there a constant $r$ such that no triangle-free graph is $r$-existentially complete? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-023",
"literature-status:open",
"owr-year:2014"
] | The conjecture that some fixed r forbids r-existentially-complete triangle-free graphs remains unresolved; even the case r=4 is reported as open, despite upper-bound progress. | [
{
"url": "https://ems.press/content/serial-article-files/46491",
"label": "Oberwolfach combinatorics report"
},
{
"url": "https://arxiv.org/abs/1708.08817",
"label": "Letzter--Sahasrabudhe, triangle-free graphs"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | A triangle-free graph is $k$-existentially complete if, for every independent set $A$ and disjoint set $B$ with $|A|+|B|\leq k$, there is a vertex adjacent to every vertex of $A$ and to no vertex of $B$. Is there a constant $r$ such that no triangle-free graph is $r$-existentially complete? | A triangle-free graph is k-existentially-complete if for every independent set A and disjoint set B with |A|+|B|\le k there is a vertex adjacent to every vertex of A and to none of B. Is there a constant r such that no triangle-free graph is r-existentially-complete? | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,473 | OWR-12861-024 | Determinant of a Longest-Increasing-Subsequence Matrix | For a permutation \sigma\in S_n, let LIS(\sigma) be its longest increasing subsequence length, choose an increasing subsequence S(\sigma) of that length, and let A have rows indexed by S_n and columns indexed by permutations \sigma with LIS(\sigma)\ge n-t, with A_{\pi,\sigma}=1 exactly when \pi and \sigma agree outside... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Unrecoverable OWR statement (The official problem session itself inconsistently names the matrix $M$ and $A$, indexes its columns by an apparent proper subset of $S_n$ w) | [] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-024",
"literature-status:open",
"owr-year:2014"
] | The source defines a rectangular matrix and then asks for its determinant; no unambiguous mathematical question can be recovered.
**What remains.** The source extraction is retained for provenance and excluded from published problem counts. | [
{
"url": "https://doi.org/10.4171/owr/2014/01",
"label": "Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follo... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | null | For a permutation \sigma\in S_n, let LIS(\sigma) be its longest increasing subsequence length, choose an increasing subsequence S(\sigma) of that length, and let A have rows indexed by S_n and columns indexed by permutations \sigma with LIS(\sigma)\ge n-t, with A_{\pi,\sigma}=1 exactly when \pi and \sigma agree outside... | unrecoverable | The official problem session itself inconsistently names the matrix $M$ and $A$, indexes its columns by an apparent proper subset of $S_n$ while asking for a determinant, and therefore does not define a square matrix unambiguously. No separate clean statement is promoted, and the original record remains visible for pro... | null | null | null | null | null | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,474 | OWR-12861-025 | Triangle Abundance Forcing Large Clique Blow-Ups | For every constant $C>0$, does there exist $\gamma=\gamma(C)>0$ such that every sufficiently large $n$-vertex graph with at least
$$\frac{n^{3/2}}{\exp(C\sqrt{\log n})}$$
triangles contains a $t$-blow-up of $K_3$ with $t\geq\gamma\sqrt{\log n}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-025",
"literature-status:open",
"owr-year:2014"
] | Known triangle-count to blow-up theorems require substantially denser hypotheses; the stated threshold and square-root-logarithmic blow-up conclusion remain unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46491",
"label": "Oberwolfach combinatorics report"
},
{
"url": "https://www.math.uni-hamburg.de/en/personen/schacht/2012/blowup.pdf",
"label": "Rödl--Schacht, complete partite subgraphs"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | For every constant $C>0$, does there exist $\gamma=\gamma(C)>0$ such that every sufficiently large $n$-vertex graph with at least
$$\frac{n^{3/2}}{\exp(C\sqrt{\log n})}$$
triangles contains a $t$-blow-up of $K_3$ with $t\geq\gamma\sqrt{\log n}$? | Is it true that every n-vertex graph with at least n^{3/2}/\exp(C\sqrt{\log n}) triangles contains a t-blow-up of K_3 with t\ge\gamma\log n for some \gamma=\gamma(C)? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,475 | OWR-12861-026 | Nonsingularity and Limit Laws for Random Matrices | Let $A(n,d)$ be the adjacency matrix of a uniformly random $d$-regular graph, where $d>2$. Is $A(n,d)$ nonsingular with probability tending to $1$ as $n\to\infty$? What are the limiting distributions of the permanent of a random $\{\pm1\}$-matrix and the determinant of a random symmetric $\{\pm1\}$-matrix? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** partially solved
... | 3 | partially_solved | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-026",
"literature-status:partially-solved",
"owr-year:2014"
] | Huang proves nonsingularity with high probability for fixed-degree random regular graphs, but limiting laws for the random-sign permanent and symmetric-sign determinant remain unresolved; the bundled problem is partially solved. | [
{
"url": "https://arxiv.org/abs/1807.06465",
"label": "Huang, random regular adjacency matrices"
},
{
"url": "https://arxiv.org/abs/0804.2362",
"label": "Tao--Vu, random discrete matrices"
},
{
"url": "https://ems.press/content/serial-article-files/46491",
"label": "Oberwolfach combi... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | Let $A(n,d)$ be the adjacency matrix of a uniformly random $d$-regular graph, where $d>2$. Is $A(n,d)$ nonsingular with probability tending to $1$ as $n\to\infty$? What are the limiting distributions of the permanent of a random $\{\pm1\}$-matrix and the determinant of a random symmetric $\{\pm1\}$-matrix? | Let A(n,d) be the adjacency matrix of G(n,d), d>2. Is A(n,d) nonsingular with probability tending to 1 as n tends to infinity? What is the limiting distribution of the permanent of a random \pm1 matrix, and what is the limiting distribution of the determinant of a random symmetric \pm1 matrix? | 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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,476 | OWR-12861-027 | Diagonal Signings and Real Eigenvalues of Random Matrices | For a random $n\times n$ matrix $M_n$ with entries in $\{\pm1\}$, does the probability tend to $1$ that no choice of signs for its diagonal entries makes it singular? Does $M_n$ have at least two real eigenvalues with probability $1-o(1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90](https://doi.org/10.4171/owr/2014/01)
## Literature review (checked 2026-08-21)
**Status:** partially solved
... | 3 | partially_solved | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12861-027",
"literature-status:partially-solved",
"owr-year:2014"
] | The diagonal-sign switching singularity conjecture remains open, while Han proves that iid Rademacher matrices have order-square-root-many real eigenvalues with high probability; the bundled problem is partially solved. | [
{
"url": "https://ems.press/content/serial-article-files/46491",
"label": "Oberwolfach combinatorics report"
},
{
"url": "https://arxiv.org/abs/2502.13819",
"label": "Han, random matrix singular values and eigenvalues"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/01 | null | null | null | For a random $n\times n$ matrix $M_n$ with entries in $\{\pm1\}$, does the probability tend to $1$ that no choice of signs for its diagonal entries makes it singular? Does $M_n$ have at least two real eigenvalues with probability $1-o(1)$? | For a random \pm1 matrix M_n, does the probability tend to 1 that no choice of signs for its diagonal entries makes it singular? Also, does M_n have at least two real eigenvalues with probability 1-o(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 | Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/01, pp. 5--90 |
30,002,477 | OWR-12862-001 | Universal Aronszajn Trees at Aleph One | Is there a model of set theory in which the universality number $u(T_{\aleph_1})$ of trees of size $\aleph_1$ without an $\aleph_1$-branch equals $1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/02, pp. 91--144](https://doi.org/10.4171/owr/2014/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessment... | 3 | open | null | 2,014 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"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-12862-001",
