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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,003,616 | OWR-15951-003 | Half-Line Spectra for Fibonacci Schrödinger Operators | Let $V_\omega$ be a continuum Fibonacci potential on $\mathbb R$, and define the separable Schrödinger operator on $\mathbb R^2$ by
$$
L^{(2)}_{\lambda_1V_\omega,\lambda_2V_\omega}=-\Delta+\lambda_1V_\omega(x)+\lambda_2V_\omega(y).
$$
Does its spectrum contain a half-line for every $\lambda_1,\lambda_2>0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spectral Structures and Topological Methods in Mathematical Quasicrystals (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/46, pp. 2781--2845](https://doi.org/10.4171/owr/2017/46)
## Lite... | 3 | open | null | 2,017 | 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-15951-003",
"literature-status:open",
"owr-year:2017"
] | High-energy half-line results are known for important Fibonacci operators and some parameter regimes, but the assertion for every pair of positive couplings remains a question. | [
{
"url": "https://doi.org/10.1016/j.jfa.2020.108911",
"label": "Damanik Fillman Gorodetski 2020"
},
{
"url": "https://doi.org/10.4171/owr/2017/46",
"label": "Oberwolfach Report 46 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/46 | null | null | null | Let $V_\omega$ be a continuum Fibonacci potential on $\mathbb R$, and define the separable Schrödinger operator on $\mathbb R^2$ by
$$
L^{(2)}_{\lambda_1V_\omega,\lambda_2V_\omega}=-\Delta+\lambda_1V_\omega(x)+\lambda_2V_\omega(y).
$$
Does its spectrum contain a half-line for every $\lambda_1,\lambda_2>0$? | For the Fibonacci continuum Schroedinger potential V_\omega defined by Eqs. (1)--(2), does the spectrum of the separable operator L_{\lambda_1V_\omega,\lambda_2V_\omega} contain a half-line for every \lambda_1,\lambda_2>0? | 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 | Spectral Structures and Topological Methods in Mathematical Quasicrystals (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/46, pp. 2781--2845 |
30,003,617 | OWR-15951-005 | Tame Dynamics of Nonamenable Group Actions | What happens for tame minimal dynamical systems when the acting group is not assumed to be commutative or even amenable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spectral Structures and Topological Methods in Mathematical Quasicrystals (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/46, pp. 2781--2845](https://doi.org/10.4171/owr/2017/46)
## Lite... | 3 | open | null | 2,017 | 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-15951-005",
"literature-status:open",
"owr-year:2017"
] | The extracted question asks for an extension to noncommutative or nonamenable acting groups, for which no general theory or resolution is supplied. | [
{
"url": "https://doi.org/10.4171/owr/2017/46",
"label": "Oberwolfach Report 46 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/46 | null | null | null | What happens for tame minimal dynamical systems when the acting group is not assumed to be commutative or even amenable? | What happens for tame minimal dynamical systems when the acting group is not assumed to be commutative or even amenable? | 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 | Spectral Structures and Topological Methods in Mathematical Quasicrystals (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/46, pp. 2781--2845 |
30,003,618 | OWR-15951-006 | Algebraic Topology of Mathematical Quasicrystals | What algebro-topological tools should be employed to study mathematical quasicrystals and their tiling spaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spectral Structures and Topological Methods in Mathematical Quasicrystals (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/46, pp. 2781--2845](https://doi.org/10.4171/owr/2017/46)
## Lite... | 3 | open | null | 2,017 | 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-15951-006",
"literature-status:open",
"owr-year:2017"
] | This is an explicitly broad methodological question about suitable algebro-topological tools, not a proposition with a known proof or disproof. | [
{
"url": "https://doi.org/10.4171/owr/2017/46",
"label": "Oberwolfach Report 46 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/46 | null | null | null | What algebro-topological tools should be employed to study mathematical quasicrystals and their tiling spaces? | What algebro-topological tools should be employed to study mathematical quasicrystals and their tiling spaces? | 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 | Spectral Structures and Topological Methods in Mathematical Quasicrystals (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/46, pp. 2781--2845 |
