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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,004,516 | OWR-1703876-009 | Maximum Complexity of Hyperplane Arrangement Levels | Determine the correct asymptotic order of the maximum size $f_k^{(d)}(n)$ of the $k$-level in an arrangement of $n$ hyperplanes in $\mathbb R^d$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** partiall... | 3 | partially_solved | null | 2,020 | 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-1703876-009",
"literature-status:partially-solved",
"owr-year:2020"
] | Expected k-level complexity is known for the stated line and great-circle random models, but the higher-dimensional problem still has an asymptotic gap. | [
{
"url": "https://page.math.tu-berlin.de/~felsner/Paper/klevel.pdf",
"label": "Felsner--Valtr, On the Average Complexity of the k-Level"
},
{
"url": "https://arxiv.org/abs/1903.07196",
"label": "On the Complexity of the k-Level in Arrangements of Pseudoplanes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | Determine the correct asymptotic order of the maximum size $f_k^{(d)}(n)$ of the $k$-level in an arrangement of $n$ hyperplanes in $\mathbb R^d$. | What is the correct asymptotic order of the maximum size f_k^{(d)}(n) of the k-level in an arrangement of n hyperplanes in \mathbb R^d, between the stated lower and upper bounds? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,517 | OWR-1703876-011 | Minimum Crossing Realizations of Spatial Polygon Angle Sequences | Given a realizable angle sequence for a polygon in $\mathbb{R}^3$, can an efficient algorithm compute the minimum number of crossings among its generic realizations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,020 | 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-1703876-011",
"literature-status:open",
"owr-year:2020"
] | The efficient minimum-crossing algorithm for generic three-dimensional realizations remains open, although realizability and planar cases are algorithmically solved. | [
{
"url": "https://jgaa.info/index.php/jgaa/article/view/paper599",
"label": "Efrat--Rote--Rutter--Shabbeer, Polygons with Prescribed Angles"
},
{
"url": "https://arxiv.org/abs/2008.10192",
"label": "Efrat--Rote--Rutter--Shabbeer, preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | Given a realizable angle sequence for a polygon in $\mathbb{R}^3$, can an efficient algorithm compute the minimum number of crossings among its generic realizations? | Given a realizable angle sequence for a polygon in \mathbb R^3, can an efficient algorithm compute the minimum number of crossings among its generic realizations? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,518 | OWR-1703876-012 | Simple Spatial Polygon Realizations from Angle Sequences | Let $A=(\alpha_0,\ldots,\alpha_{n-1})$, $n\geq 3$, be realizable by a polygon in $\mathbb{R}^3$. Can $A$ be realized without self-intersections if and only if $n$ is even or $\sum_{i=0}^{n-1}(\pi-\alpha_i)\neq\pi$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,020 | 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/23287074",
"checked_at": "2026-10-10",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-10] I have released an unrefereed preprint, **Polygons with Prescribed Turning Angles in Three Dimensions: A Counterexample to a Conjecture of Efrat, Fulek, Kobourov and Tóth, and the Corrected Criterion** (Alper Ferudun, Mercury Software GmbH). The conjecture of this record is ... | [
"owr",
"oberwolfach-reports",
"OWR-1703876-012",
"literature-status:open",
"owr-year:2020"
] | The stated if-and-only-if criterion is still a conjecture; only its necessary direction and realizability algorithms are proved. | [
{
"url": "https://jgaa.info/index.php/jgaa/article/view/paper599",
"label": "Efrat--Rote--Rutter--Shabbeer, Polygons with Prescribed Angles"
},
{
"url": "https://ems.press/content/serial-article-files/46867",
"label": "Oberwolfach Reports 2020/30"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | Let $A=(\alpha_0,\ldots,\alpha_{n-1})$, $n\geq 3$, be realizable by a polygon in $\mathbb{R}^3$. Can $A$ be realized without self-intersections if and only if $n$ is even or $\sum_{i=0}^{n-1}(\pi-\alpha_i)\neq\pi$? | Let A=(\alpha_0,\ldots,\alpha_{n-1}), n\geq3, be realizable by a polygon in \mathbb R^3. Can A be realized without self-intersections if and only if n is even or \sum_{i=0}^{n-1}(\pi-\alpha_i)\neq\pi? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,519 | OWR-1703876-013 | Connectivity of Bistellar Flip Graphs in Dimensions Three and Four | Are the bistellar-flip graphs of triangulations of every point set connected in dimensions $3$ and $4$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,020 | 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-1703876-013",
"literature-status:open",
"owr-year:2020"
] | Bistellar flip-graph connectivity is known to fail in dimensions at least five but remains open for dimensions three and four. | [
{
"url": "https://doi.org/10.1007/s00454-022-00436-2",
"label": "Rote--Santos--Stump, Connectivity of Triangulation Flip Graphs"
},
{
"url": "https://topp.openproblem.net/p28",
"label": "TOPP, Flip Graph Connectivity in 3D"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | Are the bistellar-flip graphs of triangulations of every point set connected in dimensions $3$ and $4$? | Are the bistellar-flip graphs of triangulations of every point set connected in dimensions 3 and 4? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,520 | OWR-1703876-014 | Stability of Longest Edge Simplex Refinement | Start with a sufficiently generic $d$-dimensional simplex, repeatedly bisect its longest edge and subdivide the simplex into two equal-volume simplices. Does the resulting subdivision stabilize after finitely many iterations for every starting simplex in every dimension, or can the simplices become arbitrarily badly sh... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,020 | 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-1703876-014",
"literature-status:open",
"owr-year:2020"
] | The longest-edge repeated-halving process is proved to stabilize in dimensions two and three and for special four-dimensional starts, but the all-simplex all-dimension question remains open. | [
{
"url": "https://page.mi.fu-berlin.de/rote/Kram/Problems-Discrete-Geometry-2020.pdf",
"label": "Rote, Open Problems in Discrete Geometry"
},
{
"url": "https://ems.press/content/serial-article-files/46867",
"label": "Oberwolfach Reports 2020/30"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | Start with a sufficiently generic $d$-dimensional simplex, repeatedly bisect its longest edge and subdivide the simplex into two equal-volume simplices. Does the resulting subdivision stabilize after finitely many iterations for every starting simplex in every dimension, or can the simplices become arbitrarily badly sh... | Start with a sufficiently generic d-dimensional simplex, repeatedly bisect its longest edge and subdivide the simplex into two equal-volume simplices. Does the resulting subdivision stabilize after finitely many iterations for every starting simplex in every dimension, or can the simplices become arbitrarily badly shap... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,521 | OWR-1703876-015 | Exact Absolute Linear Harbourne Constants | For the absolute linear Harbourne constant $H(d)=\min_K\min_{|L|=d}H(K,L)$ of $d$ lines in the projective plane, compute $H(d)$ for every positive integer $d$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,020 | 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-1703876-015",
"literature-status:open",
"owr-year:2020"
] | Exact values are known through d=31 and for projective-plane orders q squared plus q plus 1, but the general computation and conjectural formula remain unresolved. | [
{
"url": "https://doi.org/10.1016/j.ffa.2018.03.001",
"label": "Dumnicki--Harrer--Szpond, On Absolute Linear Harbourne Constants"
},
{
"url": "https://ems.press/content/serial-article-files/46867",
"label": "Oberwolfach Reports 2020/30"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | For the absolute linear Harbourne constant $H(d)=\min_K\min_{|L|=d}H(K,L)$ of $d$ lines in the projective plane, compute $H(d)$ for every positive integer $d$. | For the absolute linear Harbourne constant H(d)=\min_K\min_{|L|=d} H(K,L) of d lines in the projective plane, compute H(d) for every positive integer d. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,522 | OWR-1703876-016 | Extremal Questions in Discrete Geometry and Topological Combinatorics | For a simplicial $4$-polytope $P$ with $n$ vertices in which every three vertices contain an edge, must its graph contain a clique of size at least $n/10$? Given two continuous probability measures on $S^2$ and $0<\alpha<1/2$, must some spherical cap have measure $\alpha$ for both? Must every simple red-blue pseudoline... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | partially_solved | null | 2,020 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | 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... | [
"OWR-1703876-017"
] | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "partial_progress",
"evidence": "published"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703876-016",
"literature-status:open",
"owr-year:2020"
] | The record bundles five independent problems (OWR 30/2020, Problems 6–10). Kupavskii–Volostnov–Yarovikov prove the Catalan lower bound for partial triangulations (Problem 10). Radtke–Keszegh–Lauff do not solve the general bichromatic-triangle problem: they prove triangle-or-quadrangle existence and triangle existence u... | [
{
"url": "https://doi.org/10.1016/j.ejc.2022.103636",
"label": "Kupavskii–Volostnov–Yarovikov, Minimum number of partial triangulations (2023)"
},
{
"url": "https://arxiv.org/abs/2104.05855",
"label": "Kupavskii–Volostnov–Yarovikov — primary manuscript"
},
{
"url": "https://arxiv.org/abs... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | For a simplicial $4$-polytope $P$ with $n$ vertices in which every three vertices contain an edge, must its graph contain a clique of size at least $n/10$? Given two continuous probability measures on $S^2$ and $0<\alpha<1/2$, must some spherical cap have measure $\alpha$ for both? Must every simple red-blue pseudoline... | For a simplicial 4-polytope P with n vertices in which every three vertices contain an edge, must its graph contain a clique of size at least n/10? Given two continuous probability measures on S^2 and 0<\alpha<1/2, must some spherical cap have measure \alpha for both? Must every simple red-blue pseudoline arrangement c... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,523 | OWR-1703876-017 | Duplicate Discrete-Geometry Problem Collection | For a hypergraph H, does m_2^*=3 imply that m_3^* is finite? What is the minimum number of partial triangulations of n points in general position in the plane, and is it the Catalan number C_{n-2}=\frac{1}{n-1}\binom{2n-4}{n-2}? The report also asks whether the graph of a simplicial 4-polytope with the stated three-ver... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** partiall... | 3 | partially_solved | null | 2,020 | 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": "published"
} | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the hypergraph-coloring, partial-triangulation, polytope, spherical-cap, and pseud) | [
"OWR-1703876-016"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703876-017",
"literature-status:partially-solved",
"owr-year:2020"
] | Duplicate extraction; the canonical question is OWR-1703876-016. The record bundles five independent problems (OWR 30/2020, Problems 6–10). Kupavskii–Volostnov–Yarovikov prove the Catalan lower bound for partial triangulations (Problem 10). Radtke–Keszegh–Lauff do not solve the general bichromatic-triangle problem: the... | [
{
"url": "https://doi.org/10.1016/j.ejc.2022.103636",
"label": "Kupavskii–Volostnov–Yarovikov, Minimum number of partial triangulations (2023)"
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{
"url": "https://arxiv.org/abs/2104.05855",
"label": "Kupavskii–Volostnov–Yarovikov — primary manuscript"
},
{
"url": "https://arxiv.org/abs... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | null | For a hypergraph H, does m_2^*=3 imply that m_3^* is finite? What is the minimum number of partial triangulations of n points in general position in the plane, and is it the Catalan number C_{n-2}=\frac{1}{n-1}\binom{2n-4}{n-2}? The report also asks whether the graph of a simplicial 4-polytope with the stated three-ver... | unrecoverable | The official report confirms that this extraction repeats the hypergraph-coloring, partial-triangulation, polytope, spherical-cap, and pseudoline questions represented together by OWR-1703876-016. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,524 | OWR-1703876-018 | Continuous Selection of Piecewise Linear Planar Extensions | For a fixed reference triangle $ABC$, does there exist a continuous function assigning to every PL one-to-one boundary map $\partial ABC\to\mathbb{R}^2$ a PL one-to-one extension $ABC\to\mathbb{R}^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,020 | 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-1703876-018",
"literature-status:open",
"owr-year:2020"
] | The listed collapsibility, centerpoint-constant, two-convex-pieces Helly, and continuous-extension questions remain unresolved in the cited literature. | [
{
"url": "https://page.mi.fu-berlin.de/rote/Kram/Problems-Discrete-Geometry-2020.pdf",
"label": "Rote, Open Problems in Discrete Geometry"
},
{
"url": "https://ems.press/content/serial-article-files/46867",
"label": "Oberwolfach Reports 2020/30"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | For a fixed reference triangle $ABC$, does there exist a continuous function assigning to every PL one-to-one boundary map $\partial ABC\to\mathbb{R}^2$ a PL one-to-one extension $ABC\to\mathbb{R}^2$? | For a fixed reference triangle ABC, does there exist a continuous function assigning to every PL one-to-one boundary map \partial ABC\to\mathbb{R}^2 a PL one-to-one extension ABC\to\mathbb{R}^2? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,525 | OWR-2654827-001 | Double Jordan Stratifications of Artinian Gorenstein Algebras | For an Artinian Gorenstein algebra and principal ideals $J,K$, can the double $Q_{J,K}$-stratification be redefined to have the expected dimensions while retaining its relation to the single-ideal $Q_J(a)$- and $Q_K(a)$-stratifications? Can the $Q_{\ell,m}$-decomposition define a Jordan order type for nongraded Artinia... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | open | null | 2,020 | 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-2654827-001",
"literature-status:open",
"owr-year:2020"
] | The proposed generalizations of the Q-stratifications and their combinatorial description remain open; existing work establishes only special Jordan-string decompositions. | [
{
"url": "https://doi.org/10.4171/owr/2020/31",
"label": "Oberwolfach Reports 2020/31"
},
{
"url": "https://arxiv.org/abs/1811.02072",
"label": "Iarrobino--Macias Marques--McDaniel, Jordan Type"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | For an Artinian Gorenstein algebra and principal ideals $J,K$, can the double $Q_{J,K}$-stratification be redefined to have the expected dimensions while retaining its relation to the single-ideal $Q_J(a)$- and $Q_K(a)$-stratifications? Can the $Q_{\ell,m}$-decomposition define a Jordan order type for nongraded Artinia... | For an Artinian Gorenstein algebra and principal ideals J,K, can the double Q_{J,K} stratification be redefined to have the expected dimensions while retaining its relation to the single-ideal Q_J(a),Q_K(a) stratifications? Can the Q_{\ell,m} decomposition define a Jordan order type for non-graded Artinian Gorenstein a... | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,526 | OWR-2654827-002 | Strong Lefschetz Property of the Zeroth Jordan Component | For an Artinian Gorenstein algebra $A$ and the component $Q(0)$ of its Jordan decomposition, can $A$ have the strong Lefschetz property while $Q(0)$ does not? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | open | null | 2,020 | 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-2654827-002",
"literature-status:open",
"owr-year:2020"
] | General Jordan-type and central-simple-module theory gives criteria for strong Lefschetzness, but does not settle whether A can be strong Lefschetz while Q(0) is not. | [
{
"url": "https://doi.org/10.1016/j.jpaa.2006.10.016",
"label": "Harima--Watanabe, Central Simple Modules"
},
{
"url": "https://doi.org/10.4171/owr/2020/31",
"label": "Oberwolfach Reports 2020/31"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | For an Artinian Gorenstein algebra $A$ and the component $Q(0)$ of its Jordan decomposition, can $A$ have the strong Lefschetz property while $Q(0)$ does not? | For an Artinian Gorenstein algebra A and the Q(0) component of its decomposition, can A have the strong Lefschetz property while Q(0) does not? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,527 | OWR-2654827-003 | Unbounded Non-Grid Geproci Point Configurations | Does there exist a family of non-grid point configurations in $\mathbb{P}^3$ with an unbounded number of points having the geproci property, and are there analogous examples in higher-dimensional projective spaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | partially_solved | null | 2,020 | 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-2654827-003",
"literature-status:partially-solved",
"owr-year:2020"