"literature-status:open",
"owr-year:2014"
] | The extracted record is not a well-formed identifiable set-theoretic proposition; without a recoverable statement or resolution it is classified open under the triage rule. | [
{
"url": "https://ems.press/content/serial-article-files/46488",
"label": "Oberwolfach set theory report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/02 | null | null | null | Is there a model of set theory in which the universality number $u(T_{\aleph_1})$ of trees of size $\aleph_1$ without an $\aleph_1$-branch equals $1$? | Is there a model of set theory in which the universality number u(T_{\aleph_1}) of trees of size \aleph_1 without an \aleph_1-branch equals 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 | Set Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/02, pp. 91--144 |
30,002,478 | OWR-12862-004 | Classifiable Conjugacy in Automorphism Groups of Simple $C^*$-Algebras | Does there exist an infinite-dimensional simple $C^*$-algebra $A$ such that conjugacy in $\operatorname{Aut}(A)$ is classifiable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/02, pp. 91--144](https://doi.org/10.4171/owr/2014/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessment... | 3 | open | null | 2,014 | 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-12862-004",
"literature-status:open",
"owr-year:2014"
] | No general classification of conjugacy in automorphism groups of infinite-dimensional simple C-star algebras is known; existing work gives substantial nonclassifiability results but does not settle the stated existence question. | [
{
"url": "https://ems.press/content/serial-article-files/46488",
"label": "Oberwolfach set theory report"
},
{
"url": "https://arxiv.org/abs/1501.03022",
"label": "Lupini, classification of C-star automorphisms"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/02 | null | null | null | Does there exist an infinite-dimensional simple $C^*$-algebra $A$ such that conjugacy in $\operatorname{Aut}(A)$ is classifiable? | Does there exist an infinite-dimensional simple C^*-algebra A such that conjugacy in Aut(A) is classifiable? | 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 | Set Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/02, pp. 91--144 |
30,002,479 | OWR-12862-005 | Strong Invariant Universality at Singular Cardinals | For generalized trees of size $\kappa$, is $\kappa^\kappa=\kappa$ necessary for embeddability to be strongly invariantly universal among $\kappa$-analytic quasi-orders? For singular $\kappa$, what is the descriptive-set-theoretic complexity of embeddability on $\operatorname{Mod}_\kappa(\varphi)$, and can it consistent... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/02, pp. 91--144](https://doi.org/10.4171/owr/2014/02)
## Literature review (checked 2026-08-21)
**Status:** partially solved
... | 3 | partially_solved | null | 2,014 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"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-12862-005",
"literature-status:partially-solved",
"owr-year:2014"
] | Strong invariant universality and related reductions to generalized trees, graphs, and groups are proved under cardinal-arithmetic hypotheses, but necessity, singular-cardinal complexity, and the full replacement questions remain unsettled. | [
{
"url": "https://ems.press/content/serial-article-files/46488",
"label": "Oberwolfach set theory report"
},
{
"url": "https://arxiv.org/abs/1903.08091",
"label": "Calderoni--Mildenberger--Motto Ros, universality"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/02 | null | null | null | For generalized trees of size $\kappa$, is $\kappa^\kappa=\kappa$ necessary for embeddability to be strongly invariantly universal among $\kappa$-analytic quasi-orders? For singular $\kappa$, what is the descriptive-set-theoretic complexity of embeddability on $\operatorname{Mod}_\kappa(\varphi)$, and can it consistent... | Is the hypothesis \kappa^\kappa=\kappa necessary in the theorem that embeddability of generalized trees of size \kappa is strongly invariantly universal for \kappa-analytic quasi-orders? For singular \kappa, what is the descriptive-set-theoretic complexity of embeddability on Mod_\kappa(\varphi), and can it consistentl... | 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 | Set Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/02, pp. 91--144 |
30,002,480 | OWR-12862-006 | Strong Colorings at Singular Cardinals | Does $\operatorname{Pr}_1(\lambda,\lambda,\lambda,\operatorname{cf}(\lambda))$ hold for every singular cardinal $\lambda$, or even does $\operatorname{Pr}_1(\lambda,\lambda,\lambda,2)$ hold for every singular cardinal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/02, pp. 91--144](https://doi.org/10.4171/owr/2014/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessment... | 3 | open | null | 2,014 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"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-12862-006",
"literature-status:open",
"owr-year:2014"
] | The stronger Pr1 relation for every singular cardinal is still described in current primary literature as the oldest open problem in this line of work. | [
{
"url": "https://ems.press/content/serial-article-files/46488",
"label": "Oberwolfach set theory report"
},
{
"url": "https://intlpress.com/site/pub/files/_fulltext/journals/mrl/2014/0021/0006/MRL-2014-0021-0006-a009.pdf",
"label": "Shelah, Pr1 at successors of singulars"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/02 | null | null | null | Does $\operatorname{Pr}_1(\lambda,\lambda,\lambda,\operatorname{cf}(\lambda))$ hold for every singular cardinal $\lambda$, or even does $\operatorname{Pr}_1(\lambda,\lambda,\lambda,2)$ hold for every singular cardinal? | Does Pr_1(\lambda,\lambda,\lambda,\operatorname{cf}(\lambda)) hold for every singular cardinal \lambda, or even does Pr_1(\lambda,\lambda,\lambda,2) hold for every singular cardinal? | 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 | Set Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/02, pp. 91--144 |
30,002,481 | OWR-12862-007 | Projective Determinacy and Zero Sharp over Third-Order Arithmetic | Over third-order arithmetic $Z_3$, does $\Pi^1_1$ determinacy imply the existence of $0^\#$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/02, pp. 91--144](https://doi.org/10.4171/owr/2014/02)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessment... | 3 | open | null | 2,014 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"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-12862-007",
"literature-status:open",
"owr-year:2014"
] | The classical ZF implication from Pi-1-1 determinacy to zero-sharp is a theorem, but the record's higher-order-arithmetic formulation is not precise and the corresponding Z3 question remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46488",
"label": "Oberwolfach set theory report"
},
{
"url": "https://arxiv.org/abs/1503.04000",
"label": "Cheng--Schindler, higher-order arithmetic"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/02 | null | null | null | Over third-order arithmetic $Z_3$, does $\Pi^1_1$ determinacy imply the existence of $0^\#$? | Over third-order arithmetic Z_3, does \Pi^1_1 determinacy imply the existence of 0^\#? | 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 | Set Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/02, pp. 91--144 |
30,002,482 | OWR-12863-001 | Symplectic Periods of Essentially Speh Representations | Let $\mathcal{G}'$ consist of representations $Q(\Delta_1,\ldots,\Delta_{2r})$ built from ladder representations such that every $Q(\Delta_{2i+1},\Delta_{2i+2})$ is essentially Speh. Is every $\theta\in\mathcal{G}'$ endowed with a symplectic period? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/03, pp. 145--212](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,014 | 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-12863-001",
"literature-status:open",
"owr-year:2014"
] | The symplectic-period assertion for the stated generic representations is posed as a conjecture beyond the classified low-rank cases; no general proof was found. | [
{
"url": "https://ems.press/content/serial-article-files/46494?nt=1",