30,003,619 | OWR-15952-003 | Absolute Continuity and Densities of Bernoulli Convolutions | For which parameters $\lambda\in(1/2,1)$ is the Bernoulli convolution $\nu_\lambda$ absolutely continuous, and what regularity properties can its density have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/47, pp. 2847--2905](https://doi.org/10.4171/owr/2017/47)
## Lit... | 3 | partially_solved | null | 2,017 | 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-15952-003",
"literature-status:partially-solved",
"owr-year:2017"
] | Absolute continuity is known for almost every parameter and outside exceptional sets of Hausdorff dimension zero, with strong algebraic-parameter results, but a full classification and density description remain open. | [
{
"url": "https://doi.org/10.4007/annals.2019.189.2.1",
"label": "Shmerkin 2019"
},
{
"url": "https://doi.org/10.1090/jams/916",
"label": "Varju 2019"
},
{
"url": "https://doi.org/10.4171/owr/2017/47",
"label": "Oberwolfach Report 47 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/47 | null | null | null | For which parameters $\lambda\in(1/2,1)$ is the Bernoulli convolution $\nu_\lambda$ absolutely continuous, and what regularity properties can its density have? | For which parameters \lambda\in(1/2,1) is the Bernoulli convolution \nu_\lambda absolutely continuous, and what can be said about its density? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/47, pp. 2847--2905 |
30,003,620 | OWR-15952-004 | Exponential Separation of Roots of Bounded Coefficient Polynomials | Let $\mathcal P_d$ be the set of polynomials of degree at most $d$ whose coefficients all lie in $\{-1,0,1\}$. Does there exist a constant $s>0$, independent of $d$, such that any distinct roots $\alpha$ and $\beta$ of polynomials in $\mathcal P_d$ satisfy $|\alpha-\beta|>s^d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/47, pp. 2847--2905](https://doi.org/10.4171/owr/2017/47)
## Lit... | 3 | open | null | 2,017 | 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-15952-004",
"literature-status:open",
"owr-year:2017"
] | The requested uniform exponential separation of distinct roots is not known; current general lower bounds are weaker than exponential in the degree. | [
{
"url": "https://arxiv.org/abs/1610.09154",
"label": "Breuillard Varju"
},
{
"url": "https://doi.org/10.4171/owr/2017/47",
"label": "Oberwolfach Report 47 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/47 | null | null | null | Let $\mathcal P_d$ be the set of polynomials of degree at most $d$ whose coefficients all lie in $\{-1,0,1\}$. Does there exist a constant $s>0$, independent of $d$, such that any distinct roots $\alpha$ and $\beta$ of polynomials in $\mathcal P_d$ satisfy $|\alpha-\beta|>s^d$? | Does there exist a constant s>0 such that for any distinct roots \alpha,\beta of polynomials in \mathcal P_d, one has |\alpha-\beta|>s^d? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/47, pp. 2847--2905 |
30,003,621 | OWR-15952-005 | Minimum Distinct Distances Among Planar Point Sets | Determine the minimum number $f(n)$ of distinct distances determined by $n$ distinct points in the Euclidean plane. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/47, pp. 2847--2905](https://doi.org/10.4171/owr/2017/47)
## Lit... | 3 | partially_solved | null | 2,017 | 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-15952-005",
"literature-status:partially-solved",
"owr-year:2017"
] | The distinct-distance problem has the Guth Katz lower bound of order n divided by log n and constructions with order n divided by the square root of log n, leaving the conjectured order unresolved. | [
{
"url": "https://doi.org/10.4007/annals.2015.181.1.2",
"label": "Guth Katz 2015"
},
{
"url": "https://doi.org/10.4171/owr/2017/47",
"label": "Oberwolfach Report 47 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/47 | null | null | null | Determine the minimum number $f(n)$ of distinct distances determined by $n$ distinct points in the Euclidean plane. | What is the minimum number f(n) of distinct distances determined by n distinct points in the plane? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/47, pp. 2847--2905 |
30,003,622 | OWR-15952-006 | Falconer Distance Conjecture in the Plane | If $K\subset\mathbb R^2$ is a Borel set with Hausdorff dimension greater than $1$, must its distance set $$D(K)=\{|x-y|:x,y\in K\}$$ have positive Lebesgue measure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/47, pp. 2847--2905](https://doi.org/10.4171/owr/2017/47)