] | Non-grid geproci examples in projective three-space have been constructed, including infinite families and the 24-point example, but the requested general series and higher-dimensional analogue remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2020/31",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1090/tran/8290",
"label": "Chiantini--Migliore"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | Does there exist a family of non-grid point configurations in $\mathbb{P}^3$ with an unbounded number of points having the geproci property, and are there analogous examples in higher-dimensional projective spaces? | Does there exist a family of non-grid point configurations in \mathbb{P}^3 with an unbounded number of points having the geproci property, and are there analogous examples in higher-dimensional projective spaces? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,528 | OWR-2654827-004 | Universal Lefschetz Parameters for Neighborly Spheres | For neighborly spheres, does every linear system of parameters have the Lefschetz property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | open | null | 2,020 | 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-2654827-004",
"literature-status:open",
"owr-year:2020"
] | The cited question whether every linear system of parameters for a neighborly sphere is Lefschetz is still presented as open; strong Lefschetz results cover important classes but not this universal assertion. | [
{
"url": "https://doi.org/10.4171/owr/2020/31",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/0802.1058",
"label": "Lefschetz properties of spheres"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | For neighborly spheres, does every linear system of parameters have the Lefschetz property? | For neighborly spheres, does every linear system of parameters have the Lefschetz property? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,529 | OWR-2654827-005 | Irreducibility of Gorenstein-Algebra Families with Fixed Hilbert Function | Given a Gorenstein sequence $T$, is the family $\operatorname{Gor}(T)$ of local Artinian Gorenstein algebras with Hilbert function $T$ irreducible? If not, how many irreducible components does it have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | partially_solved | null | 2,020 | 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-2654827-005",
"literature-status:partially-solved",
"owr-year:2020"
] | The proposed irreducibility statement is false in general: Gor(T) is reducible for known Hilbert functions, while irreducibility and component counts have been determined only in selected cases. | [
{
"url": "https://arxiv.org/abs/2112.14664",
"label": "Iarrobino--Macias Marques"
},
{
"url": "https://arxiv.org/abs/2302.00287",
"label": "Gorenstein component studies"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | Given a Gorenstein sequence $T$, is the family $\operatorname{Gor}(T)$ of local Artinian Gorenstein algebras with Hilbert function $T$ irreducible? If not, how many irreducible components does it have? | Given a Gorenstein sequence T, is the family Gor(T) of local Artinian Gorenstein algebras with Hilbert function T irreducible? If not, how many irreducible components does it have? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,530 | OWR-2654827-008 | Computed Exceptional Hilbert Series | For R_{n,m,d}=k[x_1,\ldots,x_n]/(\ell_1^d,\ldots,\ell_m^d) with general linear forms, the Hilbert series in the cases (n,m,d)=(4,6,5),(6,8,3),(8,10,2),(8,10,3),(10,12,2),(10,12,3) differ in their leading terms from the values predicted by Froberg's conjecture, namely 10t^9,42t^6,15t^4,135t^8,22t^5,88t^{10}, respectivel... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | open | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (a theorem, not an open problem)) | null | null | [Discussion #4 literature review, 2026-10-14] **solved (a theorem, not an open problem)**; the dataset currently labels it open. The record (for six triples (n,m,d), the Hilbert series of k[x₁,…,xₙ]/(ℓ₁^d,…,ℓ_m^d), ℓᵢ general linear forms, differ in the leading term from Fröberg's prediction) is Theorem 6 of M. Boij's ... | [
"owr",
"oberwolfach-reports",
"OWR-2654827-008",
"literature-status:open",
"owr-year:2020"
] | The extracted text is a polynomial fragment rather than a complete proposition and omits the ring and genericity hypotheses, so its apparent comparison with Fröberg predictions cannot be classified as a resolved or disproved claim. | [
{
"url": "https://doi.org/10.4171/owr/2020/31",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/0001-8708(78)90045-2",
"label": "Stanley"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | null | For R_{n,m,d}=k[x_1,\ldots,x_n]/(\ell_1^d,\ldots,\ell_m^d) with general linear forms, the Hilbert series in the cases (n,m,d)=(4,6,5),(6,8,3),(8,10,2),(8,10,3),(10,12,2),(10,12,3) differ in their leading terms from the values predicted by Froberg's conjecture, namely 10t^9,42t^6,15t^4,135t^8,22t^5,88t^{10}, respectivel... | unrecoverable | The official report presents this record as a theorem listing computed Hilbert-series exceptions to Fröberg’s prediction, not as an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,531 | OWR-2654827-010 | Lefschetz Properties of Tropical Varieties | Can one find other combinatorially interesting families of tropical varieties with the Lefschetz property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | partially_solved | null | 2,020 | 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-2654827-010",
"literature-status:partially-solved",
"owr-year:2020"
] | Tropical Lefschetz theorems are known for smooth tropical varieties and matroidal or Bergman-fan constructions, but the open-ended search for further combinatorially interesting families has not been exhausted or classified. | [
{
"url": "https://arxiv.org/abs/1401.7301",
"label": "Adiprasito--Bjoerner"
},
{
"url": "https://arxiv.org/abs/2007.07826",
"label": "Amini--Piquerez"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | Can one find other combinatorially interesting families of tropical varieties with the Lefschetz property? | Can one find other combinatorially interesting families of tropical varieties with the Lefschetz property? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,532 | OWR-2654827-011 | Nonunimodal Codimension-Four Gorenstein h-Vectors | Do there exist non-unimodal Gorenstein h-vectors of codimension 4 for standard graded Artinian Gorenstein algebras? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | open | null | 2,020 | 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-2654827-011",
"literature-status:open",
"owr-year:2020"
] | The existence of a non-unimodal Gorenstein h-vector in codimension four remains unresolved; partial results constrain the possible vectors but do not produce a counterexample or prove universal unimodality. | [
{
"url": "https://arxiv.org/abs/1011.2732",
"label": "Seo--Srinivasan"
},
{
"url": "https://intlpress.com/site/pub/files/_fulltext/journals/mrl/2008/0015/0002/MRL-2008-0015-0002-a011.pdf",
"label": "Migliore--Nagel--Zanello"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | Do there exist non-unimodal Gorenstein h-vectors of codimension 4 for standard graded Artinian Gorenstein algebras? | Do there exist non-unimodal Gorenstein h-vectors of codimension 4 for standard graded Artinian Gorenstein algebras? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,533 | OWR-2654827-015 | Asymptotic Minimal Quadratic Growth of Gorenstein Algebras | Let
$$\nu(r)=\min_{A\in QG(r)}\dim A_2,$$
where $QG(r)$ consists of codimension-$r$ Artinian Gorenstein algebras presented by quadrics and having socle degree $4$. Is
$$\lim_{r\to\infty}\frac{\nu(r)}{r^{2/3}}=6$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | open | null | 2,020 | 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-2654827-015",
"literature-status:open",
"owr-year:2020"
] | The asymptotic formula for quadratic-presented Gorenstein algebras remains a conjecture; published work gives partial results and continues to formulate the asymptotic question rather than prove the limit. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S002240492030133X",
"label": "Socle-degree-four study"
},
{
"url": "https://doi.org/10.1007/s13398-023-01523-6",
"label": "Recent partial results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | Let
$$\nu(r)=\min_{A\in QG(r)}\dim A_2,$$
where $QG(r)$ consists of codimension-$r$ Artinian Gorenstein algebras presented by quadrics and having socle degree $4$. Is
$$\lim_{r\to\infty}\frac{\nu(r)}{r^{2/3}}=6$$? | For the minimum \nu(r)=\min_{A\in QG(r)}\dim A_2 among Artinian Gorenstein algebras presented by quadrics with socle degree 4 and codimension r, is it true that \lim_{r\to\infty}\nu(r)/r^{2/3}=6? | corrected_verified | The official report was checked. The class QG(r), the minimum, and the conjectured limit were retained. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,534 | OWR-2654827-016 | Eventual Lefschetz Dichotomies for Symmetric Ideal Chains | Let $(I_n)$ be a $\operatorname{Sym}$-invariant chain of Artinian ideals. Is each Lefschetz property eventually constant along the chain: either $I_n$ has the strong, respectively weak, Lefschetz property for every sufficiently large $n$, or it fails that property for every sufficiently large $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | open | null | 2,020 | 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-2654827-016",
"literature-status:open",
"owr-year:2020"
] | The extracted passage contains only a general remark about possible limit behavior and no identifiable theorem or conjecture, so the unresolved claim must be classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2020/31",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | Let $(I_n)$ be a $\operatorname{Sym}$-invariant chain of Artinian ideals. Is each Lefschetz property eventually constant along the chain: either $I_n$ has the strong, respectively weak, Lefschetz property for every sufficiently large $n$, or it fails that property for every sufficiently large $n$? | For a Sym-invariant chain of Artinian ideals (I_n), does there exist an eventual dichotomy in which either I_n has the strong or weak Lefschetz property for all sufficiently large n, or it fails that property for all sufficiently large n? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,535 | OWR-2654827-017 | Eventual Linearity of Homological Invariants in Symmetric Ideal Chains | Let $(I_n)$ be a $\operatorname{Sym}$-invariant chain of ideals in polynomial rings $R_n$. Are $\operatorname{pd}_{R_n}(R_n/I_n)$ and $\operatorname{reg}(I_n)$ eventually linear in $n$? Equivalently, do integers $A,B,C,D$ exist such that
$$\operatorname{pd}_{R_n}(R_n/I_n)=An+B,\qquad \operatorname{reg}(I_n)=Cn+D$$
fo... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600](https://doi.org/10.4171/owr/2020/31)
## Literature review ... | 3 | partially_solved | null | 2,020 | 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-2654827-017",
"literature-status:partially-solved",
"owr-year:2020"
] | Eventual linearity of projective dimension and regularity is proved for several monomial, saturated, and related special classes, but the full conjecture for Sym-invariant chains remains open. | [
{
"url": "https://arxiv.org/abs/2206.15141",
"label": "Le--Nguyen"
},
{
"url": "https://arxiv.org/abs/1806.00457",
"label": "Regularity conjecture"
},
{
"url": "https://arxiv.org/abs/1809.06877",
"label": "Projective-dimension conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/31 | null | null | null | Let $(I_n)$ be a $\operatorname{Sym}$-invariant chain of ideals in polynomial rings $R_n$. Are $\operatorname{pd}_{R_n}(R_n/I_n)$ and $\operatorname{reg}(I_n)$ eventually linear in $n$? Equivalently, do integers $A,B,C,D$ exist such that
$$\operatorname{pd}_{R_n}(R_n/I_n)=An+B,\qquad \operatorname{reg}(I_n)=Cn+D$$
fo... | For a Sym-invariant chain of ideals (I_n), are pd_{R_n}(R_n/I_n) and reg(I_n) eventually linear functions of n; that is, do there exist integers A,B,C,D such that pd_{R_n}(R_n/I_n)=An+B and reg(I_n)=Cn+D for all sufficiently large n? | corrected_verified | The official report was checked. The symmetric-chain setting and both eventual-linearity formulas were restored in publication notation. | null | null | null | null | null | Lefschetz Properties in Algebra, Geometry and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/31, pp. 1539--1600 |
30,004,536 | OWR-2654828-001 | Persistence and Exit Times of Integrated Self-Similar Processes | For the integral of a general self-similar Markov process, can one determine persistence and exit-time asymptotics? In particular, can one compute $\mathbb{P}_x(T_a\wedge T_b>t)$ as $t\to\infty$, solve the analogous exit-time problem for the integral of a stable Lévy process, and compute the area under a general stable... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656](https://doi.org/10.4171/owr/2020/32)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,020 | 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-2654828-001",
"literature-status:partially-solved",
"owr-year:2020"
] | Exit and persistence questions for integrated stable processes have been solved in important one-sided and spectrally positive cases, including excursion-area results, but the general stable excursion and all listed variants remain open. | [
{
"url": "https://doi.org/10.1007/s00440-014-0577-5",
"label": "Profeta--Simon"
},
{
"url": "https://arxiv.org/abs/2009.01504",
"label": "Stable excursion area"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/32 | null | null | null | For the integral of a general self-similar Markov process, can one determine persistence and exit-time asymptotics? In particular, can one compute $\mathbb{P}_x(T_a\wedge T_b>t)$ as $t\to\infty$, solve the analogous exit-time problem for the integral of a stable Lévy process, and compute the area under a general stable... | For the integral of a general self-similar Markov process, can one determine persistence and exit-time asymptotics? In particular, can one compute P_x(T_a\wedge T_b>t) as t\to\infty, solve the analogous exit-time problem for the integral of a stable Levy process, and compute the area under a general stable excursion? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656 |
30,004,537 | OWR-2654828-002 | Existence of Gaussian Persistence Exponents | For a Gaussian stationary process with persistence probability $P_f(N)$, what conditions ensure the existence of the exact asymptotic constant $\theta_f=-\lim_{N\to\infty}N^{-1}\log P_f(N)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656](https://doi.org/10.4171/owr/2020/32)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,020 | 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-2654828-002",
"literature-status:partially-solved",
"owr-year:2020"
] | Existence of the persistence exponent limit is proved under broad spectral-density and positivity hypotheses, but necessary and sufficient conditions and the general exact-asymptotic problem remain unresolved. | [
{
"url": "https://arxiv.org/abs/2112.04820",
"label": "Gaussian persistence exponents"
},
{
"url": "https://arxiv.org/abs/2605.20587",
"label": "Exact log-asymptotics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/32 | null | null | null | For a Gaussian stationary process with persistence probability $P_f(N)$, what conditions ensure the existence of the exact asymptotic constant $\theta_f=-\lim_{N\to\infty}N^{-1}\log P_f(N)$? | For a Gaussian stationary process with persistence probability P_f(N), what conditions ensure the existence of the exact asymptotic constant \theta_f=-\lim_{N\to\infty}N^{-1}\log P_f(N)? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656 |
30,004,538 | OWR-2654828-003 | Values and Conditioned Shapes of Gaussian Persistence | For Gaussian stationary processes, can the persistence exponent be computed in specific examples? What is the typical shape of a process conditioned to persist above a level $\ell$ on $[0,T]$, and can the results be extended to non-Gaussian or non-stationary models? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656](https://doi.org/10.4171/owr/2020/32)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,020 | 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"
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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-2654828-003",
"literature-status:partially-solved",
"owr-year:2020"
] | Conditioned persistence shapes and extensions beyond the basic stationary Gaussian setting are known for several spectral-singularity classes, but the typical shape and non-Gaussian or non-stationary generalizations in full generality remain open. | [
{
"url": "https://arxiv.org/abs/2112.04820",
"label": "Gaussian persistence exponents"
},
{
"url": "https://arxiv.org/abs/2605.20587",
"label": "Conditioned field asymptotics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/32 | null | null | null | For Gaussian stationary processes, can the persistence exponent be computed in specific examples? What is the typical shape of a process conditioned to persist above a level $\ell$ on $[0,T]$, and can the results be extended to non-Gaussian or non-stationary models? | For Gaussian stationary processes, can the persistence exponent be computed in specific examples? What is the typical shape of a process conditioned to persist above a level \ell on [0,T], and can the results be extended to non-Gaussian or non-stationary models? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656 |