"label": "Oberwolfach representation theory report"
},
{
"url": "https://arxiv.org/abs/1601.03611",
"label": "Mitra, symplectic periods for GL representations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/03 | null | null | null | Let $\mathcal{G}'$ consist of representations $Q(\Delta_1,\ldots,\Delta_{2r})$ built from ladder representations such that every $Q(\Delta_{2i+1},\Delta_{2i+2})$ is essentially Speh. Is every $\theta\in\mathcal{G}'$ endowed with a symplectic period? | Let \mathcal G' be the class of representations Q(\Delta_1,\ldots,\Delta_{2r}) built from ladder representations such that each Q(\Delta_{2i+1},\Delta_{2i+2}) is essentially Speh. Is every \theta\in\mathcal G' endowed with a symplectic period? | 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 | Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/03, pp. 145--212 |
30,002,483 | OWR-12863-003 | Density of Whittaker Distributions on Spherical Spaces | Let $G$ be quasisplit with Borel subgroup $B$ and nilradical $U$, let $\psi$ be a nondegenerate character of $U$, let $H\subset G$ be reductive and spherical, and put $X=G/H$. If $O$ is the union of the open $B$-orbits in $G$, is
$$\sum_{x\in O}S^*(Ux)^{U,\psi}$$
dense in $S^*(X)^{U,\psi}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/03, pp. 145--212](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,014 | 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-12863-003",
"literature-status:partially-solved",
"owr-year:2014"
] | Vanishing theorems establish important cases away from open B-orbits and related density statements under additional hypotheses, but the full Archimedean spherical-space density conjecture remains unresolved. | [
{
"url": "https://arxiv.org/abs/1311.6111",
"label": "Aizenbud--Gourevitch, spherical-space distributions"
},
{
"url": "https://arxiv.org/abs/1405.2540",
"label": "Aizenbud--Gourevitch--Sayag--Kemarsky, z-finite distributions"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/03 | null | null | null | Let $G$ be quasisplit with Borel subgroup $B$ and nilradical $U$, let $\psi$ be a nondegenerate character of $U$, let $H\subset G$ be reductive and spherical, and put $X=G/H$. If $O$ is the union of the open $B$-orbits in $G$, is
$$\sum_{x\in O}S^*(Ux)^{U,\psi}$$
dense in $S^*(X)^{U,\psi}$? | Let G be quasisplit with Borel subgroup B and nilradical U, let \psi be a non-degenerate character of U, let H\subset G be reductive and spherical, and put X=G/H. If O is the union of the open B-orbits in G, is the sum of the one-dimensional spaces S^*(U x)^{U,\psi} for x\in O dense in S^*(X)^{U,\psi}? | 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 | Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/03, pp. 145--212 |
30,002,484 | OWR-12863-004 | Dirac Cohomology of Tempered Modules | Does every tempered module with a solvable central character have nonzero Dirac cohomology? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/03, pp. 145--212](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,014 | 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-12863-004",
"literature-status:open",
"owr-year:2014"
] | Dirac-cohomology results cover parameters with solvable centralizer and related special cases, but the conjecture for arbitrary parameters and reflection groups remains unproved. | [
{
"url": "https://ems.press/content/serial-article-files/46494?nt=1",
"label": "Oberwolfach representation theory report"
},
{
"url": "https://arxiv.org/abs/1407.0956",
"label": "Chan, twisted Euler--Poincare pairing"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/03 | null | null | null | Does every tempered module with a solvable central character have nonzero Dirac cohomology? | Does every tempered module with a solvable central character have nonzero Dirac cohomology? | 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 | Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/03, pp. 145--212 |
30,002,485 | OWR-12863-006 | Homology Comparison for Real Spherical Subalgebras | Let $\mathfrak h$ be a real spherical subalgebra, let $V$ be a Harish–Chandra module, and let $V^\infty$ be its smooth moderate-growth completion. Is the natural map
$$\Phi_p:H_p(\mathfrak h,V)\longrightarrow H_p(\mathfrak h,V^\infty)$$
an isomorphism for every $p$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/03, pp. 145--212](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,014 | 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-12863-006",
"literature-status:partially-solved",
"owr-year:2014"
] | The comparison theorem is proved for standard minimal parabolic nilradicals, but the broader comparison conjecture for real spherical subalgebras stated in the record is not fully established. | [
{
"url": "https://citeseerx.ist.psu.edu/document?doi=332f58afd544ba575d7c9f67e9d1ec8034b6d52c\\&repid=rep1\\&type=pdf",
"label": "Aizenbud--Gourevitch--Kroetz--Liu, homology comparison"
},
{
"url": "https://arxiv.org/abs/2102.03204",
"label": "Li--Liu--Yu, Casselman comparison theorem"
},
{
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/03 | null | null | null | Let $\mathfrak h$ be a real spherical subalgebra, let $V$ be a Harish–Chandra module, and let $V^\infty$ be its smooth moderate-growth completion. Is the natural map
$$\Phi_p:H_p(\mathfrak h,V)\longrightarrow H_p(\mathfrak h,V^\infty)$$
an isomorphism for every $p$? | Let h be a real spherical subalgebra, let V be a Harish-Chandra module, let V^\infty be its smooth moderate-growth completion, and let \Phi_p:H_p(h,V)\to H_p(h,V^\infty) be the natural map. Is \Phi_p an isomorphism for every p? | 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 | Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/03, pp. 145--212 |
30,002,486 | OWR-12864-001 | Mixing and Transport from Finite-Time Noisy Data | Extend the theory of mixing and transport from periodic, quasiperiodic, and single-frequency-dominated models to realistic finite-time noisy observations, including stochastic effects. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixing, Transport and Coherent Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/04, pp. 213--286](https://doi.org/10.4171/owr/2014/04)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,014 | 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-12864-001",
"literature-status:open",
"owr-year:2014"
] | The record asks for a general extension from idealized periodic or quasiperiodic models to finite-time noisy and stochastic data. Later work studies uncertainty in Lagrangian coherent-structure diagnostics, but no general theorem resolving this transition is established. | [
{
"url": "https://doi.org/10.4171/owr/2014/04",
"label": "OWR report"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0167278922002846",
"label": "uncertainty study for LCS methods"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/04 | null | null | null | Extend the theory of mixing and transport from periodic, quasiperiodic, and single-frequency-dominated models to realistic finite-time noisy observations, including stochastic effects. | How can insights from periodic, quasi-periodic, and single-frequency models of mixing and transport be extended to theoretical results for realistic finite-time noisy data, including stochastic effects? | 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 | Mixing, Transport and Coherent Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/04, pp. 213--286 |
30,002,487 | OWR-12864-002 | Burnstile Lobe Sequences and Loss of Primary Intersections | In burnstile theory for propagating fronts, characterize the sequence of modified entrance and exit lobes: is there a unique locally smallest lobe, what transport questions are answered by the other lobes, and can continuous-time treatment improve efficiency? What are the physical consequences when the stable and unsta... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixing, Transport and Coherent Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/04, pp. 213--286](https://doi.org/10.4171/owr/2014/04)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,014 | 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-12864-002",
"literature-status:open",
"owr-year:2014"
] | The lobe-sequence questions concern uniqueness of locally smallest lobes, continuous-time efficiency, and the effects of losing a pip. The cited report poses these as research questions, and the literature located does not give a general answer covering them. | [