## Lit... | 3 | partially_solved | null | 2,017 | 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-15952-006",
"literature-status:partially-solved",
"owr-year:2017"
] | Falconer's distance conjecture remains open in its critical Hausdorff-dimension range, despite major partial threshold results and many special-case theorems. | [
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC11700919/",
"label": "Mattila Sjoelin type theorem 2025"
},
{
"url": "https://doi.org/10.4171/owr/2017/47",
"label": "Oberwolfach Report 47 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/47 | null | null | null | If $K\subset\mathbb R^2$ is a Borel set with Hausdorff dimension greater than $1$, must its distance set $$D(K)=\{|x-y|:x,y\in K\}$$ have positive Lebesgue measure? | Falconer distance conjecture: if K\subset\mathbb R^2 is a Borel set with Hausdorff dimension greater than 1, then its distance set D(K) has positive Lebesgue length. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/47, pp. 2847--2905 |
30,003,623 | OWR-15954-001 | Totik–Widom Bounds Beyond Parreau–Widom Sets | Does there exist a compact set $E\subset\mathbb R$ that is not Parreau–Widom but whose Chebyshev constants satisfy a Totik–Widom bound? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/49, pp. 2943--2985](https://doi.org/10.4171/owr/2017/49)
## Liter... | 3 | open | null | 2,017 | 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-15954-001",
"literature-status:open",
"owr-year:2017"
] | A conditional converse proves the Totik--Widom bound implies the Parreau--Widom property when a canonical generator exists, but the unrestricted non-Parreau--Widom example asked for remains unresolved. | [
{
"url": "https://arxiv.org/abs/1709.06707",
"label": "Christiansen--Simon--Yuditskii--Zinchenko"
},
{
"url": "https://doi.org/10.4171/owr/2017/49",
"label": "Oberwolfach Report 49/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/49 | null | null | null | Does there exist a compact set $E\subset\mathbb R$ that is not Parreau–Widom but whose Chebyshev constants satisfy a Totik–Widom bound? | Does there exist a compact set E\subset\mathbb R that is not Parreau--Widom, but for which the Chebyshev constants satisfy a Totik--Widom bound? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/49, pp. 2943--2985 |
30,003,624 | OWR-15954-002 | Transitional Asymptotics for Toda Shock Waves | For the Toda shock problem, what are the long-time asymptotics in the transitional regions near the critical rays $n/t=\xi_{\rm cr}$ and $n/t=\xi_{\rm cr,1}$, including possible asymptotic solitons? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/49, pp. 2943--2985](https://doi.org/10.4171/owr/2017/49)
## Liter... | 3 | open | null | 2,017 | 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-15954-002",
"literature-status:open",
"owr-year:2017"
] | The extracted record only names asymptotics in transitional regions and does not specify the quantity or regime, so no definitive resolution can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2017/49",
"label": "Oberwolfach Report 49/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/49 | null | null | null | For the Toda shock problem, what are the long-time asymptotics in the transitional regions near the critical rays $n/t=\xi_{\rm cr}$ and $n/t=\xi_{\rm cr,1}$, including possible asymptotic solitons? | For the Toda shock problem, what are the long-time asymptotics in the transitional regions near the critical rays n/t=\xi_{\rm cr} and n/t=\xi_{\rm cr,1}, including possible asymptotic solitons? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/49, pp. 2943--2985 |
30,003,625 | OWR-15954-006 | Endpoint Lieb–Thirring Bounds for Infinite-Gap Jacobi Matrices | For perturbations of Jacobi matrices in infinite-gap isospectral tori, does the Lieb–Thirring inequality hold at the endpoint $p=1$? More generally, which infinite-gap spectral sets admit a Lieb–Thirring bound? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/49, pp. 2943--2985](https://doi.org/10.4171/owr/2017/49)
## Liter... | 3 | open | null | 2,017 | 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-15954-006",
"literature-status:open",
"owr-year:2017"
] | Lieb--Thirring bounds are known in periodic, finite-gap, and additional controlled infinite-gap settings, but the endpoint p=1 problem for general infinite-gap isospectral tori and a full characterization of admissible sets remain unresolved. | [