30,004,539 | OWR-2654828-004 | Convergence Radii of Autoregressive and Moving Average Persistence Series | What is the radius of convergence of the power series in $\rho$ for the persistence exponent of the Gaussian autoregressive process of order one, and is the radius of convergence one for the analogous moving-average process of order one? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656](https://doi.org/10.4171/owr/2020/32)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,020 | 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"
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"id": 3,
"level": 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-2654828-004",
"literature-status:open",
"owr-year:2020"
] | For the AR(1) series only lower bounds on the radius are known in the cited work, and the MA(1) radius-one assertion is explicitly conjectural; no complete proof of the requested radius is available. | [
{
"url": "https://arxiv.org/abs/1810.09861",
"label": "AR(1) persistence series"
},
{
"url": "https://arxiv.org/abs/2407.06870",
"label": "MA(1) persistence series"
},
{
"url": "https://ems.press/content/serial-article-files/46870",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/32 | null | null | null | What is the radius of convergence of the power series in $\rho$ for the persistence exponent of the Gaussian autoregressive process of order one, and is the radius of convergence one for the analogous moving-average process of order one? | What is the radius of convergence of the power series in \rho for the persistence exponent of the Gaussian autoregressive process of order one, and is the radius of convergence one for the analogous moving-average process of order one? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656 |
30,004,540 | OWR-2654828-005 | Resolved Weighted-Gaussian-Persistence Lead-In | What is the asymptotic behavior of the persistence probability for an infinitely correlated Gaussian stationary process, and how does it depend on whether its correlation function is summable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656](https://doi.org/10.4171/owr/2020/32)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 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 | Unrecoverable OWR statement (The official report presents this as a lead-in to results on weighted sums of correlated Gaussian stationary processes and then states how t) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-2654828-005",
"literature-status:open",
"owr-year:2020"
] | The extracted phrase describing a Pa-infinity-correlated Gaussian process is malformed and does not identify a precise model or theorem; existing persistence results do not settle this unspecified generalization. | [
{
"url": "https://doi.org/10.4171/owr/2020/32",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1709.00204",
"label": "Persistence spectral methods"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/32 | null | null | null | null | What is the asymptotic behavior of the persistence probability for an infinitely correlated Gaussian stationary process, and how does it depend on whether its correlation function is summable? | unrecoverable | The official report presents this as a lead-in to results on weighted sums of correlated Gaussian stationary processes and then states how the answer depends on summability of the correlation function; the supplied extraction is also malformed and does not define the weighted process. No separate clean statement is pro... | null | null | null | null | null | Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656 |
30,004,541 | OWR-2654828-006 | Extinction Criteria for the Derrida–Retaux Process | For the continuous-time Derrida–Retaux process with initial distribution $\mu_0$ on $\mathbb R_+$, find necessary and sufficient conditions on $\mu_0$ for $F_\infty(\mu_0)=0$. Does $F_\infty(\mu_0)=0$ imply that $X_t\to0$ in probability as $t\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656](https://doi.org/10.4171/owr/2020/32)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,020 | 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"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-2654828-006",
"literature-status:open",
"owr-year:2020"
] | For the continuous-time Derrida--Retaux process with general initial law, necessary and sufficient conditions for F-infinity(mu-zero)=0 are explicitly posed as an open question; only special initial distributions are solved. | [
{
"url": "https://doi.org/10.4171/owr/2020/32",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/32 | null | null | null | For the continuous-time Derrida–Retaux process with initial distribution $\mu_0$ on $\mathbb R_+$, find necessary and sufficient conditions on $\mu_0$ for $F_\infty(\mu_0)=0$. Does $F_\infty(\mu_0)=0$ imply that $X_t\to0$ in probability as $t\to\infty$? | For the model with an initial distribution \mu_0 on \mathbb{R}_+, what necessary and sufficient conditions on \mu_0 imply F_\infty(\mu_0)=0? The report also conjectures that F_\infty(\mu_0)=0 implies X_t\to0 in probability as t\to\infty. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656 |
30,004,542 | OWR-2654828-007 | Speed Convergence in Convex Hull Avoiding Walks | For the finite-memory convex-hull-avoiding process in dimension $d$, is it true that $\lim_{k\to\infty}v_{d,k}=v_{d,\infty}$, where $v_{d,\infty}$ is the conjectural speed of the infinite-memory model? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656](https://doi.org/10.4171/owr/2020/32)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,020 | 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-2654828-007",
"literature-status:open",
"owr-year:2020"
] | Finite-memory ballisticity is proved, but the infinite-memory model remains conjecturally ballistic and the convergence of v-sub-d-k to its conjectural speed is still posed as Conjecture 5. | [
{
"url": "https://doi.org/10.1016/j.indag.2019.11.002",
"label": "Finite-memory convex-hull walk"
},
{
"url": "https://doi.org/10.4171/owr/2020/32",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/32 | null | null | null | For the finite-memory convex-hull-avoiding process in dimension $d$, is it true that $\lim_{k\to\infty}v_{d,k}=v_{d,\infty}$, where $v_{d,\infty}$ is the conjectural speed of the infinite-memory model? | For the finite-memory convex-hull-avoiding process in dimension d, is it true that \lim_{k\to\infty}v_{d,k}=v_{d,\infty}, where v_{d,\infty} is the conjectural speed of the infinite-memory model? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Stochastic Processes under Constraints (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/32, pp. 1601--1656 |
30,004,543 | OWR-2654829-001 | Complex Structures on the Six-Sphere and Rational Homotopy Types | Does the six-sphere $S^6$ admit the structure of a complex manifold? More generally, which rational homotopy types can occur for complex manifolds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691](https://doi.org/10.4171/owr/2020/33)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,020 | 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-2654829-001",
"literature-status:open",
"owr-year:2020"
] | Whether the smooth six-sphere admits an integrable complex structure remains unresolved; known almost-complex structures and obstructions for restricted classes do not decide the general problem. | [
{
"url": "https://arxiv.org/abs/1405.3405",
"label": "Chern study"
},
{
"url": "https://doi.org/10.1515/coma-2025-0011",
"label": "Complex Manifolds 2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/33 | null | null | null | Does the six-sphere $S^6$ admit the structure of a complex manifold? More generally, which rational homotopy types can occur for complex manifolds? | Does the six-sphere S^6 admit a complex-manifold structure, and more generally what are the rational homotopy types of complex manifolds? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691 |
30,004,544 | OWR-2654829-002 | Kähler Criteria from Nonintegrable Bundle Spectral Theory | For compact complex manifolds of complex dimension greater than two, develop an analogue of the Lamari–Buchdahl criteria for the existence of Kähler metrics using the spectral theory of nonintegrable complex vector bundles. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691](https://doi.org/10.4171/owr/2020/33)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,020 | 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-2654829-002",
"literature-status:partially-solved",
"owr-year:2020"
] | The record is partly outdated: Siu proved deformation invariance of plurigenera in the projective general-type setting, while transcendental Morse inequalities and the higher-dimensional Lamari--Buchdahl analogue remain open or only partially solved. | [
{
"url": "https://doi.org/10.1007/s002220050276",
"label": "Siu invariance of plurigenera"
},
{
"url": "https://arxiv.org/abs/2309.04978",
"label": "Transcendental Morse inequalities"
},
{
"url": "https://doi.org/10.4171/owr/2020/33",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/33 | null | null | null | For compact complex manifolds of complex dimension greater than two, develop an analogue of the Lamari–Buchdahl criteria for the existence of Kähler metrics using the spectral theory of nonintegrable complex vector bundles. | For compact complex manifolds of complex dimension greater than two, develop an analogue of the results of Lamari and Buchdahl on the existence of K\ddot{a}hler metrics, in the context of the spectral theory of non-integrable complex vector bundles. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691 |
30,004,545 | OWR-2654829-004 | The Tamed-to-Compatible Symplectic Conjecture | If an almost-complex structure $J$ on a compact $4$-manifold is tamed by a symplectic form, does there exist a symplectic form compatible with $J$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691](https://doi.org/10.4171/owr/2020/33)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,020 | 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-2654829-004",
"literature-status:partially-solved",
"owr-year:2020"
] | The tamed-to-compatible question is not solved in general. Positive results cover b^+=1 and further subclasses, so the four-dimensional question has substantial partial answers but no general theorem. | [
{
"url": "https://doi.org/10.1007/s42543-021-00045-7",
"label": "Tan--Wang--Zhang, On tamed almost complex four-manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2020/33",
"label": "Oberwolfach Report 33/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/33 | null | null | null | If an almost-complex structure $J$ on a compact $4$-manifold is tamed by a symplectic form, does there exist a symplectic form compatible with $J$? | If an almost-complex structure J on a compact 4-manifold is tamed by a symplectic form, does there exist a symplectic form compatible with J? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691 |
30,004,546 | OWR-2654829-006 | Bott–Chern and Aeppli Cohomology for Almost-Complex Manifolds | For an almost-complex manifold, which Bott–Chern and Aeppli cohomology groups complete the vertical row of the Dolbeault–de Rham diagram while recovering the classical integrable case, respecting the natural maps and spectral sequences, carrying a real structure, and possessing the expected algebra and module structure... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691](https://doi.org/10.4171/owr/2020/33)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,020 | 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-2654829-006",
"literature-status:open",
"owr-year:2020"
] | For nonintegrable almost-complex structures the usual Dolbeault, Bott--Chern, and Aeppli cohomologies are not generally defined; harmonic replacements exist, but a canonical almost-complex partialpartial-lemma and the requested vertical comparison remain unsettled. | [
{
"url": "https://doi.org/10.1515/coma-2020-0006",
"label": "Tardini--Tomassini, 2020"
},
{
"url": "https://doi.org/10.4171/owr/2020/33",
"label": "Oberwolfach Report 33/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/33 | null | null | null | For an almost-complex manifold, which Bott–Chern and Aeppli cohomology groups complete the vertical row of the Dolbeault–de Rham diagram while recovering the classical integrable case, respecting the natural maps and spectral sequences, carrying a real structure, and possessing the expected algebra and module structure... | For an almost-complex manifold, what Bott--Chern and Aeppli-type cohomology groups can fill the vertical row of the Dolbeault--de Rham diagram while agreeing with the classical integrable case, fitting the natural maps and spectral sequences, carrying a real structure, and having the expected algebra and module structu... | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691 |
30,004,547 | OWR-2654829-008 | Topological Obstructions to Integrability of Geometric Structures | For a closed manifold equipped with an almost-complex structure $J$ or a nondegenerate $2$-form $\omega$, what additional topological restrictions follow from integrability? In particular, what topological restrictions does integrability of $J$ impose? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691](https://doi.org/10.4171/owr/2020/33)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,020 | 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-2654829-008",
"literature-status:open",
"owr-year:2020"
] | The broad topological restrictions imposed by integrability of J remain unresolved; known results constrain special cases and rational-homology spheres, but no general classification of underlying manifolds is known. | [
{
"url": "https://doi.org/10.4171/owr/2020/33",
"label": "Oberwolfach Report 33/2020"
},
{
"url": "https://arxiv.org/abs/1805.04751",
"label": "Albanese--Milivojevic, 2019"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/33 | null | null | null | For a closed manifold equipped with an almost-complex structure $J$ or a nondegenerate $2$-form $\omega$, what additional topological restrictions follow from integrability? In particular, what topological restrictions does integrability of $J$ impose? | For closed manifolds equipped with an almost-complex structure J or a non-degenerate 2-form \omega, what additional topological restrictions follow when J or \omega is integrable; in particular, what topological restrictions does integrability of J impose? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691 |
30,004,548 | OWR-2654829-009 | Cohomology Rings of Almost-Complex Manifolds | Which rational cohomology rings can be realized by closed manifolds that admit almost-complex structures? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691](https://doi.org/10.4171/owr/2020/33)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,020 | 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-2654829-009",
"literature-status:partially-solved",
"owr-year:2020"
] | The stated connected-sum construction and the associated rational-cohomology observation are established, while the broader realization problem for rational cohomology rings of almost-complex manifolds remains only partially classified. | [
{
"url": "https://arxiv.org/abs/1805.04751",
"label": "Albanese--Milivojevic, 2019"
},
{
"url": "https://doi.org/10.1515/coma-2021-0133",
"label": "Milivojevic, 2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/33 | null | null | null | Which rational cohomology rings can be realized by closed manifolds that admit almost-complex structures? | Which rational cohomology rings can be realized by closed manifolds that admit almost-complex structures? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691 |
30,004,549 | OWR-2654829-012 | Generic Vanishing of Anti-Invariant Cohomology in Dimension Four | For a generic almost-complex structure $J$ on a compact $4$-manifold $M$, is the dimension $h_J^-$ of the space of closed $J$-anti-invariant $2$-forms zero? If $h_J^-\geq3$, must $J$ be integrable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691](https://doi.org/10.4171/owr/2020/33)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,020 | 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-2654829-012",
"literature-status:partially-solved",
"owr-year:2020"
] | Generic vanishing h^-_J=0 is proved, but the stronger assertion h^-_J\ge3\Rightarrow J integrable remains a conjecture; only bounds and special cases are known. | [
{
"url": "https://doi.org/10.1007/s12220-014-9477-2",
"label": "Tan--Wang--Zhang, 2015"
},
{
"url": "https://doi.org/10.4171/owr/2020/33",
"label": "Oberwolfach Report 33/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/33 | null | null | null | For a generic almost-complex structure $J$ on a compact $4$-manifold $M$, is the dimension $h_J^-$ of the space of closed $J$-anti-invariant $2$-forms zero? If $h_J^-\geq3$, must $J$ be integrable? | Conjecture: for a generic almost-complex structure J on a compact 4-manifold M, the dimension h^-_J of the space of closed J-anti-invariant 2-forms is zero; and if h^-_J \geq 3, then J is integrable. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Almost Complex Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/33, pp. 1657--1691 |
30,004,550 | OWR-2654830-001 | Minimal Discontinuity Under Continuous Weihrauch Reducibility | Is there a simplest discontinuous multi-valued problem $f:\subseteq\mathbb{N}^{\mathbb{N}}\Rightarrow\mathbb{N}^{\mathbb{N}}$ under continuous Weihrauch reducibility? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757](https://doi.org/10.4171/owr/2020/34)
## Literature review (... | 3 | partially_solved | null | 2,020 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-2654830-001",
"literature-status:partially-solved",
"owr-year:2020"