{
"url": "https://doi.org/10.4171/owr/2014/04",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/04 | null | null | null | In burnstile theory for propagating fronts, characterize the sequence of modified entrance and exit lobes: is there a unique locally smallest lobe, what transport questions are answered by the other lobes, and can continuous-time treatment improve efficiency? What are the physical consequences when the stable and unsta... | What further structure can be proved for the lobe sequence: is there a unique locally smallest lobe, what questions do the other lobes answer, and can continuous-time treatment improve efficiency? What are the physical consequences of losing a primary intersection point, especially for ballistic front progress, and can... | 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 | Mixing, Transport and Coherent Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/04, pp. 213--286 |
30,002,488 | OWR-12864-003 | Spectral Bifurcations and Entropy Changes | Does the observed correspondence between bifurcations in the eigenspectrum of the Perron–Frobenius operator and changes in a dynamical system’s topological entropy hold beyond the studied lid-driven-cavity flows? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixing, Transport and Coherent Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/04, pp. 213--286](https://doi.org/10.4171/owr/2014/04)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,014 | 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-12864-003",
"literature-status:open",
"owr-year:2014"
] | The reported correspondence between Perron-Frobenius spectral bifurcations and entropy changes is proved only in model settings. The primary follow-up develops the almost-cyclic-set method and model-specific entropy bounds, not a general theorem, so the stated generalization remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/04",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1063/1.4768666",
"label": "almost-cyclic-set bifurcation study"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/04 | null | null | null | Does the observed correspondence between bifurcations in the eigenspectrum of the Perron–Frobenius operator and changes in a dynamical system’s topological entropy hold beyond the studied lid-driven-cavity flows? | Does the relationship between bifurcations in the Perron-Frobenius eigenspectrum and changes in system entropy hold more generally? | 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 | Mixing, Transport and Coherent Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/04, pp. 213--286 |
30,002,489 | OWR-12864-004 | Relations and Accuracy Among Unsteady Flow-Barrier Definitions | How are the competing definitions of unsteady flow barriers related, for example curves of extremal deformation versus transfer-operator eigenfunctions or mesohyperbolic trajectories versus extremal flux? How accurately does each definition identify barriers, which properties are essential, and must a valid definition ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixing, Transport and Coherent Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/04, pp. 213--286](https://doi.org/10.4171/owr/2014/04)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,014 | 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-12864-004",
"literature-status:open",
"owr-year:2014"
] | Subsequent work provides several competing finite-time coherent-structure and barrier diagnostics, but does not establish a universal equivalence with transfer-operator eigenfunctions or a definitive frame-invariant barrier definition. | [
{
"url": "https://doi.org/10.4171/owr/2014/04",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1146/annurev-fluid-010313-141322",
"label": "Lagrangian coherent-structure review"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0167278922002846",
"label": "uncert... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/04 | null | null | null | How are the competing definitions of unsteady flow barriers related, for example curves of extremal deformation versus transfer-operator eigenfunctions or mesohyperbolic trajectories versus extremal flux? How accurately does each definition identify barriers, which properties are essential, and must a valid definition ... | How are curves of extremal deformation related to eigenfunctions of the transfer operator, and are mesohyperbolic trajectories associated with extremal flux? Which proposed definitions and features, such as extremal stretching and frame invariance, correctly characterize flow barriers? | 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 | Mixing, Transport and Coherent Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/04, pp. 213--286 |
30,002,490 | OWR-12864-005 | Finite-Time Invariant Manifolds and Unsteady Transport | Develop a theory of finite-time invariant manifolds that genuinely captures the time dependence of aperiodic unsteady flows. In particular, quantify transport created by intersecting or nonintersecting stable and unstable manifold segments and relate those manifolds to practical flow-barrier diagnostics. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixing, Transport and Coherent Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/04, pp. 213--286](https://doi.org/10.4171/owr/2014/04)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,014 | 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-12864-005",
"literature-status:open",
"owr-year:2014"
] | The fragment asks whether finite-time methods capture time variation and how intersections or nonintersections of invariant structures produce transport. The report identifies these as unresolved issues, and no general resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2014/04",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1146/annurev-fluid-010313-141322",
"label": "Lagrangian coherent-structure review"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/04 | null | null | null | Develop a theory of finite-time invariant manifolds that genuinely captures the time dependence of aperiodic unsteady flows. In particular, quantify transport created by intersecting or nonintersecting stable and unstable manifold segments and relate those manifolds to practical flow-barrier diagnostics. | Does the proposed description capture time variation, and how do intersections or their absence produce transport? | 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 | Mixing, Transport and Coherent Structures (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/04, pp. 213--286 |
30,002,491 | OWR-12865-002 | Unifying Constructions of Exceptional Monodromy Local Systems | Can the automorphic and constructive approaches to producing local systems with prescribed exceptional algebraic monodromy be unified? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Langlands Correspondence and Constructive Galois Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/05, pp. 287--334](https://doi.org/10.4171/owr/2014/05)
## Literature review (check... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12865-002",
"literature-status:open",
"owr-year:2014"
] | The question asks whether automorphic constructions and explicit geometric local systems can be brought together. Later work constructs important local systems and exceptional monodromy examples, but there is no general synthesis or explicit trace calculation answering this broad question. | [
{
"url": "https://doi.org/10.4171/owr/2014/05",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1005.2765",
"label": "Kloosterman sheaves for reductive groups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/05 | null | null | null | Can the automorphic and constructive approaches to producing local systems with prescribed exceptional algebraic monodromy be unified? | Can the automorphic and constructive approaches to constructing local systems with prescribed exceptional algebraic monodromy be brought together? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Langlands Correspondence and Constructive Galois Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/05, pp. 287--334 |