{
"url": "https://arxiv.org/abs/1609.09566",
"label": "Christiansen--Zinchenko"
},
{
"url": "https://doi.org/10.4171/owr/2017/49",
"label": "Oberwolfach Report 49/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/49 | null | null | null | For perturbations of Jacobi matrices in infinite-gap isospectral tori, does the Lieb–Thirring inequality hold at the endpoint $p=1$? More generally, which infinite-gap spectral sets admit a Lieb–Thirring bound? | For perturbations of Jacobi matrices from infinite-gap isospectral tori, does the Lieb--Thirring inequality hold at the endpoint p=1, and which infinite-gap sets admit a Lieb--Thirring bound? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/49, pp. 2943--2985 |
30,003,626 | OWR-15954-007 | Sharp Eigenvalue Bounds for Nonselfadjoint Jacobi Perturbations | Let $E\subset\mathbb R$ be a finite-gap set, let $J_0\in\mathcal T_E$, and let $J=J_0+\delta J$ be a compact nonselfadjoint Jacobi perturbation. Does the bound
$$\sum_{z\in\sigma_d(J)}\frac{\operatorname{dist}(z,E)^{p+\varepsilon}(1+\lvert z\rvert)^{1/2-2\varepsilon}}{\operatorname{dist}(z,\partial E)^{1/2}}\leq L_{\v... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/49, pp. 2943--2985](https://doi.org/10.4171/owr/2017/49)
## Liter... | 3 | open | null | 2,017 | 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-15954-007",
"literature-status:open",
"owr-year:2017"
] | The finite-gap complex perturbation estimate is proved with epsilon greater than zero, but the endpoint epsilon equal to zero and the proposed replacement of the boundary-distance denominator are not resolved. | [
{
"url": "https://doi.org/10.1007/s11005-017-0961-z",
"label": "Christiansen--Zinchenko"
},
{
"url": "https://doi.org/10.4171/owr/2017/49",
"label": "Oberwolfach Report 49/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/49 | null | null | null | Let $E\subset\mathbb R$ be a finite-gap set, let $J_0\in\mathcal T_E$, and let $J=J_0+\delta J$ be a compact nonselfadjoint Jacobi perturbation. Does the bound
$$\sum_{z\in\sigma_d(J)}\frac{\operatorname{dist}(z,E)^{p+\varepsilon}(1+\lvert z\rvert)^{1/2-2\varepsilon}}{\operatorname{dist}(z,\partial E)^{1/2}}\leq L_{\v... | For the finite-gap non-self-adjoint Jacobi perturbation bound (7), does the inequality remain valid when \epsilon=0, and can the denominator factor dist(z,\partial E)^{1/2} be replaced by dist(z,E)^{1/2}? | corrected_verified | The official report was checked. The reconstruction replaces the dangling reference to inequality (7) with its full finite-gap Jacobi setup and bound. | null | null | null | null | null | Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/49, pp. 2943--2985 |
30,003,627 | OWR-15955-001 | Heegaard–Floer Homology and Lattice Cohomology Conjecture | Conjecture: for a rational homology sphere 3-manifold M and \mathfrak s\in Spin^c(M), the reduced Heegaard Floer homology and reduced lattice cohomology are isomorphic up to the grading shift d(M,\mathfrak s). | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033](https://doi.org/10.4171/owr... | 3 | solved | null | 2,017 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | Duplicate/merged OWR extraction (The official report shows that this summary extraction duplicates the precise parity-refined Heegaard–Floer and lattice-cohomology conjectur) | [
"OWR-15955-003"
] | null | [Discussion #4 literature review, 2026-09-30] , from the same passage, should get the same status or be merged. | [
"owr",
"oberwolfach-reports",
"OWR-15955-001",
"literature-status:open",
"owr-year:2017"
] | The extracted record is only a lead-in to a conjecture and omits the conjecture itself, so its mathematical content and current status cannot be established. | [
{
"url": "https://doi.org/10.4171/owr/2017/50",
"label": "Oberwolfach Report 50/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/50 | null | null | null | null | Conjecture: for a rational homology sphere 3-manifold M and \mathfrak s\in Spin^c(M), the reduced Heegaard Floer homology and reduced lattice cohomology are isomorphic up to the grading shift d(M,\mathfrak s). | unrecoverable | The official report shows that this summary extraction duplicates the precise parity-refined Heegaard–Floer and lattice-cohomology conjecture retained as OWR-15955-003. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033 |