] | Brattka proves that DIS is least for effectively discontinuous problems, and under ZF+DC+AD it is least among all discontinuous problems; in ZFC non-effectively-discontinuous counterexamples exist, so the unrestricted question is not settled unconditionally. | [
{
"url": "https://doi.org/10.1017/jsl.2021.106",
"label": "Brattka, The Discontinuity Problem"
},
{
"url": "https://doi.org/10.4171/owr/2020/34",
"label": "Oberwolfach Report 34/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/34 | null | null | null | Is there a simplest discontinuous multi-valued problem $f:\subseteq\mathbb{N}^{\mathbb{N}}\Rightarrow\mathbb{N}^{\mathbb{N}}$ under continuous Weihrauch reducibility? | Is there a simplest discontinuous multi-valued problem f:\subseteq\mathbb{N}^{\mathbb{N}}\Rightarrow\mathbb{N}^{\mathbb{N}} under continuous Weihrauch reducibility? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757 |
30,004,551 | OWR-2654830-004 | Capture Strategies in the Circular Lion-and-Man Game | In the discrete equal-speed lion-and-man pursuit-evasion game on a closed circular arena, what tactics should the lion use to guarantee capture, or equivalently, under what geometric conditions does the lion win? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757](https://doi.org/10.4171/owr/2020/34)
## Literature review (... | 3 | partially_solved | null | 2,020 | 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-2654830-004",
"literature-status:partially-solved",
"owr-year:2020"
] | For the discrete epsilon-capture version, the lion wins in uniformly convex bounded domains with an extracted uniform rate; the unrestricted classical equal-speed closed-arena formulation is a known negative result of Besicovitch, so the queue problem is only partially resolved. | [
{
"url": "https://doi.org/10.2140/pjm.2021.310.181",
"label": "Kohlenbach--Lopez-Acedo--Nicolae, 2021"
},
{
"url": "https://doi.org/10.4171/owr/2020/34",
"label": "Oberwolfach Report 34/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/34 | null | null | null | In the discrete equal-speed lion-and-man pursuit-evasion game on a closed circular arena, what tactics should the lion use to guarantee capture, or equivalently, under what geometric conditions does the lion win? | In the discrete equal-speed lion-and-man pursuit-evasion game on a closed circular arena, what tactics should the lion use to guarantee capture, or equivalently, under what geometric conditions does the lion win? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757 |
30,004,552 | OWR-2654830-005 | Incompleteness and Self-Consistency Below Robinson Arithmetic | Let $R$ be Robinson’s arithmetic, and let $\mathcal D$ be the set of recursively axiomatizable consistent theories $T\lhd R$ for which $G1$ holds, meaning that every recursively axiomatizable consistent theory interpreting $T$ is incomplete. Such theories are known to exist. Is the interpretability ordering $(\mathcal ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757](https://doi.org/10.4171/owr/2020/34)
## Literature review (... | 3 | partially_solved | null | 2,020 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-2654830-005",
"literature-status:partially-solved",
"owr-year:2020"
] | Cheng constructs recursively enumerable theories U with U\triangleleft R for which G1 holds, answering the first question; the companion question whether G2 holds for R remains open in the cited literature. | [
{
"url": "https://doi.org/10.1017/bsl.2020.9",
"label": "Cheng, Finding the Limit of Incompleteness I"
},
{
"url": "https://doi.org/10.4171/owr/2020/34",
"label": "Oberwolfach Report 34/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/34 | null | null | null | Let $R$ be Robinson’s arithmetic, and let $\mathcal D$ be the set of recursively axiomatizable consistent theories $T\lhd R$ for which $G1$ holds, meaning that every recursively axiomatizable consistent theory interpreting $T$ is incomplete. Such theories are known to exist. Is the interpretability ordering $(\mathcal ... | For Robinson's theory R, can one find a recursively axiomatizable consistent theory T such that G1 holds for T and T is properly interpretable below R, and does G2 hold for R? Here G1 means that every recursively axiomatizable consistent theory interpreting T is incomplete, while G2 means that T proves its own consiste... | corrected_verified | The official report was checked. It defines G2 as nonprovability of a theory’s own consistency, not self-consistency provability; it also records the below-R existence theorem and leaves the interpretability well-foundedness and G2 questions open. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757 |
30,004,553 | OWR-2654830-007 | Proof-Theoretic Strength of Minimalist Foundations | What is the exact proof-theoretic strength of the Minimalist Foundation MF and of its classical extension MF+EM by the law of excluded middle? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757](https://doi.org/10.4171/owr/2020/34)
## Literature review (... | 3 | open | null | 2,020 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-2654830-007",
"literature-status:open",
"owr-year:2020"
] | The exact proof-theoretic strength of MF and MF+EM remains open; recent work establishes equiconsistency and useful upper bounds but does not identify the exact ordinal or proof-theoretic calibration. | [
{
"url": "https://doi.org/10.1016/j.apal.2024.103524",
"label": "Maietti--Sabelli, 2024"
},
{
"url": "https://doi.org/10.4171/owr/2020/34",
"label": "Oberwolfach Report 34/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/34 | null | null | null | What is the exact proof-theoretic strength of the Minimalist Foundation MF and of its classical extension MF+EM by the law of excluded middle? | What is the exact proof-theoretic strength of the Minimalist Foundation MF and of its classical extension MF+EM by the law of excluded middle? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757 |
30,004,554 | OWR-2654830-008 | Proof Mining for Quantitative Tauberian Remainders | Can proof-theoretic methods such as the Dialectica interpretation produce new remainder theorems in Tauberian theory, and are there abstract quantitative metatheorems that unify and generalize related Tauberian theorems? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757](https://doi.org/10.4171/owr/2020/34)
## Literature review (... | 3 | partially_solved | null | 2,020 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-2654830-008",
"literature-status:partially-solved",
"owr-year:2020"
] | Proof mining has produced concrete Tauberian remainder theorems and rates for specific results, but the requested general remainder theory and unifying quantitative metatheorems remain open. | [
{
"url": "https://doi.org/10.1016/j.apal.2022.103231",
"label": "Powell, 2023"
},
{
"url": "https://doi.org/10.4171/owr/2020/34",
"label": "Oberwolfach Report 34/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/34 | null | null | null | Can proof-theoretic methods such as the Dialectica interpretation produce new remainder theorems in Tauberian theory, and are there abstract quantitative metatheorems that unify and generalize related Tauberian theorems? | Can proof-theoretic methods such as the Dialectica interpretation produce new remainder theorems in Tauberian theory, and are there abstract quantitative metatheorems that unify and generalize related Tauberian theorems? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757 |
30,004,555 | OWR-2654830-010 | Optimality and Practical Efficiency of Proof Search | How should proof-search algorithms be compared, and is there an optimal way to search for propositional proofs; why is searching in stronger proof systems apparently unhelpful; and how can practical SAT and automated-theorem-proving algorithms perform well on very long formulas despite exponential lower bounds for asso... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757](https://doi.org/10.4171/owr/2020/34)
## Literature review (... | 3 | open | null | 2,020 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-2654830-010",
"literature-status:open",
"owr-year:2020"
] | The comparison of proof-search algorithms, optimal search across proof systems, and the gap between practical SAT performance and proof-length lower bounds remain open research problems; known results cover restricted notions and fixed systems. | [
{
"url": "https://eccc.weizmann.ac.il/report/2021/053/",
"label": "Krajicek, Proof Search Problem"
},
{
"url": "https://doi.org/10.4171/owr/2020/34",
"label": "Oberwolfach Report 34/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/34 | null | null | null | How should proof-search algorithms be compared, and is there an optimal way to search for propositional proofs; why is searching in stronger proof systems apparently unhelpful; and how can practical SAT and automated-theorem-proving algorithms perform well on very long formulas despite exponential lower bounds for asso... | How should proof-search algorithms be compared, and is there an optimal way to search for propositional proofs; why is searching in stronger proof systems apparently unhelpful; and how can practical SAT and automated-theorem-proving algorithms perform well on very long formulas despite exponential lower bounds for asso... | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757 |
30,004,556 | OWR-2654830-011 | Maximal Proof-Search Algorithms on Natural Tautology Sets | For a natural family of tautology test sets, does there exist a proof-search algorithm $(A,P)$ that is maximal among all proof-search algorithms under the quasi-order comparing running times up to polynomial factors? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757](https://doi.org/10.4171/owr/2020/34)
## Literature review (... | 3 | open | null | 2,020 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-2654830-011",
"literature-status:open",
"owr-year:2020"
] | No unconditional construction is known of a natural test set supporting an{\succeq}-maximal proof-search algorithm; the problem remains explicitly open in the current proof-complexity literature. | [
{
"url": "https://eccc.weizmann.ac.il/report/2021/053/",
"label": "Krajicek, Proof Search Problem"
},
{
"url": "https://doi.org/10.4171/owr/2020/34",
"label": "Oberwolfach Report 34/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/34 | null | null | null | For a natural family of tautology test sets, does there exist a proof-search algorithm $(A,P)$ that is maximal among all proof-search algorithms under the quasi-order comparing running times up to polynomial factors? | For some natural test sets of tautologies, does there exist a proof-search algorithm (A,P) that is maximal among all proof-search algorithms under the test-set quasi-order comparing running times up to polynomial factors? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757 |
30,004,557 | OWR-2654830-012 | Constructive Definitional Extensions and Morita Equivalence | Is the constructive equivalence generated by adding abbreviations, logical constructors, unique-existence terms, and standard sorts such as subsorts, quotient sorts, finite products, and finite disjoint unions the same as constructive Morita equivalence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757](https://doi.org/10.4171/owr/2020/34)
## Literature review (... | 3 | open | null | 2,020 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-2654830-012",
"literature-status:open",
"owr-year:2020"
] | The reported conservative-extension phenomena are related to Morita equivalence, but no result identified here proves that the constructive notion in the question is exactly constructive Morita equivalence; the identification remains open. | [
{
"url": "https://doi.org/10.4171/owr/2020/34",
"label": "Oberwolfach Report 34/2020"
},
{
"url": "https://arxiv.org/abs/1507.02302",
"label": "Rynasiewicz--Tsementzis, 2015"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/34 | null | null | null | Is the constructive equivalence generated by adding abbreviations, logical constructors, unique-existence terms, and standard sorts such as subsorts, quotient sorts, finite products, and finite disjoint unions the same as constructive Morita equivalence? | Is the constructive equivalence generated by adding abbreviations, logical constructors, unique-existence terms, and standard sorts such as subsorts, quotient sorts, finite products, and finite disjoint unions the same as constructive Morita equivalence? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757 |
30,004,558 | OWR-2654830-013 | Partial Proof Objects in Martin-Löf Type Theory | In Martin–Löf type theory, which mathematical objects or formal mechanisms can serve as partial proofs, analogously to the partial functions used in the predicative construction of Mahlo universes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757](https://doi.org/10.4171/owr/2020/34)
## Literature review (... | 3 | open | null | 2,020 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-2654830-013",
"literature-status:open",
"owr-year:2020"
] | The source explicitly presents partial proofs as a puzzling question and gives no completed definition or theorem; the problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2020/34",
"label": "OWR 2020/34 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/34 | null | null | null | In Martin–Löf type theory, which mathematical objects or formal mechanisms can serve as partial proofs, analogously to the partial functions used in the predicative construction of Mahlo universes? | In Martin-L\ddot{o}f type theory, what mathematical objects or formal mechanisms could serve as partial proofs, analogous to the partial functions used in the predicative construction of Mahlo universes? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/34, pp. 1693--1757 |
30,004,559 | OWR-2654831-001 | Free-Boundary Dimer Convergence to Arc Loop Ensembles | For every monomer fugacity $z>0$, does the collection $\mathcal C$ of boundary-touching curves in the free-boundary dimer model on the upper half-plane converge in the scaling limit to $\operatorname{ALE}_{-\lambda,\lambda}$, with loops conditionally independent and distributed as $\operatorname{CLE}_4$ in the connecte... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/35, pp. 1759--1789](https://doi.org/10.4171/owr/2020/35)... | 3 | open | null | 2,020 | 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-2654831-001",
"literature-status:open",
"owr-year:2020"
] | The free-boundary dimer scaling statement is still a conjectural ALE and CLE4 convergence claim; recent work proves important boundary statistics but not the full asserted convergence. | [
{
"url": "https://arxiv.org/abs/2102.12873",
"label": "Laslier and Ray, free-boundary dimers"
},
{
"url": "https://arxiv.org/abs/2409.18015",
"label": "Conformally invariant boundary arcs in double dimers"
},
{
"url": "https://doi.org/10.4171/owr/2020/35",
"label": "OWR 2020/35 repor... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/35 | null | null | null | For every monomer fugacity $z>0$, does the collection $\mathcal C$ of boundary-touching curves in the free-boundary dimer model on the upper half-plane converge in the scaling limit to $\operatorname{ALE}_{-\lambda,\lambda}$, with loops conditionally independent and distributed as $\operatorname{CLE}_4$ in the connecte... | Conjecture: for every monomer fugacity z>0, in the scaling limit of the free-boundary dimer model on the upper half-plane, the collection C of boundary-touching curves converges to the Arc Loop Ensemble ALE_{-\lambda,\lambda}, and conditional on the ALE the loops are independent CLE_4 in each connected component of its... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/35, pp. 1759--1789 |
30,004,560 | OWR-2654831-003 | Existence and Uniqueness of Perfect T-Embeddings | Does every nondegenerate weighted bipartite graph $G$ with sphere topology and a marked face have an augmented dual $G^*$ admitting a perfect t-embedding, equivalently a p-embedding? Is it unique up to Lorentz isometries of $\mathbb R^{2+1}$ preserving the unit hyperboloid $\mathbb H$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/35, pp. 1759--1789](https://doi.org/10.4171/owr/2020/35)... | 3 | partially_solved | null | 2,020 | 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-2654831-003",
"literature-status:partially-solved",
"owr-year:2020"
] | Existence of p-embeddings is established in important special families and related t-embedding existence results are available, but general existence and the required perfect or canonical p-embedding theory remain unresolved. | [
{
"url": "https://arxiv.org/abs/2109.06272",
"label": "Chelkak, Laslier and Russkikh, s-embeddings"
},
{
"url": "https://arxiv.org/abs/2408.05441",
"label": "Berggren, Nicoletti and Russkikh, p-embeddings"
},
{
"url": "https://arxiv.org/abs/2410.09574",
"label": "Galashin, amplituhed... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/35 | null | null | null | Does every nondegenerate weighted bipartite graph $G$ with sphere topology and a marked face have an augmented dual $G^*$ admitting a perfect t-embedding, equivalently a p-embedding? Is it unique up to Lorentz isometries of $\mathbb R^{2+1}$ preserving the unit hyperboloid $\mathbb H$? | Does every suitably non-degenerate weighted bipartite graph with sphere topology and a marked face have an augmented dual admitting a perfect t-embedding, and is that p-embedding unique up to Lorentz isometries preserving the unit hyperboloid? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/35, pp. 1759--1789 |