30,002,492 | OWR-12865-004 | Maeda Conjecture for Level-One Cusp Forms | For every normalized Hecke eigenform $f\in S_k(1)$, is $[\mathbb Q_f:\mathbb Q]=\dim S_k(1)=m_k$, with the Galois group of the normal closure of $\mathbb Q_f/\mathbb Q$ isomorphic to the symmetric group $S_{m_k}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Langlands Correspondence and Constructive Galois Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/05, pp. 287--334](https://doi.org/10.4171/owr/2014/05)
## Literature review (check... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12865-004",
"literature-status:open",
"owr-year:2014"
] | Maeda's prediction of one Galois orbit, the full coefficient-field degree, and symmetric normal-closure group for level-one cusp forms remains unproved in general. Modern work explicitly continues to describe the level-one case as an open problem, despite extensive computation and partial results for related levels. | [
{
"url": "https://doi.org/10.4171/owr/2014/05",
"label": "OWR report"
},
{
"url": "https://doi.org/10.4171/JEMS/1073",
"label": "Galois orbits of newforms"
},
{
"url": "https://arxiv.org/abs/1207.3480",
"label": "computational evidence for Maeda's conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/05 | null | null | null | For every normalized Hecke eigenform $f\in S_k(1)$, is $[\mathbb Q_f:\mathbb Q]=\dim S_k(1)=m_k$, with the Galois group of the normal closure of $\mathbb Q_f/\mathbb Q$ isomorphic to the symmetric group $S_{m_k}$? | Maeda's conjecture asserts that for every f in S_k(1), [Q_f:Q]=dim S_k(1)=m_k and the Galois group of the normal closure of Q_f over Q is the symmetric group S_{m_k}. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Langlands Correspondence and Constructive Galois Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/05, pp. 287--334 |
30,002,493 | OWR-12865-008 | Algebraic Cycles Spanning Predicted Tate Classes | For the basic Newton stratum of a Hodge-type Shimura variety or a moduli space of shtukas, families of cycles $\{Z_\gamma\}$ are parameterized by Mirković–Vilonen cycles. Do the classes of the cycles $Z_\gamma$ span all Tate classes predicted by the Langlands conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Langlands Correspondence and Constructive Galois Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/05, pp. 287--334](https://doi.org/10.4171/owr/2014/05)
## Literature review (check... | 3 | partially_solved | null | 2,014 | 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-12865-008",
"literature-status:partially-solved",
"owr-year:2014"
] | The reported MV-cycle families and their geometric partition are established, and linear independence realizes the expected Tate classes in generic function-field type-A cases. General spanning of all predicted Tate classes for the broader Shimura-variety setting remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/05",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1707.05700",
"label": "cycles on Shimura varieties via geometric Satake"
},
{
"url": "https://doi.org/10.2140/ant.2017.11.2213",
"label": "Tate cycles on unitary Shimura varieties... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/05 | null | null | null | For the basic Newton stratum of a Hodge-type Shimura variety or a moduli space of shtukas, families of cycles $\{Z_\gamma\}$ are parameterized by Mirković–Vilonen cycles. Do the classes of the cycles $Z_\gamma$ span all Tate classes predicted by the Langlands conjecture? | Can the indicated cycle classes be proved to span the Tate classes predicted by the Langlands conjecture? | 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 | Langlands Correspondence and Constructive Galois Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/05, pp. 287--334 |
30,002,494 | OWR-12865-009 | Triviality of Stratified Bundles on Étale-Simply-Connected Varieties | Let $U$ be a smooth quasi-projective variety over an algebraically closed field $k$ of characteristic $p>0$. Does $\pi_1^{\mathrm{\acute et}}(U)=0$ imply that every stratified bundle on $U$ is trivial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Langlands Correspondence and Constructive Galois Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/05, pp. 287--334](https://doi.org/10.4171/owr/2014/05)
## Literature review (check... | 3 | open | null | 2,014 | 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-12865-009",
"literature-status:open",
"owr-year:2014"
] | The question concerns smooth quasi-projective varieties in characteristic p and the implication from trivial etale fundamental group to trivial stratified bundles. Projective analogues were solved, but the quasi-projective implication and the requested geometry are not settled in general. | [
{
"url": "https://doi.org/10.4171/owr/2014/05",
"label": "OWR report"
},
{
"url": "https://journals.sns.it/index.php/annaliscienze/article/download/355/345/574",
"label": "Esnault--Sun projective theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/05 | null | null | null | Let $U$ be a smooth quasi-projective variety over an algebraically closed field $k$ of characteristic $p>0$. Does $\pi_1^{\mathrm{\acute et}}(U)=0$ imply that every stratified bundle on $U$ is trivial? | What is the geometry of a variety U whose etale fundamental group pi_1^{et}(U) is trivial, as required in problem (ii) of the report? | 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 | Langlands Correspondence and Constructive Galois Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/05, pp. 287--334 |
30,002,495 | OWR-12866-002 | Real-Variable Proof of the Nyman Criterion | Give a real-variable proof of the equivalence between the following assertions: for every $\varepsilon>0$,
$$\pi(x)=\operatorname{li}(x)+O(x^{1/2+\varepsilon});$$
and, for every $\delta>0$, there are coefficients $c_\alpha$, with $\alpha>1$, such that
$$\int_0^\infty\left|\chi(t)-\sum_\alpha c_\alpha e_\alpha(t)\right|... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12866-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-002",
"literature-status:open",
"owr-year:2014"
] | The extracted methodological question asks for a real-variable proof of an equivalence in the Nyman--Beurling framework. Existing proofs use analytic or arithmetic machinery, and no such real-variable proof was found; the question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "OWR report"
},
{
"url": "https://doi.org/10.48550/arXiv.math/0011254",
"label": "Baez-Duarte real-variable reformulation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | Give a real-variable proof of the equivalence between the following assertions: for every $\varepsilon>0$,
$$\pi(x)=\operatorname{li}(x)+O(x^{1/2+\varepsilon});$$
and, for every $\delta>0$, there are coefficients $c_\alpha$, with $\alpha>1$, such that
$$\int_0^\infty\left|\chi(t)-\sum_\alpha c_\alpha e_\alpha(t)\right|... | Is there a real-variable proof of the equivalence of assertions (2) and (3) in the report? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,496 | OWR-12866-003 | Duplicate Composite: Nyman Criterion and Autocorrelation Maximum | Is there a real-variable proof of the equivalence of assertions (2) and (3), and does A have a strict local maximum at some positive irrational argument? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This extraction merely combines the two source questions represented canonically and separately by OWR-12866-002 and OWR-12866-004. No separ) | [
"OWR-12866-002",
"OWR-12866-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-003",
"literature-status:open",
"owr-year:2014"
] | The record combines the methodological Nyman--Beurling question with the question of a strict local maximum of the multiplicative autocorrelation function at a positive irrational. The rational local maxima and differentiability criteria are known, but neither the requested proof nor the irrational local-maximum existe... | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1007/s11139-005-0834-4",
"label": "multiplicative autocorrelation study"
},
{
"url": "https://arxiv.org/abs/1305.4395",
"label": "differentiability of the autocorrelation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | null | Is there a real-variable proof of the equivalence of assertions (2) and (3), and does A have a strict local maximum at some positive irrational argument? | unrecoverable | This extraction merely combines the two source questions represented canonically and separately by OWR-12866-002 and OWR-12866-004. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,497 | OWR-12866-004 | Irrational Local Maxima of the Fractional-Part Autocorrelation | For