30,003,628 | OWR-15955-003 | Parity-Refined Heegaard–Floer and Lattice Cohomology Correspondence | Let $M$ be a negative-definite plumbed rational homology $3$-sphere and let $\sigma\in\operatorname{Spin}^c(M)$. Are there grading-shifted isomorphisms $$HF^+_{\mathrm{red,even/odd}}(-M,\sigma)\cong\bigoplus_{q\ \mathrm{even/odd}}\mathbb H^q_{\mathrm{red}}(M,\sigma)[-d(M,\sigma)]$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033](https://doi.org/10.4171/owr... | 3 | solved | null | 2,017 | 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... | [
"OWR-15955-001"
] | {
"source_url": "https://doi.org/10.1215/00127094-2024-0044",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes, over F₂)**. A. Némethi (OWR 50/2017, p. 2999, Conjecture 2): for negative-definite plumbed rational homology spheres, HF⁺_red,even/odd(−M, σ) ≅ ⊕_{q even/odd} H^q_red(M, σ)[−d(M, σ)]. Zemke, [Duke Math. J. 174 (2025)](https://doi.org/10.1215/00127094-2024-004... | [
"owr",
"oberwolfach-reports",
"OWR-15955-003",
"literature-status:open",
"owr-year:2017"
] | The extracted record is an incomplete continuation ending at the word conjecture, without the mathematical assertion needed for a literature determination. | [
{
"url": "https://doi.org/10.4171/owr/2017/50",
"label": "Oberwolfach Report 50/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/50 | null | null | null | Let $M$ be a negative-definite plumbed rational homology $3$-sphere and let $\sigma\in\operatorname{Spin}^c(M)$. Are there grading-shifted isomorphisms $$HF^+_{\mathrm{red,even/odd}}(-M,\sigma)\cong\bigoplus_{q\ \mathrm{even/odd}}\mathbb H^q_{\mathrm{red}}(M,\sigma)[-d(M,\sigma)]$$? | Conjecture: for every \mathfrak s\in Spin^c(M), HF^+_{\rm red,even/odd}(-M,\mathfrak s) is isomorphic, up to the shift d(M,\mathfrak s), to \bigoplus_{q \rm even/odd} H^q_{\rm red}(M,\mathfrak s)[-d(M,\mathfrak s)]. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033 |
30,003,629 | OWR-15955-004 | Nontorus Abelian Duality Manifolds | Does there exist a closed orientable manifold that is an abelian duality space but is not a real torus? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033](https://doi.org/10.4171/owr... | 3 | partially_solved | null | 2,017 | 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 | {
"source_url": "https://arxiv.org/abs/1709.02870",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes; ours)**. Y. Liu (joint with L. Maxim and B. Wang; OWR 50/2017, p. 3008, Question 6; Question 6.4 of [arXiv:1709.02870](https://arxiv.org/abs/1709.02870), in [Adv. Math. 335 (2018)](https://doi.org/10.1016/j.aim.2018.07.012)) asks for a closed orientable abeli... | [
"owr",
"oberwolfach-reports",
"OWR-15955-004",
"literature-status:open",
"owr-year:2017"
] | The question remains open in the primary follow-up literature: compact Kahler abelian-duality manifolds are forced to be complex tori, and the Heisenberg nilmanifold is explicitly ruled out, but no closed orientable non-torus example is known. | [
{
"url": "https://arxiv.org/abs/1709.02870",
"label": "Liu--Maxim--Wang"
},
{
"url": "https://doi.org/10.4171/owr/2017/50",
"label": "Oberwolfach Report 50/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/50 | null | null | null | Does there exist a closed orientable manifold that is an abelian duality space but is not a real torus? | Does there exist a closed orientable manifold that is an abelian duality space but is not a real torus? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033 |
30,003,630 | OWR-15955-005 | Group Extensions Realized by Kodaira Fibrations | Characterize the extensions $$1\longrightarrow\pi_1(F_b)\longrightarrow G\longrightarrow\pi_1(B)\longrightarrow1,$$ where $B$ and $F_b$ are curves, for which $G$ is the fundamental group of a Kodaira fibration. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033](https://doi.org/10.4171/owr... | 3 | partially_solved | null | 2,017 | 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-15955-005",
"literature-status:partially-solved",
"owr-year:2017"
] | Vidussi derives necessary restrictions and gives extensions that cannot be realized by Kodaira fibrations, but no complete characterization of the extensions that do arise is available. | [
{
"url": "https://arxiv.org/abs/1706.03197",
"label": "Vidussi"
},
{
"url": "https://doi.org/10.4171/owr/2017/50",
"label": "Oberwolfach Report 50/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/50 | null | null | null | Characterize the extensions $$1\longrightarrow\pi_1(F_b)\longrightarrow G\longrightarrow\pi_1(B)\longrightarrow1,$$ where $B$ and $F_b$ are curves, for which $G$ is the fundamental group of a Kodaira fibration. | For which extensions 1\to\pi_1(F_b)\to G\to\pi_1(B)\to1, with B and F_b curves as in a Kodaira fibration, is G the fundamental group of a Kodaira surface? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033 |