30,004,561 | OWR-2654831-004 | Dimer Theory and Lorentz-Minimal Scaling-Limit Surfaces | What is the correspondence between the classical Kenyon–Okounkov theory and Lorentz-minimal surfaces, and how does local graph structure lead to conjectural Lorentz-minimality of scaling-limit surfaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/35, pp. 1759--1789](https://doi.org/10.4171/owr/2020/35)... | 3 | open | null | 2,020 | 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-2654831-004",
"literature-status:open",
"owr-year:2020"
] | Classical Kenyon--Okounkov limit-shape theory and Lorentz-minimal-surface formulations are related in special dimer and embedding settings, but no general correspondence answering the question has been established. | [
{
"url": "https://arxiv.org/abs/math-ph/0507007",
"label": "Kenyon and Okounkov, limit shapes and complex Burgers"
},
{
"url": "https://arxiv.org/abs/2109.06272",
"label": "Chelkak, Laslier and Russkikh, s-embeddings"
},
{
"url": "https://doi.org/10.4171/owr/2020/35",
"label": "OWR 2... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/35 | null | null | null | What is the correspondence between the classical Kenyon–Okounkov theory and Lorentz-minimal surfaces, and how does local graph structure lead to conjectural Lorentz-minimality of scaling-limit surfaces? | What is the correspondence between the classical Kenyon--Okounkov theory and Lorentz-minimal surfaces, and how does local graph structure lead to conjectural Lorentz-minimality of scaling-limit surfaces? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/35, pp. 1759--1789 |
30,004,562 | OWR-2654831-005 | Bilinear Forms behind Resistor and Ising Integrable Equations | Why do symmetric bilinear forms lead to the resistor subvariety and the BKP equation, whereas antisymmetric bilinear forms lead to the Ising subvariety and the CKP equation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/35, pp. 1759--1789](https://doi.org/10.4171/owr/2020/35)... | 3 | open | null | 2,020 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-2654831-005",
"literature-status:open",
"owr-year:2020"
] | The symmetric-bilinear-to-resistor/BKP and antisymmetric-to-Ising/CKP pattern is documented in examples, but a general conceptual explanation or theorem identifying the mechanism is still an open question. | [
{
"url": "https://arxiv.org/abs/2305.02212",
"label": "Affolter, discrete differential geometry and cluster algebras"
},
{
"url": "https://doi.org/10.4171/owr/2020/35",
"label": "OWR 2020/35 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/35 | null | null | null | Why do symmetric bilinear forms lead to the resistor subvariety and the BKP equation, whereas antisymmetric bilinear forms lead to the Ising subvariety and the CKP equation? | Why do symmetric bilinear forms lead to the resistor subvariety and the BKP equation, whereas anti-symmetric bilinear forms lead to the Ising subvariety and the CKP equation? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/35, pp. 1759--1789 |
30,004,563 | OWR-2654831-006 | Maximum Central Points in Cube-Move $\alpha$-Immersions | For $\alpha$-immersions with $\alpha>1$, is three the maximal possible number of potential central points produced by the cube-move construction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/35, pp. 1759--1789](https://doi.org/10.4171/owr/2020/35)... | 3 | open | null | 2,020 | 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-2654831-006",
"literature-status:open",
"owr-year:2020"
] | The cube-move analysis proves existence for alpha>1 and exhibits configurations with up to three potential central points, but the claim that three is maximal remains a conjecture without a general proof. | [
{
"url": "https://arxiv.org/abs/2003.08941",
"label": "Cube moves for s-embeddings and alpha-realizations"
},
{
"url": "https://doi.org/10.4171/owr/2020/35",
"label": "OWR 2020/35 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/35 | null | null | null | For $\alpha$-immersions with $\alpha>1$, is three the maximal possible number of potential central points produced by the cube-move construction? | For \alpha-immersions with \alpha>1, is three the maximal possible number of potential central points produced by the cube-move construction? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Dimers, Ising and Spanning Trees beyond the Critical Isoradial Case (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/35, pp. 1759--1789 |
30,004,564 | OWR-2654832-001 | Retracted versus Intrinsic Thin Plate Splines on Manifolds | How does a retracted thin plate spline on a Riemannian manifold differ from the intrinsic manifold thin plate spline, particularly in the interpolation case $\lambda=\infty$ and as a function of the manifold's closeness to Euclidean space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Computational Optimization on Manifolds (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/36, pp. 1791--1821](https://doi.org/10.4171/owr/2020/36)
## Literature review (chec... | 3 | partially_solved | null | 2,020 | 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-2654832-001",
"literature-status:partially-solved",
"owr-year:2020"
] | Manifold thin-plate splines and retraction-based splines are established, and their interpolation difference is quantified under epsilon-flatness, but a general comparison of smoothness properties remains unsettled. | [
{
"url": "https://doi.org/10.1111/j.1467-8659.2008.01141.x",
"label": "Steinke et al., manifold-valued thin-plate splines"
},
{
"url": "https://doi.org/10.4171/owr/2020/36",
"label": "OWR 2020/36 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/36 | null | null | null | How does a retracted thin plate spline on a Riemannian manifold differ from the intrinsic manifold thin plate spline, particularly in the interpolation case $\lambda=\infty$ and as a function of the manifold's closeness to Euclidean space? | How does a retracted thin plate spline on a Riemannian manifold differ from the intrinsic manifold thin plate spline, particularly in the interpolation case \lambda=\infty and as a function of the manifold's closeness to Euclidean space? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Computational Optimization on Manifolds (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/36, pp. 1791--1821 |
30,004,565 | OWR-2654833-001 | Minimizers of Nonlocal Knot Self-Avoidance Energies | For nonlocal self-avoidance energies on embeddings, do minimizers or stationary points exist within prescribed isotopy classes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/37, pp. 1823--1856](https://doi.org/10.4171/owr/2020/37)
## Literature rev... | 3 | partially_solved | null | 2,020 | 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-2654833-001",
"literature-status:partially-solved",
"owr-year:2020"
] | Existence of minimizers and stationary knots is known for broad classes of O'Hara-type energies and many isotopy classes, but the source's qualification is still valid for some energies or isotopy constraints. | [
{
"url": "https://doi.org/10.1007/s00208-017-1540-4",
"label": "The gradient flow of O'Hara's knot energies"
},
{
"url": "https://arxiv.org/abs/2505.02719",
"label": "Palais--Smale condition in knot theory"
},
{
"url": "https://doi.org/10.4171/owr/2020/37",
"label": "OWR 2020/37 repo... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/37 | null | null | null | For nonlocal self-avoidance energies on embeddings, do minimizers or stationary points exist within prescribed isotopy classes? | For nonlocal self-avoidance energies on embeddings, do minimizers or stationary points exist within prescribed isotopy classes? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/37, pp. 1823--1856 |
30,004,566 | OWR-2654833-002 | Sharp Relations Between Knot Ropelength and Crossing Number | How is the ropelength of a knot $K$ related to its crossing number $\operatorname{Cr}(K)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/37, pp. 1823--1856](https://doi.org/10.4171/owr/2020/37)
## Literature rev... | 3 | partially_solved | null | 2,020 | 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-2654833-002",
"literature-status:partially-solved",
"owr-year:2020"
] | Ropelength and crossing number satisfy substantial upper and lower bounds, including near-linear upper bounds with logarithmic loss, but the sharp asymptotic relation and optimal exponents remain unknown. | [
{
"url": "https://arxiv.org/abs/0912.3282",
"label": "Diao et al., ropelength and crossing number"
},
{
"url": "https://doi.org/10.1016/S0166-8641(03)00168-8",
"label": "Cantarella, Faber and Mullikin, upper bounds for ropelength"
},
{
"url": "https://doi.org/10.1016/S0166-8641(97)00211-... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/37 | null | null | null | How is the ropelength of a knot $K$ related to its crossing number $\operatorname{Cr}(K)$? | How is the ropelength of a knot K related to its crossing number Cr(K)? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/37, pp. 1823--1856 |
30,004,567 | OWR-2654833-003 | Folded Ribbonlength Bounds and Knot Complexity | For folded ribbon knots and links, can one prove lower bounds for folded ribbonlength; can one find embeddings with $\operatorname{Rib}(K_w)\leq O(\operatorname{Cr}(K)^p)$ for some $1\leq p<3/2$ or families with superlinear folded ribbonlength in crossing number; and how does folded ribbonlength depend on ribbon equiva... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/37, pp. 1823--1856](https://doi.org/10.4171/owr/2020/37)
## Literature rev... | 3 | partially_solved | null | 2,020 | 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-2654833-003",
"literature-status:partially-solved",
"owr-year:2020"
] | General folded-ribbon upper bounds and linear bounds for important knot families are known, while recent work also gives bounded examples; the proposed universal polynomial or superlinear characterization is not settled. | [
{
"url": "https://arxiv.org/abs/2010.03611",
"label": "Denne, folded ribbonlength"
},
{
"url": "https://arxiv.org/abs/2208.03669",
"label": "Kim et al., ribbonlength of two-bridge knots"
},
{
"url": "https://arxiv.org/abs/2509.18370",
"label": "Denne and Patterson, ribbonlength of to... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/37 | null | null | null | For folded ribbon knots and links, can one prove lower bounds for folded ribbonlength; can one find embeddings with $\operatorname{Rib}(K_w)\leq O(\operatorname{Cr}(K)^p)$ for some $1\leq p<3/2$ or families with superlinear folded ribbonlength in crossing number; and how does folded ribbonlength depend on ribbon equiva... | For folded ribbon knots and links, can one prove lower bounds for folded ribbonlength; can one find embeddings with Rib(K_w)\leq O(Cr(K)^p) for some 1\leq p<3/2 or families with superlinear folded ribbonlength in crossing number; and how does folded ribbonlength depend on ribbon equivalence and framing? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/37, pp. 1823--1856 |
30,004,568 | OWR-2654833-004 | Convergence of Self-Contact Penalty Forces | For elastic models without higher-order regularizing terms, can analogous convergence results be proved for the nonlocal self-contact penalty, and do the functional derivatives of the penalty energy converge to the forces caused by self-contact in the constrained limit problem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/37, pp. 1823--1856](https://doi.org/10.4171/owr/2020/37)
## Literature rev... | 3 | partially_solved | null | 2,020 | 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-2654833-004",
"literature-status:partially-solved",
"owr-year:2020"
] | Gamma-convergence and penalization results exist for restricted linear or regular settings, but convergence of forces and a general low-order model without higher-order terms remain open. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0307904X23002731",
"label": "Surface penalization of self-interpenetration"
},
{
"url": "https://doi.org/10.4171/owr/2020/37",
"label": "OWR 2020/37 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/37 | null | null | null | For elastic models without higher-order regularizing terms, can analogous convergence results be proved for the nonlocal self-contact penalty, and do the functional derivatives of the penalty energy converge to the forces caused by self-contact in the constrained limit problem? | For elastic models without higher-order regularizing terms, can analogous convergence results be proved for the nonlocal self-contact penalty, and do the functional derivatives of the penalty energy converge to the forces caused by self-contact in the constrained limit problem? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/37, pp. 1823--1856 |
30,004,569 | OWR-2654834-001 | Deterministic-to-Stochastic Transition in the Vlasov Approximation | Can one rigorously characterize the transition, in the quasilinear approximation of the Vlasov equation, from the short-time deterministic regime to the long-time stochastic regime in which randomness drives the effective diffusion? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical and Quantum Mechanical Models of Many-Particle Systems (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/38, pp. 1857--1902](https://doi.org/10.4171/owr/2020/38)
## Literature re... | 3 | open | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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{
"url": "https://doi.org/10.4171/owr/2020/38",
"label": "OWR 2020/38 report"
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{
"url": "https://www.cirm-math.fr/RepOrga/2355/Abstracts/Claude_BARDOS.pdf",
"label": "Bardos, deterministic and stochastic Vlasov dynamics"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/38 | null | null | null | Can one rigorously characterize the transition, in the quasilinear approximation of the Vlasov equation, from the short-time deterministic regime to the long-time stochastic regime in which randomness drives the effective diffusion? | For the transition from a short-time deterministic regime to a long-time stochastic regime in the many-particle kinetic model described in the report, can this transition be characterized rigorously? | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Classical and Quantum Mechanical Models of Many-Particle Systems (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/38, pp. 1857--1902 |
30,004,570 | OWR-2654835-001 | Additional Measurements for Semilinear Fractional Inverse Sources | For an inverse source problem in a semilinear fractional PDE, what additional measurement is sufficient to recover the unknown source term? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Inverse Problems for Partial Differential Equations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/39, pp. 1903--1954](https://doi.org/10.4171/owr/2020/39)
## Literature r... | 3 | partially_solved | null | 2,020 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/39 | null | null | null | For an inverse source problem in a semilinear fractional PDE, what additional measurement is sufficient to recover the unknown source term? | For an inverse source problem in a semilinear fractional PDE, what additional measurement is sufficient to recover the unknown source term? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Computational Inverse Problems for Partial Differential Equations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/39, pp. 1903--1954 |
30,004,571 | OWR-2654835-002 | Single-Point Recovery of Time-Dependent Heat Sources | For $u_t-u_{xx}=h(t)f(x)$ on $\Omega=(0,1)$ with homogeneous Dirichlet boundary conditions and zero initial data, can a single-point measurement $m(t)=u(t,x_0)$ determine $h(t)$, and which locations $x_0$ give uniqueness? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Inverse Problems for Partial Differential Equations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/39, pp. 1903--1954](https://doi.org/10.4171/owr/2020/39)
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"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (answered qualitatively in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered qualitatively in the source)**. M. Slodička (joint with K. Šišková; OWR 39/2020, p. 1937) asks whether u(t,x₀) determines h in u_t − u_xx = h(t)f(x) on (0,1), and for which x₀; his qualitative answer: avoid all eigenfunction zeros, a dense set Q, where un... | [
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"url": "https://doi.org/10.1016/j.aml.2012.08.013",
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{
"url": "https://doi.org/10.... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/39 | null | null | null | For $u_t-u_{xx}=h(t)f(x)$ on $\Omega=(0,1)$ with homogeneous Dirichlet boundary conditions and zero initial data, can a single-point measurement $m(t)=u(t,x_0)$ determine $h(t)$, and which locations $x_0$ give uniqueness? | For u_t-u_{xx}=h(t)f(x) on \Omega=(0,1) with homogeneous Dirichlet boundary and zero initial data, can a single-point measurement m(t)=u(t,x_0) determine h(t), and which locations x_0 give uniqueness? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Computational Inverse Problems for Partial Differential Equations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/39, pp. 1903--1954 |
30,004,572 | OWR-2654836-002 | Global Well-Posedness of Three-Dimensional Navier–Stokes | Can one establish global well-posedness for the three-dimensional Navier–Stokes equations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Rough Path Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/40, pp. 1955--2019](https://doi.org/10.4171/owr/2020/40)