$$A(\lambda)=\int_0^\infty \{t\}\{\lambda t\}\,\frac{dt}{t^2},$$
does there exist a positive irrational $\lambda$ at which $A$ has a strict local maximum? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12866-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-004",
"literature-status:open",
"owr-year:2014"
] | The positive-irrational strict-local-maximum question for the multiplicative autocorrelation function remains explicitly unresolved. Later work characterizes differentiability through continued fractions but does not produce or exclude such an irrational maximum. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1305.4395",
"label": "autocorrelation differentiability study"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | For
$$A(\lambda)=\int_0^\infty \{t\}\{\lambda t\}\,\frac{dt}{t^2},$$
does there exist a positive irrational $\lambda$ at which $A$ has a strict local maximum? | Does the autocorrelation function A have a strict local maximum at a positive irrational argument? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,498 | OWR-12866-005 | Invariant Dirichlet-Series Subspace Characterized by Zeta Divisibility | Let $E^2$ be the Hilbert space of Dirichlet series $D(s)$ for which $D(s)/s$ extends to a function in $H^2(\operatorname{Re}s>1/2)$. Let $V$ be the closure in $E^2$ of the functions
$$\zeta(s)\sum_{k=1}^n c_k k^{-s}\qquad\text{with}\qquad \sum_{k=1}^n\frac{c_k}{k}=0.$$
Is
$$V=\{D\in E^2:D(s)/\zeta(s)\text{ is holomorph... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-005",
"literature-status:open",
"owr-year:2014"
] | The proposed identification of V with the holomorphic-divisibility space is known conditionally under the Riemann hypothesis, while the report asks for an unconditional proof or disproof. Since the required unconditional input remains unavailable, the claim is open. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "OWR report"
},
{
"url": "https://doi.org/10.48550/arXiv.math/0011254",
"label": "Nyman--Beurling criterion"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | Let $E^2$ be the Hilbert space of Dirichlet series $D(s)$ for which $D(s)/s$ extends to a function in $H^2(\operatorname{Re}s>1/2)$. Let $V$ be the closure in $E^2$ of the functions
$$\zeta(s)\sum_{k=1}^n c_k k^{-s}\qquad\text{with}\qquad \sum_{k=1}^n\frac{c_k}{k}=0.$$
Is
$$V=\{D\in E^2:D(s)/\zeta(s)\text{ is holomorph... | Is V equal to the set of D in E^2 such that D(s)/zeta(s) is holomorphic for Re(s)>1/2? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,499 | OWR-12866-007 | Almost-Everywhere Fourier Convergence in $L^{1}$ | Characterize the functions $f\in L^1(\mathbb T)$, for $\mathbb T=\mathbb R/\mathbb Z$, whose Fourier series converges almost everywhere. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-007",
"literature-status:open",
"owr-year:2014"
] | Carleson and Hunt establish almost-everywhere convergence for Lp with p greater than one, while Kolmogorov gives L1 divergence examples. A complete characterization of the L1 functions with almost-everywhere Fourier convergence remains an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | Characterize the functions $f\in L^1(\mathbb T)$, for $\mathbb T=\mathbb R/\mathbb Z$, whose Fourier series converges almost everywhere. | Characterize the functions f in L^1(T), for T=R/Z, whose Fourier series converges almost everywhere. | 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 | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,500 | OWR-12866-008 | Attainable Zero Counts of Nonnegative Bivariate Polynomials | Let $P(x,y)\geq0$ be a real polynomial of degree $n$ whose real zeros are isolated. Its number of real zeros is at most $n^2$, while examples give at least $\lfloor n^2/4\rfloor$. Can every integer between these two bounds occur as the number of real zeros of such a polynomial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-008",
"literature-status:open",
"owr-year:2014"
] | The question asks which intermediate cardinalities of real zero sets can occur for nonnegative bivariate polynomials with isolated zeros. Modern work still describes the corresponding general zero-count problem for the nonnegativity cone as open, although special cones and dimensions are understood. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2020.106602",
"label": "real zeros of nonnegative circuit polynomials"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | Let $P(x,y)\geq0$ be a real polynomial of degree $n$ whose real zeros are isolated. Its number of real zeros is at most $n^2$, while examples give at least $\lfloor n^2/4\rfloor$. Can every integer between these two bounds occur as the number of real zeros of such a polynomial? | For the polynomial class P described in the report, can every integer between the established lower and upper bounds for the number of real zeros of P occur? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,501 | OWR-12866-010 | A BMO Approach to the Lindelöf Hypothesis | Can a BMO theory or another functional-analytic method be used to prove the Lindelöf hypothesis? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-010",
"literature-status:open",
"owr-year:2014"
] | The proposed BMO route targets the Lindelof hypothesis. BMO-type spaces in the report are shown not to be the right endpoint space, and later work continues to treat Lindelof as an unresolved hypothesis; no BMO proof is known. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.aim.2021.107762",
"label": "current Lindelof-hypothesis study"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | Can a BMO theory or another functional-analytic method be used to prove the Lindelöf hypothesis? | Can functional analysis, specifically a BMO theory, be used to prove the Lindelof hypothesis? | 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 | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,502 | OWR-12866-011 | Intermediate BMO Spaces for Dirichlet Series | Does there exist a BMO-type space $\mathcal B$ for Dirichlet series, intermediate between $H^\infty$ and the candidate Dirichlet-series BMO spaces, such that: for every $f\in\mathcal B$, $\sigma>0$, and $p<\infty$,
$$\limsup_{T\to\infty}\frac1{2T}\int_{-T}^{T}|f(\sigma+it)|^p\,dt<\infty;$$
and, for every $\sigma>1/2$, ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-011",
"literature-status:open",
"owr-year:2014"
] | The question asks for a smaller intermediate space satisfying both stated multiplier properties. The report records it as an open problem, and the literature located does not identify a space with both required properties. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | Does there exist a BMO-type space $\mathcal B$ for Dirichlet series, intermediate between $H^\infty$ and the candidate Dirichlet-series BMO spaces, such that: for every $f\in\mathcal B$, $\sigma>0$, and $p<\infty$,
$$\limsup_{T\to\infty}\frac1{2T}\int_{-T}^{T}|f(\sigma+it)|^p\,dt<\infty;$$
and, for every $\sigma>1/2$, ... | Does there exist a space between the candidate BMO spaces and H^infinity that satisfies both properties (2) and (3) stated in the report? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,503 | OWR-12866-012 | Stationarity of Perfect Squares for the Pisier Norm | Is the set of perfect squares stationary for the Pisier norm? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-012",
"literature-status:open",
"owr-year:2014"
] | No published yes-or-no resolution of whether the set of perfect squares is stationary was found; later work establishes general properties and related square-frequency results but does not settle this question. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "Oberwolfach Report 06/2014"
},
{
"url": "https://eudml.org/doc/210549",
"label": "Lefevre, stationary sets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | Is the set of perfect squares stationary for the Pisier norm? | Is the set of perfect squares stationary for the Pisier norm? | 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 | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,504 | OWR-12866-013 | Rectangular Factorization in the Disk Algebra | Does every $f$ in the disk algebra $A(\mathbb D)$ admit a rectangular factorization $f=g*h$ with $g,h\in A(\mathbb D)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-013",