30,003,631 | OWR-15955-006 | Connected Monodromy Groups of Kodaira Fibrations | Which groups occur as connected monodromy groups of Kodaira fibrations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033](https://doi.org/10.4171/owr... | 3 | partially_solved | null | 2,017 | 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-15955-006",
"literature-status:partially-solved",
"owr-year:2017"
] | Flapan classifies the possible connected monodromy groups in the specified genus-three construction, but realizability in the remaining cases and the corresponding question for arbitrary fiber genus are not completely settled. | [
{
"url": "https://doi.org/10.1002/mana.202000189",
"label": "Flapan"
},
{
"url": "https://doi.org/10.4171/owr/2017/50",
"label": "Oberwolfach Report 50/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/50 | null | null | null | Which groups occur as connected monodromy groups of Kodaira fibrations? | Which groups can arise as the connected monodromy group of a Kodaira fibration? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033 |
30,003,632 | OWR-15955-007 | Kähler, Projective, and Quasiprojective Group Realizability | For a natural class of groups, characterize which members are Kähler groups, projective groups, or quasiprojective groups. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033](https://doi.org/10.4171/owr... | 3 | open | null | 2,017 | 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-15955-007",
"literature-status:open",
"owr-year:2017"
] | The cited examples settle several individual classes of groups, but the extracted broad classification question for Kähler, projective, and quasiprojective realizability has no general solution. | [
{
"url": "https://doi.org/10.4171/owr/2017/50",
"label": "Oberwolfach Report 50/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/50 | null | null | null | For a natural class of groups, characterize which members are Kähler groups, projective groups, or quasiprojective groups. | Given a class of groups, which groups in that class are Kaehler, projective, or quasiprojective? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033 |
30,003,633 | OWR-15955-009 | Nonabelian Quotients of the String Link Solvable Filtration | For $m\geq2$ and $n\geq0$, is the quotient $\mathcal F_n^m/\mathcal F_{n.5}^m$ in the $n$-solvable filtration of the $m$-component string-link concordance group nonabelian? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033](https://doi.org/10.4171/owr... | 3 | partially_solved | null | 2,017 | 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-15955-009",
"literature-status:partially-solved",
"owr-year:2017"
] | Known results prove substantial nontrivial and nonabelian successive quotients in low levels and for suitable numbers of components, but the full nonabelianity question in the extracted record remains unresolved in general. | [
{
"url": "https://msp.org/agt/2014/14-5/agt-v14-n5-p05-s.pdf",
"label": "Otto"
},
{
"url": "https://arxiv.org/abs/math/0609378",
"label": "Harvey"
},
{
"url": "https://doi.org/10.4171/owr/2017/50",
"label": "Oberwolfach Report 50/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/50 | null | null | null | For $m\geq2$ and $n\geq0$, is the quotient $\mathcal F_n^m/\mathcal F_{n.5}^m$ in the $n$-solvable filtration of the $m$-component string-link concordance group nonabelian? | Are the successive quotients F_n^m/F_{n.5}^m of the n-solvable filtration of the m-component string-link concordance group non-abelian for m\ge2 and n\ge0? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033 |
30,003,634 | OWR-15955-011 | Derived Pure Braid Groups in the Solvable Filtration | For every $n\geq1$, is the $(n+2)$-nd derived subgroup $(P_m)^{(n+2)}$ of the pure braid group contained in $\mathcal F_n^m$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033](https://doi.org/10.4171/owr... | 3 | open | null | 2,017 | 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-15955-011",
"literature-status:open",
"owr-year:2017"
] | Only the base containment of the squared pure braid group in the zero-level filtration is established in the checked sources; the stated higher-derived inclusion remains unresolved. | [
{
"url": "https://msp.org/agt/2014/14-5/agt-v14-n5-p05-s.pdf",
"label": "Otto"
},
{