## Literature review (checked 2026-08-22)
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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30,004,573 | OWR-2654836-003 | Support of Renormalized Singular Stochastic Equations | For a singular SPDE with renormalisation, can the topological support of the solution law $\mathcal{L}_T(u)$ be characterized in terms of solutions to the associated renormalised controlled equations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Rough Path Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/40, pp. 1955--2019](https://doi.org/10.4171/owr/2020/40)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,020 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "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 | [
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{
"url": "https://arxiv.org/abs/1909.05526",
"label": "Hairer and Schonbauer, support of singular SPDEs"
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{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/40 | null | null | null | For a singular SPDE with renormalisation, can the topological support of the solution law $\mathcal{L}_T(u)$ be characterized in terms of solutions to the associated renormalised controlled equations? | For a singular SPDE with renormalisation, can the topological support of the solution law L_T(u) be characterized in terms of solutions to the associated renormalised controlled equations? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | New Directions in Rough Path Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/40, pp. 1955--2019 |
30,004,574 | OWR-2654836-007 | Density Estimates and Short-Time Asymptotics for Rough Equations | How do sharp uniform density estimates for SDEs driven by fractional Brownian motion relate to existing short-time asymptotic expansions for elliptic and hypoelliptic SDEs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Rough Path Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/40, pp. 1955--2019](https://doi.org/10.4171/owr/2020/40)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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{
"url": "https://arxiv.org/abs/2007.16178",
"label": "Geng, Ouyang and Tindel, density estimates"
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"url": "https://arxiv.org/abs/2008.01229",
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"url": "https://arxiv.org/abs/1902.05219",
"label": "Inahama and Naganuma... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/40 | null | null | null | How do sharp uniform density estimates for SDEs driven by fractional Brownian motion relate to existing short-time asymptotic expansions for elliptic and hypoelliptic SDEs? | How do sharp uniform density estimates for SDEs driven by fractional Brownian motion relate to existing short-time asymptotic expansions for elliptic and hypoelliptic SDEs? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | New Directions in Rough Path Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/40, pp. 1955--2019 |
30,004,575 | OWR-2654836-008 | Sharp Fractional Brownian Density Estimates with Drift | Can the sharp density-estimate results for fractional-Brownian rough differential equations be extended to equations with drift, despite the loss of fractional-Brownian scaling and the required sub-Riemannian accessibility conditions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Rough Path Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/40, pp. 1955--2019](https://doi.org/10.4171/owr/2020/40)
## Literature review (checked 2026-08-22)
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"owr",
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{
"url": "https://doi.org/10.1016/j.bulsci.2021.103011",
"label": "Density for rough equations with irregular drift"
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{
"url": "https://arxiv.org/abs/2008.01229",
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{
"url": "https://doi.org/10.4171/owr/2020/40",
"label": ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/40 | null | null | null | Can the sharp density-estimate results for fractional-Brownian rough differential equations be extended to equations with drift, despite the loss of fractional-Brownian scaling and the required sub-Riemannian accessibility conditions? | Can the sharp density-estimate results for fractional-Brownian rough differential equations be extended to equations with drift, despite the loss of fractional-Brownian scaling and the required sub-Riemannian accessibility conditions? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | New Directions in Rough Path Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/40, pp. 1955--2019 |
30,004,576 | OWR-2654836-009 | Sharp Density Estimates for General Gaussian Rough Paths | Can the sharp density-estimate results be extended from fractional Brownian motion to more general Gaussian processes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Rough Path Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/40, pp. 1955--2019](https://doi.org/10.4171/owr/2020/40)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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{
"url": "https://annals.math.princeton.edu/2010/171-3/p15",
"label": "Baudoin, Hairer and others, Gaussian rough differential equations"
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{
"url": "https://doi.org/10.1016/j.spa.2014.09.012",
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"url": "https://do... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/40 | null | null | null | Can the sharp density-estimate results be extended from fractional Brownian motion to more general Gaussian processes? | Can the sharp density-estimate results be extended from fractional Brownian motion to more general Gaussian processes? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | New Directions in Rough Path Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/40, pp. 1955--2019 |
30,004,577 | OWR-2654837-001 | Cultural and Social Variation in Numeracy | Is numeracy a single, uniform phenomenon, or does it vary across cultures and social contexts? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of Mathematics: A Global Cultural Approach (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/41, pp. 2021--2092](https://doi.org/10.4171/owr/2020/41)
## Literature review (checked ... | 3 | open | null | 2,020 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"slug": "oberwolfach-reports-open... | null | null | History of Everyday Numeracy workshop report (19th-century/medieval historiography, not a mathematical research problem) | null | null | null | [
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/41 | null | null | null | Is numeracy a single, uniform phenomenon, or does it vary across cultures and social contexts? | Is numeracy a single, uniform phenomenon, or does it vary across cultures and social contexts? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | History of Mathematics: A Global Cultural Approach (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/41, pp. 2021--2092 |
30,004,578 | OWR-2654837-002 | Objects and Scope of Ancient Mathematics | In ancient Greek and Roman thought, what does mathematics study; are mathematical objects distinct from empirical phenomena; and how do the objects of arithmetic, geometry, and applied fields such as harmonics, astronomy, statics, dynamics, mechanics, and cartography relate? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of Mathematics: A Global Cultural Approach (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/41, pp. 2021--2092](https://doi.org/10.4171/owr/2020/41)
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30,004,579 | OWR-2654837-003 | Reach of Axiomatic Deduction and Mathematical Explanation | What modes of cognition does mathematics secure; how far can axiomatic-deductive demonstration be applied; and what understanding of nature, the cosmos, and humanity can mathematics yield, including how far its claims to be the best or only sound method must be qualified? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of Mathematics: A Global Cultural Approach (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/41, pp. 2021--2092](https://doi.org/10.4171/owr/2020/41)
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30,004,580 | OWR-2654837-004 | Demographics of Medieval Mathematical Practitioners | In medieval mathematical professions across different contexts, what were practitioners' demographics, and how did those demographics affect their work, collaboration, and communication? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of Mathematics: A Global Cultural Approach (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/41, pp. 2021--2092](https://doi.org/10.4171/owr/2020/41)
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30,004,581 | OWR-2654837-005 | Professional Status of Medieval Mathematical Practitioners | In the medieval period, what was mathematical practitioners' professional status relative to other disciplines, and how did public attitudes affect their profession? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of Mathematics: A Global Cultural Approach (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/41, pp. 2021--2092](https://doi.org/10.4171/owr/2020/41)
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30,004,582 | OWR-2654837-006 | Acquisition of Everyday Numeracy in the Nineteenth Century | In the long nineteenth century, how did people acquire everyday numeracy? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of Mathematics: A Global Cultural Approach (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/41, pp. 2021--2092](https://doi.org/10.4171/owr/2020/41)
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"slug": "oberwolfach-reports-open... | null | null | History of Everyday Numeracy workshop report (19th-century/medieval historiography, not a mathematical research problem) | null | null | null | [
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30,004,583 | OWR-2654837-007 | Arithmetic Education and Numerical Resources in the Nineteenth Century | In the long nineteenth century, to what extent was arithmetic education available and to whom; what forms did it take and what skills did textbooks impart; what systems of weights, measures, and currency existed; and what resources supported everyday numerical computation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of Mathematics: A Global Cultural Approach (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/41, pp. 2021--2092](https://doi.org/10.4171/owr/2020/41)
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30,004,584 | OWR-2654837-008 | Worldviews as Historical Categories in Mathematics | In nineteenth-century mathematics and culture, what did “worldviews” mean, and should the term be treated as an actors’ category or an observers’ category? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of Mathematics: A Global Cultural Approach (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/41, pp. 2021--2092](https://doi.org/10.4171/owr/2020/41)
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"slug": "oberwolfach-reports-open... | null | null | History of Everyday Numeracy workshop report (19th-century/medieval historiography, not a mathematical research problem) | null | null | null | [
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30,004,585 | OWR-4990369-004 | Classification of Equationally Complete Theories | Can equationally complete theories, equivalently minimal varieties, be classified? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homogeneous Structures: Model Theory meets Universal Algebra (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/1, pp. 5--32](https://doi.org/10.4171/owr/2021/1)
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30,004,586 | OWR-4990370-001 | Spectral Shapes of Group-Based Graph Operators | What shapes can occur as spectra of weighted Laplace or Markov operators on graphs arising from groups? Can a Cayley graph have Cantor spectrum? Can a Cayley graph of a torsion-free group have a spectral gap? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry, Dynamics and Spectrum of Operators on Discrete Spaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/2, pp. 33--85](https://doi.org/10.4171/owr/2021/2)
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30,004,587 | OWR-4990370-005 | Tensor Stability of Quantum Markov Gradient Estimates | Is the quantum Markov gradient estimate $\operatorname{GE}(K,\infty)$ stable under tensor products of quantum Markov semigroups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry, Dynamics and Spectrum of Operators on Discrete Spaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/2, pp. 33--85](https://doi.org/10.4171/owr/2021/2)
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}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/2 | null | null | null | Is the quantum Markov gradient estimate $\operatorname{GE}(K,\infty)$ stable under tensor products of quantum Markov semigroups? | Is the gradient estimate GE(K,\infty) stable under tensor products of quantum Markov semigroups? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Geometry, Dynamics and Spectrum of Operators on Discrete Spaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/2, pp. 33--85 |
30,004,588 | OWR-4990373-001 | Noise Sensitivity and Exceptional Times in Spin-System Dynamics | For Ising Glauber dynamics on transitive graphs and heat-bath dynamics in FK random-cluster models, does the weighted-majority characterization of noise sensitivity persist; are the log-Sobolev constants comparable to relaxation times; are critical planar crossing events noise sensitive; and do exceptional times exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224](https://doi.org/10.4171/owr/2021/4)
## Literature review (checked 2026-08-22)
**Status:... | 3 | partially_solved | null | 2,021 | 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-4990373-001",
"literature-status:partially-solved",
"owr-year:2021"
] | Some components are settled, including absence of exceptional times for critical Ising Glauber dynamics on the square lattice, while the bundled FK, noise-sensitivity, log-Sobolev, and crossing questions remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/4",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.4007/annals.2010.171.619",
"label": "Schramm and Steif"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/4 | null | null | null | For Ising Glauber dynamics on transitive graphs and heat-bath dynamics in FK random-cluster models, does the weighted-majority characterization of noise sensitivity persist; are the log-Sobolev constants comparable to relaxation times; are critical planar crossing events noise sensitive; and do exceptional times exist? | For Ising Glauber dynamics on transitive graphs and heat-bath dynamics in FK random-cluster models, does the weighted-majority characterization of noise sensitivity persist; are the log-Sobolev constants comparable to relaxation times; are critical planar crossing events noise sensitive; and do exceptional times exist? | exact | The three conjectural components were retained while their mathematical notation and sentence structure were normalized. | null | null | null | null | null | Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224 |
30,004,589 | OWR-4990373-003 | Reconstruction Threshold for Critical Ising Models on the Torus | What is the exact reconstruction threshold for the critical Ising model on the torus $\mathbb{Z}_n^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224](https://doi.org/10.4171/owr/2021/4)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,021 | 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-4990373-003",
"literature-status:open",
"owr-year:2021"
] | Subsequent work gives nontrivial upper and lower reconstruction regimes for critical two-dimensional Ising boxes, but the exact threshold asked for in the record remains unresolved. | [
{
"url": "https://arxiv.org/abs/2406.09232",
"label": "Galicza and Pete, Ising and factor measures"
},
{
"url": "https://doi.org/10.4171/owr/2021/4",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/4 | null | null | null | What is the exact reconstruction threshold for the critical Ising model on the torus $\mathbb{Z}_n^2$? | What is the exact reconstruction threshold for the critical Ising model on the torus \mathbb Z_n^2? | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224 |
30,004,590 | OWR-4990373-004 | Fixation Times and Consensus in Majority Dynamics | For majority dynamics on a given graph, if fixation occurs, how quickly is the final configuration reached, and is unanimity reached or do both opinions survive? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224](https://doi.org/10.4171/owr/2021/4)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,021 | 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-4990373-004",
"literature-status:open",
"owr-year:2021"
] | General convergence speed and consensus-versus-coexistence behavior for majority and median dynamics are not characterized; primary work proves results only for selected graph classes and explicitly leaves general conjectures open. | [
{
"url": "https://doi.org/10.1016/j.spa.2022.10.015",
"label": "Amir, Baldasso and Beilin"
},
{
"url": "https://doi.org/10.4171/owr/2021/4",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/4 | null | null | null | For majority dynamics on a given graph, if fixation occurs, how quickly is the final configuration reached, and is unanimity reached or do both opinions survive? | For majority dynamics on a given graph, if fixation occurs, how quickly is the final configuration reached, and is unanimity reached or do both opinions survive? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224 |