"literature-status:open",
"owr-year:2014"
] | The rectangular factorization problem for the disk algebra remains unresolved in the literature checked; no theorem was found proving or refuting factorization for every element. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "Oberwolfach Report 06/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | Does every $f$ in the disk algebra $A(\mathbb D)$ admit a rectangular factorization $f=g*h$ with $g,h\in A(\mathbb D)$? | Does every function f in the disk algebra A(D) admit a rectangular factorization f=g*h with both g and h in A(D)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,505 | OWR-12866-014 | Averaging Times for $H^p$ Dirichlet Polynomials | For $C>1$, let $T_p(N,C)$ be the least $T$ such that
$$\frac1T\int_0^T|f(it)|^p\,dt\leq C\|f\|_p^p$$
for every Dirichlet polynomial $f(s)=\sum_{n=1}^N a_n n^{-s}$ of degree at most $N$. How does $T_p(N,C)$ depend on $p$? In particular, is $T_p(N,C)=O(N)$ for $1\leq p<2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-014",
"literature-status:open",
"owr-year:2014"
] | The dependence of the Dirichlet-polynomial averaging time on p, including the stated linear bound for 1 less than or equal to p less than 2, remains open in the sources checked. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "Oberwolfach Report 06/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | For $C>1$, let $T_p(N,C)$ be the least $T$ such that
$$\frac1T\int_0^T|f(it)|^p\,dt\leq C\|f\|_p^p$$
for every Dirichlet polynomial $f(s)=\sum_{n=1}^N a_n n^{-s}$ of degree at most $N$. How does $T_p(N,C)$ depend on $p$? In particular, is $T_p(N,C)=O(N)$ for $1\leq p<2$? | How does T_p(N,C), as defined in the report in connection with the triangle Hilbert integral, depend on p? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,506 | OWR-12866-016 | Bohr-Radius Characterization of $\ell^1$ | Let $X$ be a Banach sequence space such that
$$\inf_n K(B_{X_n})>0,$$
where $K(B_{X_n})$ is the Bohr radius of the unit ball of its first $n$ coordinates. Must $X=\ell^1$ as sets? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-016",
"literature-status:open",
"owr-year:2014"
] | No general proof or counterexample was found for the assertion that a sequence space with positive infimum Bohr radius must equal ell one as a set; available work treats related Bohr-radius and monomial-convergence questions. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "Oberwolfach Report 06/2014"
},
{
"url": "https://riunet.upv.es/bitstreams/aaf75982-880b-4910-a99e-76252cefcfad/download",
"label": "Recent monomial-convergence work"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | Let $X$ be a Banach sequence space such that
$$\inf_n K(B_{X_n})>0,$$
where $K(B_{X_n})$ is the Bohr radius of the unit ball of its first $n$ coordinates. Must $X=\ell^1$ as sets? | Is it true that X equals ell^1 as sets? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,507 | OWR-12866-017 | A Dirichlet Series with Exactly One Zero | Does there exist an ordinary Dirichlet series that converges in an open half-plane and has exactly one zero there? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-017",
"literature-status:open",
"owr-year:2014"
] | A proposed construction of a Dirichlet series with exactly one zero appeared as an arXiv preprint, but the associated paper was subsequently retracted; the existence question therefore remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "Oberwolfach Report 06/2014"
},
{
"url": "https://arxiv.org/abs/1812.11880",
"label": "Hilberdink--Saias preprint"
},
{
"url": "https://mathoverflow.net/questions/330714/dirichlet-series-with-a-single-zero",
"label": "Current r... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | Does there exist an ordinary Dirichlet series that converges in an open half-plane and has exactly one zero there? | Does there exist an ordinary Dirichlet series converging in an open half-plane and having exactly one zero there? Is D(lambda) continuous and strictly decreasing as a function of lambda? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,508 | OWR-12866-018 | Continuity and Strict Monotonicity of Nyman–Beurling Distances | In $L^2((0,\infty),t^{-2}dt)$, let $\chi(t)=\mathbf 1_{(1,\infty)}(t)$, let $e_\alpha(t)=\{t/\alpha\}$, and define
$$D(\lambda)=\operatorname{dist}\!\left(\chi,\operatorname{span}\{e_\alpha:1\leq\alpha\leq\lambda\}\right),\qquad\lambda>1.$$
Is $D(\lambda)$ continuous? Is it strictly decreasing? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393](https://doi.org/10.4171/owr/2014/06)
## Literature review (checked 202... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12866-018",
"literature-status:open",
"owr-year:2014"
] | The continuity and strict decrease of the Nyman--Beurling distance function D of lambda remain unresolved in the literature checked. | [
{
"url": "https://doi.org/10.4171/owr/2014/06",
"label": "Oberwolfach Report 06/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/06 | null | null | null | In $L^2((0,\infty),t^{-2}dt)$, let $\chi(t)=\mathbf 1_{(1,\infty)}(t)$, let $e_\alpha(t)=\{t/\alpha\}$, and define
$$D(\lambda)=\operatorname{dist}\!\left(\chi,\operatorname{span}\{e_\alpha:1\leq\alpha\leq\lambda\}\right),\qquad\lambda>1.$$
Is $D(\lambda)$ continuous? Is it strictly decreasing? | Is D(lambda) continuous as a function of lambda, and is it strictly decreasing? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Dirichlet Series and Function Theory in Polydiscs (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/06, pp. 335--393 |
30,002,509 | OWR-12867-001 | Optimal-Dimensional Spines for Teichmüller and Arithmetic Spaces | Construct a spine of Teichmüller space $\mathcal T_g$ of dimension $4g-5$. More generally, if a nonuniform arithmetic subgroup $\Gamma<G$ acts on the symmetric space $X$, construct a $\Gamma$-equivariant spine of dimension $\operatorname{vcd}(\Gamma)=\dim X-\operatorname{rank}_{\mathbb Q}(\Gamma)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452](https://doi.org/10.4171/owr/2014/07)
## Literature review (che... | 3 | open | null | 2,014 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12867-001",
"literature-status:open",
"owr-year:2014"
] | Spines of the expected virtual-cohomological dimension are known in low codimension and for related decorated spaces, but no general spine of dimension 4g minus 5, nor the corresponding optimal arithmetic construction, is known. | [
{
"url": "https://doi.org/10.4171/owr/2014/07",
"label": "Oberwolfach Report 07/2014"
},
{
"url": "https://arxiv.org/abs/2310.15618",
"label": "Thurston spine dimension estimates"
},
{
"url": "https://arxiv.org/abs/2409.04392",
"label": "Decorated Teichmuller spines"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/07 | null | null | null | Construct a spine of Teichmüller space $\mathcal T_g$ of dimension $4g-5$. More generally, if a nonuniform arithmetic subgroup $\Gamma<G$ acts on the symmetric space $X$, construct a $\Gamma$-equivariant spine of dimension $\operatorname{vcd}(\Gamma)=\dim X-\operatorname{rank}_{\mathbb Q}(\Gamma)$. | Construct a spine of Teichmuller space T_g of dimension 4g-5; more generally, for a nonuniform arithmetic subgroup Gamma of G acting on the symmetric space X, construct a Gamma-spine of dimension vcd(Gamma)=dim X-Q-rank(Gamma). | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452 |
30,002,510 | OWR-12867-002 | Good Spines of Teichmüller Space | Construct geometrically natural, mapping-class-group-equivariant spines of Teichmüller space $\mathcal T_g$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452](https://doi.org/10.4171/owr/2014/07)
## Literature review (che... | 3 | open | null | 2,014 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12867-002",
"literature-status:open",
"owr-year:2014"
] | Several explicit spines and dimension estimates are available, but a satisfactory general construction of good spines for Teichmuller space remains an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2014/07",
"label": "Oberwolfach Report 07/2014"
},
{
"url": "https://arxiv.org/abs/2310.15618",
"label": "Thurston spine dimension estimates"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/07 | null | null | null | Construct geometrically natural, mapping-class-group-equivariant spines of Teichmüller space $\mathcal T_g$. | Construct good spines of Teichmuller space T_g. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452 |