"url": "https://doi.org/10.4171/owr/2017/50",
"label": "Oberwolfach Report 50/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/50 | null | null | null | For every $n\geq1$, is the $(n+2)$-nd derived subgroup $(P_m)^{(n+2)}$ of the pure braid group contained in $\mathcal F_n^m$? | Is (P_m)^{n+2}\subset F_n^m for every n\ge1? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033 |
30,003,635 | OWR-15955-012 | Pure Braid Squares in the Symmetric Grope Filtration | Is the square subgroup $(P_m)^2$ of the pure braid group contained in the second stage $\mathcal G_2^m$ of the symmetric grope filtration? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033](https://doi.org/10.4171/owr... | 3 | open | null | 2,017 | 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-15955-012",
"literature-status:open",
"owr-year:2017"
] | Containment in the second Whitney-tower stage is known, but the stronger containment in the second symmetric-grope subgroup asked for here remains open. | [
{
"url": "https://msp.org/agt/2014/14-5/agt-v14-n5-p05-s.pdf",
"label": "Otto"
},
{
"url": "https://doi.org/10.4171/owr/2017/50",
"label": "Oberwolfach Report 50/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/50 | null | null | null | Is the square subgroup $(P_m)^2$ of the pure braid group contained in the second stage $\mathcal G_2^m$ of the symmetric grope filtration? | Is (P_m)^2\subset G_2^m? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033 |
30,003,636 | OWR-15955-013 | Characteristic Varieties of Divisors Beyond Line Arrangements | Does the characterization of high-dimensional essential components of the characteristic variety for a union of lines in $\mathbb P^2$ extend to more general divisors on smooth projective surfaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033](https://doi.org/10.4171/owr... | 3 | partially_solved | null | 2,017 | 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-15955-013",
"literature-status:partially-solved",
"owr-year:2017"
] | Later work gives broader finiteness and free-quotient results for smooth quasiprojective settings, but it does not establish a complete analogue of the line-arrangement criterion in every divisor and surface setting. | [
{
"url": "https://arxiv.org/abs/1904.00969",
"label": "Cogolludo--Libgober"
},
{
"url": "https://doi.org/10.4171/owr/2017/50",
"label": "Oberwolfach Report 50/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/50 | null | null | null | Does the characterization of high-dimensional essential components of the characteristic variety for a union of lines in $\mathbb P^2$ extend to more general divisors on smooth projective surfaces? | Is the characterization of high-dimensional essential components of the characteristic variety for a union of lines in \mathbb P^2 specific to unions of lines, or does it hold more generally for divisors on smooth projective surfaces? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/50, pp. 2987--3033 |
30,003,637 | OWR-15956-003 | Small Möbius Sums in Generalized Integer Systems | For a Beurling generalized integer system whose counting function satisfies $N(x)=x^{1+o(1)}$, how small can the generalized Möbius summatory function
$$
M_{\mathcal P}(x)=\sum_{\substack{n\leq x\\ n\in\mathcal N}}\mu_{\mathcal P}(n)
$$
be? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 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-15956-003",
"literature-status:open",
"owr-year:2017"
] | Later work proves lower bounds and special-case estimates for Beurling generalized numbers, but no general construction with exponent below one half or the proposed nonperiodic zero-set improvement resolves the extracted problem. | [
{
"url": "https://arxiv.org/abs/1901.06866",
"label": "Neamah--Hilberdink"
},
{
"url": "https://arxiv.org/abs/2406.00736",
"label": "Vindas"
},
{
"url": "https://doi.org/10.4171/owr/2017/51",
"label": "Oberwolfach Report 51/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | For a Beurling generalized integer system whose counting function satisfies $N(x)=x^{1+o(1)}$, how small can the generalized Möbius summatory function
$$
M_{\mathcal P}(x)=\sum_{\substack{n\leq x\\ n\in\mathcal N}}\mu_{\mathcal P}(n)
$$