30,004,591 | OWR-4990373-005 | Monotonicity of Opinion Distributions in Median Dynamics | In median dynamics on a graph $G=(V,E)$, each vertex starts with an independent uniform opinion in $[0,1]$ and updates at rate one to the median of its neighbors' opinions, including its own opinion when the degree is even. If $\mu_t(x)$ is the marginal opinion measure at vertex $x$ at time $t$, is $t\mapsto\mu_t(x)$ m... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224](https://doi.org/10.4171/owr/2021/4)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,021 | 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-4990373-005",
"literature-status:open",
"owr-year:2021"
] | The monotonicity conjecture for the median-dynamics marginal is proved only on special graphs in the primary work; no general proof or counterexample was found. | [
{
"url": "https://doi.org/10.1016/j.spa.2022.10.015",
"label": "Amir, Baldasso and Beilin"
},
{
"url": "https://doi.org/10.4171/owr/2021/4",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/4 | null | null | null | In median dynamics on a graph $G=(V,E)$, each vertex starts with an independent uniform opinion in $[0,1]$ and updates at rate one to the median of its neighbors' opinions, including its own opinion when the degree is even. If $\mu_t(x)$ is the marginal opinion measure at vertex $x$ at time $t$, is $t\mapsto\mu_t(x)$ m... | In median dynamics on a graph G=(V,E), each vertex starts with an independent uniform opinion in [0,1] and updates at rate one to the median of its neighbors' opinions, including its own opinion for even degree. If \mu_t(x) is the marginal opinion measure at x at time t, then for every x\in V and every \alpha>1/2, the ... | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224 |
30,004,592 | OWR-4990373-006 | Percolation Thresholds During Planar Majority Dynamics | For majority dynamics on $\mathbb{Z}^2$ with i.i.d. Bernoulli-$p$ initial opinions, let $p_c(t)$ be the critical probability for an infinite opinion-1 cluster at time $t$. Is $p_c(t)$ strictly decreasing in $t$? Is $t\mapsto p_c(t)$ continuous at $\infty$, and is $p_c(\infty)=1/2$? For the hexagonal lattice, is $p_c(t)... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224](https://doi.org/10.4171/owr/2021/4)
## Literature review (checked 2026-08-22)
**Status:... | 3 | partially_solved | null | 2,021 | 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-4990373-006",
"literature-status:partially-solved",
"owr-year:2021"
] | For square-lattice majority dynamics, finite-time results include continuity and monotone non-increase of the critical probability, but strict decrease, the limit at infinity, and the hexagonal-lattice questions remain open. | [
{
"url": "https://doi.org/10.4171/owr/2021/4",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1902.03349",
"label": "Amir and Baldasso, majority percolation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/4 | null | null | null | For majority dynamics on $\mathbb{Z}^2$ with i.i.d. Bernoulli-$p$ initial opinions, let $p_c(t)$ be the critical probability for an infinite opinion-1 cluster at time $t$. Is $p_c(t)$ strictly decreasing in $t$? Is $t\mapsto p_c(t)$ continuous at $\infty$, and is $p_c(\infty)=1/2$? For the hexagonal lattice, is $p_c(t)... | For majority dynamics on \mathbb Z^2 with i.i.d. Bernoulli-p initial opinions, let p_c(t) be the critical probability for an infinite opinion-1 cluster at time t. Is p_c(t) strictly decreasing in t, is t\mapsto p_c(t) continuous at \infty, and is p_c(\infty)=1/2? For the hexagonal lattice, is p_c(t)=1/2 for all t and a... | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224 |
30,004,593 | OWR-4990373-007 | Critical Fixation Threshold for Zero-Temperature Glauber Dynamics | For zero-temperature Glauber dynamics on $\mathbb{Z}^d$, started from i.i.d. Bernoulli-$p$ opinions with fair-coin tie breaking, is the critical threshold $p_c(d)$ separating eventual fixation from infinite opinion changes equal to $1/2$ for every $d\geq 2$, in particular for $\mathbb{Z}^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224](https://doi.org/10.4171/owr/2021/4)
## Literature review (checked 2026-08-22)
**Status:... | 3 | partially_solved | null | 2,021 | 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-4990373-007",
"literature-status:partially-solved",
"owr-year:2021"
] | The record combines some proved finite-time square-lattice properties with unresolved strictness, limiting, hexagonal-lattice, and zero-temperature Glauber questions; high-dimensional asymptotics are known but the conjecture is not settled. | [
{
"url": "https://doi.org/10.4171/owr/2021/4",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00440-009-0259-x",
"label": "Morris, zero-temperature Glauber dynamics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/4 | null | null | null | For zero-temperature Glauber dynamics on $\mathbb{Z}^d$, started from i.i.d. Bernoulli-$p$ opinions with fair-coin tie breaking, is the critical threshold $p_c(d)$ separating eventual fixation from infinite opinion changes equal to $1/2$ for every $d\geq 2$, in particular for $\mathbb{Z}^2$? | For zero-temperature Glauber dynamics on \mathbb Z^d, started from i.i.d. Bernoulli-p opinions with fair-coin tie breaking, the critical threshold p_c(d) separating eventual fixation from infinite opinion changes is conjectured to satisfy p_c(d)=1/2 for every d\ge 2, in particular for \mathbb Z^2. | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224 |
30,004,594 | OWR-4990373-008 | Survival Versus Percolation Thresholds in the Contact Process | For the classical nearest-neighbor contact process, determine whether the critical infection threshold for survival satisfies $\lambda_c<\lambda_p$, where $\lambda_p$ is the corresponding percolation threshold. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224](https://doi.org/10.4171/owr/2021/4)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,021 | 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-4990373-008",
"literature-status:open",
"owr-year:2021"
] | The strict inequality for the classical nearest-neighbor contact process remains the open case; the cited primary work resolves only the sufficiently spread-out model. | [
{
"url": "https://doi.org/10.4171/owr/2021/4",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1912.09825",
"label": "Rath and Valesin, spread-out contact process"
},
{
"url": "https://doi.org/10.1016/j.anihpb.2005.04.002",
"label": "Liggett and Steif"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/4 | null | null | null | For the classical nearest-neighbor contact process, determine whether the critical infection threshold for survival satisfies $\lambda_c<\lambda_p$, where $\lambda_p$ is the corresponding percolation threshold. | For the classical nearest-neighbor contact process, determine whether the critical infection threshold for survival satisfies \lambda_c<\lambda_p, where \lambda_p is the corresponding percolation threshold. | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224 |
30,004,595 | OWR-4990373-010 | Continuity of the Zero-Level Gaussian Percolation Transition | For a planar stationary Gaussian field $f$, such as the random plane wave, is the phase transition at level $0$ continuous; equivalently, does the excursion set $\{f\leq 0\}$ have only bounded connected components? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224](https://doi.org/10.4171/owr/2021/4)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,021 | 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-4990373-010",
"literature-status:open",
"owr-year:2021"
] | The critical level is established for the random plane wave, but boundedness of the zero-level components remains unresolved; the cited Gaussian-percolation work explicitly leaves no percolation at criticality open. | [
{
"url": "https://arxiv.org/abs/2010.11770",
"label": "Muirhead--Rivera--Vanneuville--Koehler-Schindler, Annals of Probability"
},
{
"url": "https://doi.org/10.4171/owr/2021/4",
"label": "Oberwolfach Report 4/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/4 | null | null | null | For a planar stationary Gaussian field $f$, such as the random plane wave, is the phase transition at level $0$ continuous; equivalently, does the excursion set $\{f\leq 0\}$ have only bounded connected components? | For a planar stationary Gaussian field f such as the random plane wave, is the phase transition at level 0 continuous; equivalently, does the excursion set \{f\le 0\} have only bounded connected components? | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224 |
30,004,596 | OWR-4990373-011 | Poisson Variance Inequalities for Arbitrary Stopping Sets | Let $\eta$ be a Poisson process with intensity measure $\lambda$, let $\eta'$ be an independent copy, and let $Z$ be an arbitrary stopping set. Prove $\mathbb E|f(\eta)-f(\eta')|\leq 2\int\mathbb P(x\in Z)\mathbb E|D_xf(\eta)|\,\lambda(dx)$; equivalently, for $\{0,1\}$-valued $f$, prove $\operatorname{Var}(f(\eta))\leq... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224](https://doi.org/10.4171/owr/2021/4)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,021 | 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-4990373-011",
"literature-status:open",
"owr-year:2021"
] | The Poisson randomized-stopping-set variance inequality is proved only in restricted settings; validity for an arbitrary stopping set is still stated as open in the primary account. | [
{
"url": "https://arxiv.org/abs/2101.07180",
"label": "Primary paper on Poisson OSSS inequalities"
},
{
"url": "https://doi.org/10.4171/owr/2021/4",
"label": "Oberwolfach Report 4/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/4 | null | null | null | Let $\eta$ be a Poisson process with intensity measure $\lambda$, let $\eta'$ be an independent copy, and let $Z$ be an arbitrary stopping set. Prove $\mathbb E|f(\eta)-f(\eta')|\leq 2\int\mathbb P(x\in Z)\mathbb E|D_xf(\eta)|\,\lambda(dx)$; equivalently, for $\{0,1\}$-valued $f$, prove $\operatorname{Var}(f(\eta))\leq... | Does the stated Poisson variance or OSSS-type inequality remain valid for an arbitrary stopping set Z, rather than only for a stopping set that is the union of an increasing family of stopping sets satisfying the stated continuity assumptions? | corrected_verified | The repaired standalone statement was checked against the official Oberwolfach report. | null | null | null | null | null | Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224 |
30,004,597 | OWR-4990373-012 | Chemical Distances in Weighted Random Connection Models | For weight-dependent random connection models in the regime without ultrasmallness, determine the asymptotic chemical distance between two vertices; in particular, decide whether the known sublogarithmic lower bound is sharp or whether the distance is linear or polylogarithmic in different parameter regimes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224](https://doi.org/10.4171/owr/2021/4)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,021 | 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-4990373-012",
"literature-status:open",
"owr-year:2021"
] | The chemical-distance limit theorem is proved in the ultrasmall regime, while the non-ultrasmall case and the conjectured sharp sublogarithmic lower bound remain unresolved. | [
{
"url": "https://doi.org/10.1007/s00220-022-04445-3",
"label": "Grauer--Gracar--Moerters, Communications in Mathematical Physics"
},
{
"url": "https://doi.org/10.4171/owr/2021/4",
"label": "Oberwolfach Report 4/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/4 | null | null | null | For weight-dependent random connection models in the regime without ultrasmallness, determine the asymptotic chemical distance between two vertices; in particular, decide whether the known sublogarithmic lower bound is sharp or whether the distance is linear or polylogarithmic in different parameter regimes. | For the weight-dependent random connection models considered, determine the asymptotic chemical distance between two vertices in the regime without ultrasmallness; in particular, is the currently obtained sublogarithmic lower bound sharp, or is the distance instead linear or polylogarithmic in different parameter regim... | corrected_verified | The repaired standalone statement was checked against the official Oberwolfach report. | null | null | null | null | null | Spatial Networks and Percolation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/4, pp. 149--224 |
30,004,598 | OWR-4990374-001 | Classification of Projective Line Arrangements with Only Triple Points | Classify all line arrangements in the projective plane whose singular points are exclusively triple points. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-001",
"literature-status:open",
"owr-year:2021"
] | Recent work adds infinite families of line arrangements with only triple points, but the requested classification of all such arrangements remains open, including over the complex numbers. | [
{
"url": "https://doi.org/10.5802/crmath.741",
"label": "Roulleau, Comptes Rendus Mathématique (2025)"
},
{
"url": "https://doi.org/10.1007/s12215-024-01047-x",
"label": "Recent line-arrangement classification results"
},
{
"url": "https://doi.org/10.4171/owr/2021/5",
"label": "Oberw... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | Classify all line arrangements in the projective plane whose singular points are exclusively triple points. | Classify all line arrangements in the projective plane whose singular points are exclusively triple points. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,599 | OWR-4990374-002 | Further Rank-Three Simplicial Arrangements | Do rank-three simplicial arrangements include further examples or infinite series beyond those currently known? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-002",
"literature-status:open",
"owr-year:2021"
] | Terao's freeness conjecture remains open even in dimension three, and the classification of rank-three simplicial arrangements is not complete. | [
{
"url": "https://doi.org/10.1112/jlms.12829",
"label": "Pagaria, Journal of the London Mathematical Society"
},
{
"url": "https://doi.org/10.1016/j.aam.2019.02.008",
"label": "Cuntz--Muecksch, Advances in Applied Mathematics"
},
{
"url": "https://doi.org/10.4171/owr/2021/5",
"label"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | Do rank-three simplicial arrangements include further examples or infinite series beyond those currently known? | Determine whether Terao's conjecture holds, namely whether freeness of a hyperplane arrangement over a fixed field depends only on its intersection lattice. Also determine whether rank-three simplicial arrangements include further examples or infinite series beyond those currently known. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,600 | OWR-4990374-003 | Congruence Normality in Simplicial Arrangements | For simplicial arrangements, classify the congruence-normal ones; determine the relation between congruence normality and freeness; find useful arrangement-theoretic properties of the shard digraph; find the smallest number of hyperplanes in a tight arrangement that is not congruence normal; and determine the behavior ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-003",
"literature-status:open",
"owr-year:2021"
] | The known finite lists and rank-three classifications do not settle completeness of congruence-normal simplicial arrangements or the listed restriction and tightness questions. | [
{
"url": "https://doi.org/10.1007/s00026-021-00555-2",
"label": "Cuntz--Elia--Labbe, Beiträge zur Algebra und Geometrie"
},
{
"url": "https://doi.org/10.4171/owr/2021/5",
"label": "Oberwolfach Report 5/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | For simplicial arrangements, classify the congruence-normal ones; determine the relation between congruence normality and freeness; find useful arrangement-theoretic properties of the shard digraph; find the smallest number of hyperplanes in a tight arrangement that is not congruence normal; and determine the behavior ... | For simplicial arrangements, classify the congruence-normal ones; determine the relation between congruence normality and freeness; find useful arrangement-theoretic properties of the shard digraph; find the smallest number of hyperplanes in a tight arrangement that is not congruence normal; and determine the behavior ... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,601 | OWR-4990374-004 | Degree Bounds for Generic Initial Ideals of Arrangements | Let $\mathcal A$ be a central arrangement in $K^\ell$, let $S=K[x_1,\ldots,x_\ell]$, and set
$$
d_0=\min\{d:x_1^d\in\operatorname{rgin}(J(\mathcal A))\}.
$$
If a minimal generator $t$ of $\operatorname{rgin}(J(\mathcal A))$ involves $x_3$, must $\deg(t)\geq d_0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-004",
"literature-status:open",
"owr-year:2021"
] | The generic-initial-ideal statement is still recorded as a conjecture in later work on Lefschetz properties; no proof or counterexample resolving it was found. | [
{
"url": "https://eprints.lib.hokudai.ac.jp/repo/huscap/all/80515/J.%20algebr.%20comb%2051-2_297-315.pdf",
"label": "Bigatti--Palezzato--Torielli, Journal of Algebraic Combinatorics"
},
{
"url": "https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/91057/1/J.%20Algebra%20590_215-233.pdf",
"la... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | Let $\mathcal A$ be a central arrangement in $K^\ell$, let $S=K[x_1,\ldots,x_\ell]$, and set
$$
d_0=\min\{d:x_1^d\in\operatorname{rgin}(J(\mathcal A))\}.