30,002,511 | OWR-12867-004 | Asymptotics Along Rays in Hitchin Components | Let $S$ be a closed oriented surface of genus at least $2$, let $(E,\varphi)$ be a stable $\operatorname{SL}(n,\mathbb C)$-Higgs bundle, and let $(E,t\varphi)$ determine flat connections $\nabla_t$, representations $\rho_t$, and parallel-transport matrices $T_{P,Q}(t)$. Determine the asymptotic behavior of $\rho_t$ and... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452](https://doi.org/10.4171/owr/2014/07)
## Literature review (che... | 3 | partially_solved | null | 2,014 | 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-12867-004",
"literature-status:partially-solved",
"owr-year:2014"
] | Detailed WKB asymptotics are proved for important cyclic and Hitchin-component rays, and newer work extends this to further cases, but the general asymptotic behavior requested for rho sub t and T sub P comma Q of t is not completely determined. | [
{
"url": "https://doi.org/10.4171/owr/2014/07",
"label": "Oberwolfach Report 07/2014"
},
{
"url": "https://doi.org/10.1016/j.aim.2016.11.031",
"label": "Collier--Li, Hitchin asymptotics"
},
{
"url": "https://arxiv.org/abs/2608.04729",
"label": "Holonomy asymptotics along quartic rays... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/07 | null | null | null | Let $S$ be a closed oriented surface of genus at least $2$, let $(E,\varphi)$ be a stable $\operatorname{SL}(n,\mathbb C)$-Higgs bundle, and let $(E,t\varphi)$ determine flat connections $\nabla_t$, representations $\rho_t$, and parallel-transport matrices $T_{P,Q}(t)$. Determine the asymptotic behavior of $\rho_t$ and... | Determine the asymptotic behavior of rho_t and T_{P,Q}(t) as t tends to infinity. | 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 | New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452 |
30,002,512 | OWR-12867-005 | Convergence of Discrete to Classical Conformality | Does discrete conformality converge to classical conformality as the triangulations of a surface become arbitrarily fine? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452](https://doi.org/10.4171/owr/2014/07)
## Literature review (che... | 3 | partially_solved | null | 2,014 | 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-12867-005",
"literature-status:partially-solved",
"owr-year:2014"
] | Convergence from discrete to classical conformality has been proved for closed surfaces under mesh-quality hypotheses, including separate positive results in positive genus and genus zero, but the unrestricted conjectural formulation is not fully settled. | [
{
"url": "https://doi.org/10.4171/owr/2014/07",
"label": "Oberwolfach Report 07/2014"
},
{
"url": "https://arxiv.org/abs/2008.06744",
"label": "Discrete uniformizations for closed surfaces"
},
{
"url": "https://arxiv.org/abs/2110.08208",
"label": "Discrete conformality in genus zero"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/07 | null | null | null | Does discrete conformality converge to classical conformality as the triangulations of a surface become arbitrarily fine? | Prove or disprove that discrete conformality converges to classical conformality as the triangulations of a surface become finer and finer. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452 |
30,002,513 | OWR-12867-006 | Generating Series for Immersed Plane Curves | Let $N(g)$ be the number, up to isotopy, of immersed curves in $\mathbb R^2$ with only transverse self-intersections and exactly $g$ such intersections. Find a combinatorial or geometric interpretation of the generating series $\sum_{g\geq 0}N(g)z^g$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452](https://doi.org/10.4171/owr/2014/07)
## Literature review (che... | 3 | open | null | 2,014 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12867-006",
"literature-status:open",
"owr-year:2014"
] | Enumeration and asymptotics of immersed plane curves with prescribed transverse self-intersections have partial results and conjectural asymptotics, but the requested classification and generating-series interpretation remain open. | [
{
"url": "https://doi.org/10.4171/owr/2014/07",
"label": "Oberwolfach Report 07/2014"
},
{
"url": "https://arxiv.org/abs/math-ph/0304034",
"label": "Schaeffer--Zinn-Justin, plane curves"
},
{
"url": "https://arxiv.org/abs/1603.00846",
"label": "Cahn--Fanoni--Petri, self-intersections... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/07 | null | null | null | Let $N(g)$ be the number, up to isotopy, of immersed curves in $\mathbb R^2$ with only transverse self-intersections and exactly $g$ such intersections. Find a combinatorial or geometric interpretation of the generating series $\sum_{g\geq 0}N(g)z^g$. | If N(g) is the number, up to isotopy, of immersed curves in R^2 with transverse self-intersections and exactly g self-intersections, interpret the generating series sum_{g>=0} N(g) z^g. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452 |
30,002,514 | OWR-12867-007 | Galois Orbits of Finite Planar Trees | Describe the orbits of $\operatorname{Gal}(\overline{\mathbb Q}/\mathbb Q)$ on isotopy classes of finite planar trees, equivalently on the associated Shabat polynomials whose only critical values are $0$ and $1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452](https://doi.org/10.4171/owr/2014/07)
## Literature review (che... | 3 | partially_solved | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12867-007",
"literature-status:partially-solved",
"owr-year:2014"
] | Galois invariants and substantial classifications of plane-tree dessins are known, and databases compute many orbits, but no complete description of Galois orbits of finite planar trees is available. | [
{
"url": "https://doi.org/10.4171/owr/2014/07",
"label": "Oberwolfach Report 07/2014"
},
{
"url": "https://www.cambridge.org/core/books/abs/grothendieck-theory-of-dessins-denfants/on-the-classification-of-plane-trees-by-their-galois-orbit/FD4DB49548FCE9389A8D980C90A757BF",
"label": "Schneps--Sha... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/07 | null | null | null | Describe the orbits of $\operatorname{Gal}(\overline{\mathbb Q}/\mathbb Q)$ on isotopy classes of finite planar trees, equivalently on the associated Shabat polynomials whose only critical values are $0$ and $1$. | Understand the orbits of the absolute Galois group Gal(Qbar/Q) on isotopy classes of finite planar trees, equivalently on the corresponding polynomials whose only critical values are 0 and 1. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452 |
30,002,515 | OWR-12867-009 | Determination of Moduli Maps by Symplectic Monodromy | Let $X$ be a finite-type Riemann surface and let $\varphi:X\to\mathcal M_g$ be holomorphic, with induced symplectic monodromy $\rho'_\varphi:\pi_1(X)\to\operatorname{Mod}_g\to\operatorname{Sp}(2g,\mathbb Z)$. If two such maps $\varphi_1$ and $\varphi_2$ satisfy $\rho'_{\varphi_1}=\rho'_{\varphi_2}$, must $\varphi_1=\va... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452](https://doi.org/10.4171/owr/2014/07)
## Literature review (che... | 3 | open | null | 2,014 | 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-12867-009",
"literature-status:open",
"owr-year:2014"
] | Rigidity results are known when the full mapping-class monodromy agrees, but equality after passing only through the symplectic representation remains unresolved in the literature checked. | [
{
"url": "https://doi.org/10.4171/owr/2014/07",
"label": "Oberwolfach Report 07/2014"
},
{
"url": "https://doi.org/10.1007/s00209-025-03893-6",
"label": "Holomorphic maps between configuration spaces"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/07 | null | null | null | Let $X$ be a finite-type Riemann surface and let $\varphi:X\to\mathcal M_g$ be holomorphic, with induced symplectic monodromy $\rho'_\varphi:\pi_1(X)\to\operatorname{Mod}_g\to\operatorname{Sp}(2g,\mathbb Z)$. If two such maps $\varphi_1$ and $\varphi_2$ satisfy $\rho'_{\varphi_1}=\rho'_{\varphi_2}$, must $\varphi_1=\va... | Let X be a finite-type Riemann surface and let rho' be the monodromy representation pi_1(X)->Mod_g->Sp(2g,Z) of a holomorphic map phi:X->M_g. If two such maps phi_1 and phi_2 have rho'_1=rho'_2, must phi_1=phi_2? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/07, pp. 395--452 |
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