$$
If a minimal generator $t$ of $\operatorname{rgin}(J(\mathcal A))$ involves $x_3$, must $\deg(t)\geq d_0$? | Let A be a central arrangement in K^\ell, let S=K[x_1,\ldots,x_\ell], and set d_0=\min\{d:x_1^d\in\operatorname{rgin}(J(A))\}. If a minimal generator t of \operatorname{rgin}(J(A)) involves the third variable of S, then the conjecture asserts that \deg(t)\ge d_0. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,602 | OWR-4990374-005 | Third Weak Lefschetz Property for Arrangement Jacobian Quotients | For every central arrangement $\mathcal A$ in $K^3$, does the quotient $S/J(\mathcal A)$ have the third weak Lefschetz property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-005",
"literature-status:open",
"owr-year:2021"
] | The conjecture that the Jacobian quotient for a central arrangement in three variables has the 3-WLP remains unresolved; the report itself notes only an intended proof and gives failures in higher-dimensional examples. | [
{
"url": "https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/91057/1/J.%20Algebra%20590_215-233.pdf",
"label": "Palezzato--Torielli, Journal of Algebra"
},
{
"url": "https://doi.org/10.4171/owr/2021/5",
"label": "Oberwolfach Report 5/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | For every central arrangement $\mathcal A$ in $K^3$, does the quotient $S/J(\mathcal A)$ have the third weak Lefschetz property? | For every central arrangement A in K^3, the quotient S/J(A) is conjectured to have the 3-WLP, the third weak Lefschetz property. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,603 | OWR-4990374-007 | Bounded Negativity for Rational Surfaces | For every smooth projective rational surface $X$ over a field, is there a constant $B_X$ such that every reduced irreducible curve $C\subset X$ satisfies $C^2\geq B_X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-007",
"literature-status:open",
"owr-year:2021"
] | The extremal H-constant questions for reduced plane curves remain unresolved; existing work supplies bounds and examples but no definitive minimum or general classification. | [
{
"url": "https://www.scielo.cl/pdf/proy/v41n2/0716-0917-proy-41-02-517.pdf",
"label": "Urzua, Proyecciones (2022)"
},
{
"url": "https://doi.org/10.1093/imrn/rnu236",
"label": "Urzua, International Mathematics Research Notices"
},
{
"url": "https://doi.org/10.4171/owr/2021/5",
"label... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | For every smooth projective rational surface $X$ over a field, is there a constant $B_X$ such that every reduced irreducible curve $C\subset X$ satisfies $C^2\geq B_X$? | Bounded Negativity Conjecture for rational surfaces: for every smooth projective rational surface X over a field, there is a constant B_X such that every reduced curve C\subset X satisfies C^2\ge B_X (equivalently, it suffices to require this for reduced irreducible curves). | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,604 | OWR-4990374-008 | Extremal H-Constants of Line Arrangements | For line arrangements, determine the most negative possible H-constant among arrangements defined over $\mathbb Q$, among complex arrangements, and among complex supersolvable arrangements. In particular, is $H(C)>-3$ for every complex supersolvable line arrangement? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-008",
"literature-status:open",
"owr-year:2021"
] | The most negative H-constants for rational and complex line arrangements, including the supersolvable subcase, are still subject to open classification and extremal-value questions. | [
{
"url": "https://www.scielo.cl/pdf/proy/v41n2/0716-0917-proy-41-02-517.pdf",
"label": "Urzua, Proyecciones (2022)"
},
{
"url": "https://doi.org/10.4171/owr/2021/5",
"label": "Oberwolfach Report 5/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | For line arrangements, determine the most negative possible H-constant among arrangements defined over $\mathbb Q$, among complex arrangements, and among complex supersolvable arrangements. In particular, is $H(C)>-3$ for every complex supersolvable line arrangement? | For line arrangements, determine the most negative possible H-constant for arrangements defined over \mathbb Q, for complex arrangements, and for complex supersolvable arrangements; in particular, is H(C)>-3 for every complex supersolvable line arrangement? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,605 | OWR-4990374-009 | Supersolvable Line Arrangements with One Modular Point | Classify all complex supersolvable line arrangements having exactly one modular singular point. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-009",
"literature-status:open",
"owr-year:2021"
] | Arrangements with two modular points are classified, but the case of exactly one modular point is explicitly left open in the complex supersolvable classification. | [
{
"url": "https://doi.org/10.1007/s10801-020-00987-8",
"label": "Hanumanthu--Harbourne, Journal of Algebraic Combinatorics"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2020.02.007",
"label": "Abe--Dimca, Journal of Algebra"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | Classify all complex supersolvable line arrangements having exactly one modular singular point. | Classify all complex supersolvable line arrangements having exactly one modular singular point. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,606 | OWR-4990374-010 | Complex Line Arrangements without Double Points | Classify complex line arrangements with no double points, that is, with $t_2=0$, where $t_2$ is the number of points of multiplicity two. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-010",
"literature-status:open",
"owr-year:2021"
] | The classification of complex line arrangements with no ordinary double points remains open; the literature identifies only several known types rather than a complete list. | [
{
"url": "https://doi.org/10.1007/s10801-020-00987-8",
"label": "Hanumanthu--Harbourne, Journal of Algebraic Combinatorics"
},
{
"url": "https://doi.org/10.4171/owr/2021/5",
"label": "Oberwolfach Report 5/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | Classify complex line arrangements with no double points, that is, with $t_2=0$, where $t_2$ is the number of points of multiplicity two. | Classify complex line arrangements with no double points, i.e. with t_2=0, where t_2 denotes the number of points of multiplicity two. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,607 | OWR-4990374-011 | Homotopy Generators from Elliptic Artin Noncancellativity | Let $A(R,G)^+$ be the elliptic Artin monoid and let $S_{\mathrm{ell}}\setminus D_{\mathrm{ell}}$ be its elliptic discriminant complement. For pairs of noncancellative quadruples $(a,b,c,d)$ and $(a',b,c,d')$, do all difference classes
$$
a\backslash R(abd,acd)/d-a'\backslash R(a'bd',a'cd')/d'
$$
generate $\pi_2(S_{\mat... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-011",
"literature-status:open",
"owr-year:2021"
] | The elliptic Artin-monoid conjectures, including the proposed generators for the second homotopy group, remain conjectural; the report cites the underlying work as in preparation. | [
{
"url": "https://ems.press/content/serial-article-files/46883",
"label": "Oberwolfach Report 5/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | Let $A(R,G)^+$ be the elliptic Artin monoid and let $S_{\mathrm{ell}}\setminus D_{\mathrm{ell}}$ be its elliptic discriminant complement. For pairs of noncancellative quadruples $(a,b,c,d)$ and $(a',b,c,d')$, do all difference classes
$$
a\backslash R(abd,acd)/d-a'\backslash R(a'bd',a'cd')/d'
$$
generate $\pi_2(S_{\mat... | For the elliptic Artin monoid and its elliptic discriminant complement, the conjecture is that all difference classes a\backslash R(abd,acd)/d-a'\backslash R(a'bd',a'cd')/d' arising from pairs of non-cancellative quadruples generate \pi_2(S_{\mathrm{ell}}\backslash D_{\mathrm{ell}},*). | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,608 | OWR-4990374-014 | Unexpected Curves from Plus-One Generated Arrangements | Can one find combinatorial conditions on plus-one generated line arrangements, analogous to those for nearly free arrangements, that imply that the dual point set admits unexpected curves? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-014",
"literature-status:open",
"owr-year:2021"
] | Recent work derives combinatorial constraints for plus-one generated line arrangements, but it does not establish the proposed general implication to unexpected curves. | [
{
"url": "https://doi.org/10.1007/s40574-025-00517-z",
"label": "Bromboszcz, Rendiconti del Seminario Matematico della Universita di Padova"
},
{
"url": "https://ems.press/content/serial-article-files/46883",
"label": "Oberwolfach Report 5/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | Can one find combinatorial conditions on plus-one generated line arrangements, analogous to those for nearly free arrangements, that imply that the dual point set admits unexpected curves? | Can one find combinatorial conditions on plus-one generated line arrangements, analogous to those for nearly free arrangements, that imply that the dual point set admits unexpected curves? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,609 | OWR-4990374-015 | Supersolvability of Low-Exponent Free Hyperplane Arrangements | Is every central free hyperplane arrangement whose exponents consist of ones and twos, with at most one exponent equal to three, supersolvable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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 | {
"source_url": "https://zenodo.org/records/23307000",
"checked_at": "2026-10-12",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-12] I have released an unrefereed preprint, **Free Hyperplane Arrangements with Exponents 1, 2 and at Most One 3 Are Supersolvable: A Proof of a Conjecture of Tohăneanu** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23307000) | [
"owr",
"oberwolfach-reports",
"OWR-4990374-015",
"literature-status:open",
"owr-year:2021"
] | The low-exponent supersolvability conjecture is proved in several ranks and for some exponent patterns, but the asserted arbitrary-rank statement remains open. | [
{
"url": "https://arxiv.org/abs/1707.07091",
"label": "Tohaneanu, Free arrangements with low exponents"
},
{
"url": "https://ems.press/content/serial-article-files/46883",
"label": "Oberwolfach Report 5/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | Is every central free hyperplane arrangement whose exponents consist of ones and twos, with at most one exponent equal to three, supersolvable? | Every central free hyperplane arrangement whose exponents consist of 1s and 2s with at most one exponent equal to 3 is conjectured to be supersolvable. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,610 | OWR-4990374-016 | Combinatorial Invariance of Hyperplane Arrangement Freeness | Over a fixed field $K$, does freeness of a central essential hyperplane arrangement $\mathcal A$ depend only on its intersection lattice $L(\mathcal A)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | open | null | 2,021 | 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-4990374-016",
"literature-status:open",
"owr-year:2021"
] | Terao's conjecture that freeness is determined by the intersection lattice is still open, including in dimension three. | [
{
"url": "https://doi.org/10.1112/jlms.12829",
"label": "Pagaria, Journal of the London Mathematical Society"
},
{
"url": "https://doi.org/10.4171/owr/2021/5",
"label": "Oberwolfach Report 5/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | Over a fixed field $K$, does freeness of a central essential hyperplane arrangement $\mathcal A$ depend only on its intersection lattice $L(\mathcal A)$? | Terao's conjecture: over a fixed field K, whether a central essential hyperplane arrangement A is free depends only on its intersection lattice L(A). | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,611 | OWR-4990374-017 | Exact Sequences for Logarithmic Derivation Sheaves | Are there short exact sequences relating the sheaves of logarithmic derivations $D$, $D'$, $D''$, and $(D_H,m_H)$ associated with an arrangement and its deletion, restriction, and Ziegler restriction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300](https://doi.org/10.... | 3 | partially_solved | null | 2,021 | 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-4990374-017",
"literature-status:partially-solved",
"owr-year:2021"
] | Short exact sequences for logarithmic derivations and forms are established in important special cases, such as non-Boolean generic arrangements, but the general deletion, restriction, and Ziegler-restriction question remains unresolved. | [
{
"url": "https://www.math.purdue.edu/~walther/research/logforms.pdf",
"label": "Local cohomology of logarithmic forms"
},
{
"url": "https://ems.press/content/serial-article-files/46883",
"label": "Oberwolfach Report 5/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/5 | null | null | null | Are there short exact sequences relating the sheaves of logarithmic derivations $D$, $D'$, $D''$, and $(D_H,m_H)$ associated with an arrangement and its deletion, restriction, and Ziegler restriction? | Are there short exact sequences relating the sheaves of logarithmic derivations D,D',D'' and (D_H,m_H) associated respectively with an arrangement and with its deletion, restriction, or Ziegler restriction? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/5, pp. 225--300 |
30,004,612 | OWR-4990375-001 | Paramodular Forms and Isogeny Classes of Abelian Surfaces | Does the Brumer–Kramer paramodular correspondence give a bijection between isogeny classes of abelian surfaces over $\mathbb Q$ of conductor $N$ and the appropriate paramodular forms of level $N$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359](https://doi.org/10.4171/owr/2021/6)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,021 | 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-4990375-001",
"literature-status:open",
"owr-year:2021"
] | The Brumer--Kramer paramodular correspondence has many verified examples and computational evidence, but both directions of the general conjecture remain open. | [
{
"url": "https://arxiv.org/abs/1004.4699",
"label": "Brumer--Kramer, Paramodular Abelian Varieties of Odd Conductor"
},
{
"url": "https://math.mit.edu/classes/18.786/2024/LectureNotes23.pdf",
"label": "MIT lecture notes, 2024 status summary"
},
{
"url": "https://doi.org/10.4171/owr/2021... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/6 | null | null | null | Does the Brumer–Kramer paramodular correspondence give a bijection between isogeny classes of abelian surfaces over $\mathbb Q$ of conductor $N$ and the appropriate paramodular forms of level $N$? | The Brumer--Kramer paramodular conjecture asserts a bijection between isogeny classes of abelian surfaces over \mathbb Q of conductor N and suitable paramodular forms of level N. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359 |
30,004,613 | OWR-4990375-003 | Weight-Dimension Coincidences for Modular Forms and Representations | For $3\leq g\leq10$, is the equality $\operatorname{weight}(F^{(g)})-19=\dim(V_g)$ between the modular-form weight and the associated representation dimension merely accidental? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359](https://doi.org/10.4171/owr/2021/6)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,021 | 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-4990375-003",
"literature-status:open",
"owr-year:2021"
] | The reported equality between a Borcherds-product weight and a representation-space dimension is observed as a coincidence; later work proves related Kodaira-dimension results but does not explain or generalize this identity. | [
{
"url": "https://doi.org/10.1017/S1474748021000013",
"label": "Ma, Journal of the Institute of Mathematics of Jussieu"
},
{
"url": "https://arxiv.org/abs/1909.03946",
"label": "Ma, Mukai models and Borcherds products"
},
{
"url": "https://doi.org/10.4171/owr/2021/6",
"label": "Oberw... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/6 | null | null | null | For $3\leq g\leq10$, is the equality $\operatorname{weight}(F^{(g)})-19=\dim(V_g)$ between the modular-form weight and the associated representation dimension merely accidental? | For 3\le g\le10, is the observed equality \operatorname{weight}(F^{(g)})-19=\dim(V_g) between the weight of the relevant modular form and the dimension of the associated representation merely accidental? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359 |
30,004,614 | OWR-4990375-004 | Vertex Algebra Partition Functions and Siegel Modular Forms | For vertex algebras not arising from quadratic forms, is it true that for sufficiently large genus their partition functions are not pullbacks of Siegel modular forms, and is a vertex algebra uniquely determined by its collection of partition functions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359](https://doi.org/10.4171/owr/2021/6)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,021 | 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-4990375-004",
"literature-status:partially-solved",
"owr-year:2021"
] | Recent work constructs Teichmuller partition functions and proves non-pullback results in broad cases, but the full non-pullback conjecture and reconstruction of a vertex algebra from all partition functions remain open. | [
{
"url": "https://arxiv.org/abs/2605.26972",
"label": "Carpi--Codogni, Vertex operator algebras, partition functions and Teichmuller modular forms"
},
{
"url": "https://doi.org/10.4171/owr/2021/6",
"label": "Oberwolfach Report 6/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/6 | null | null | null | For vertex algebras not arising from quadratic forms, is it true that for sufficiently large genus their partition functions are not pullbacks of Siegel modular forms, and is a vertex algebra uniquely determined by its collection of partition functions? | For vertex algebras not arising from quadratic forms, is it true that for sufficiently large genus their partition functions are not pullbacks of Siegel modular forms, and is a vertex algebra uniquely determined by its collection of partition functions? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359 |
30,004,615 | OWR-4990375-005 | Descent of Freeness for Orthogonal Modular Form Algebras | Let $\Gamma<O^+(M)$ be a finite-index subgroup generated by reflections, and let $\Gamma'$ be a finite-index subgroup of $\Gamma$. If $M_*(\Gamma')$ is a free graded algebra of modular forms, must $M_*(\Gamma)$ also be free? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359](https://doi.org/10.4171/owr/2021/6)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,021 | 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-4990375-005",
"literature-status:open",
"owr-year:2021"
] | The extracted fragment points to Wang's conjecture that freeness of an orthogonal modular-form algebra descends from a finite-index reflection subgroup; the classification paper formulates this conjecture but does not prove it. | [
{
"url": "https://doi.org/10.4171/owr/2021/6",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2006.02291",
"label": "Wang, classification of free algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/6 | null | null | null | Let $\Gamma<O^+(M)$ be a finite-index subgroup generated by reflections, and let $\Gamma'$ be a finite-index subgroup of $\Gamma$. If $M_*(\Gamma')$ is a free graded algebra of modular forms, must $M_*(\Gamma)$ also be free? | Let \Gamma< O^+(M) be a finite-index subgroup generated by reflections, and let \Gamma' be a finite-index subgroup of \Gamma. If the graded algebra of modular forms M_*(\Gamma') is free, must the smaller algebra M_*(\Gamma) also be free? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359 |
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