be? | Assuming the counting function of a generalized integer system satisfies N(x)=x^{1+o(1)}, how small can the generalized Möbius summatory function M(x)=\sum_{n\leq x, n\in\mathbb N}\mu_P(n) be? | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,638 | OWR-15956-004 | Sub-Square-Root Möbius Bounds for Generalized Primes | Does there exist a Beurling generalized prime system for which $M_{\mathcal P}(x)=O(x^\alpha)$ for some $\alpha<1/2$? Can constructions based on periodic errors $N(x)-x$ be adapted to nonperiodic approximations of $\lfloor x\rfloor$ whose associated Mellin transforms have zeros with real parts approaching $1/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 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-15956-004",
"literature-status:open",
"owr-year:2017"
] | The Beurling-system question about improving the x^{1/2} remainder below exponent 1/2 for non-periodic approximations remains unresolved; later work gives related constructions and Omega results but no general affirmative theorem. | [
{
"url": "https://doi.org/10.4171/owr/2017/51",
"label": "Oberwolfach Report 51, open-problems session"
},
{
"url": "https://doi.org/10.1016/j.jnt.2004.09.001",
"label": "Hilberdink, Well-behaved Beurling primes and integers"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | Does there exist a Beurling generalized prime system for which $M_{\mathcal P}(x)=O(x^\alpha)$ for some $\alpha<1/2$? Can constructions based on periodic errors $N(x)-x$ be adapted to nonperiodic approximations of $\lfloor x\rfloor$ whose associated Mellin transforms have zeros with real parts approaching $1/2$? | Can one obtain M(x)=O(x^\alpha) for some \alpha<1/2 in another generalized prime system, and can the method be adapted to better non-periodic approximations to [x] whose zero real parts have supremum greater than 1/2? | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,639 | OWR-15956-005 | Keating–Snaith Moment Conjecture for the Zeta Function | For fixed $k$, is $\frac{1}{T}\int_0^T|\zeta(1/2+it)|^{2k}\,dt\sim a(k)\frac{G(k+1)^2}{G(2k+1)}\left(\log\frac{T}{2\pi}\right)^{k^2}$, where $G$ is the Barnes G-function and $a(k)$ is the arithmetic factor? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 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-15956-005",
"literature-status:open",
"owr-year:2017"
] | The Keating--Snaith asymptotic is proved for the second and fourth moments, but the displayed all-k moment conjecture is not proved in general; current surveys still describe the full asymptotics as beyond reach. | [
{
"url": "https://doi.org/10.1007/s002200000261",
"label": "Keating--Snaith, Random matrix theory and zeta"
},
{
"url": "https://doi.org/10.1112/jlms.70376",
"label": "Florea, survey of moment bounds for zeta"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | For fixed $k$, is $\frac{1}{T}\int_0^T|\zeta(1/2+it)|^{2k}\,dt\sim a(k)\frac{G(k+1)^2}{G(2k+1)}\left(\log\frac{T}{2\pi}\right)^{k^2}$, where $G$ is the Barnes G-function and $a(k)$ is the arithmetic factor? | For fixed k, the Keating--Snaith conjecture predicts \frac1T\int_0^T|\zeta(1/2+it)|^{2k}dt\sim a(k)\frac{G(k+1)^2}{G(2k+1)}\left(\log\frac{T}{2\pi}\right)^{k^2}, where G is the Barnes G-function and a(k) is the arithmetic factor. | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,640 | OWR-15956-006 | Maximum Size of the Zeta Function | Is $\max_{0\leq t\leq T}|\zeta(1/2+it)|=\exp\!\left((1+o(1))\sqrt{\tfrac12\log T\log\log T}\right)$ as $T\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 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-15956-006",
"literature-status:open",
"owr-year:2017"
] | The Farmer--Gonek--Hughes prediction for the maximum of zeta on the critical line remains a conjecture; later work supplies bounds and evidence but not the asserted asymptotic. | [
{
"url": "https://doi.org/10.1515/CRELLE.2007.064",
"label": "Farmer--Gonek--Hughes, The maximum size of L-functions"
},
{
"url": "https://doi.org/10.4171/owr/2017/51",
"label": "Oberwolfach Report 51, open-problems session"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | Is $\max_{0\leq t\leq T}|\zeta(1/2+it)|=\exp\!\left((1+o(1))\sqrt{\tfrac12\log T\log\log T}\right)$ as $T\to\infty$? | The Farmer--Gonek--Hughes conjecture predicts \max_{0\leq t\leq T}|\zeta(1/2+it)|=\exp\left((1+o(1))\sqrt{\tfrac12\log T\log\log T}\right) as T\to\infty. | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,641 | OWR-15956-007 | Partition Regularity of Pythagorean Triples | Is the Pythagorean equation $x^2+y^2=z^2$ partition regular on $\mathbb{N}$, meaning that every finite coloring of $\mathbb{N}$ has a nontrivial monochromatic solution? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 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-15956-007",
"literature-status:open",
"owr-year:2017"
] | The equation x^2+y^2=z^2 is known to be partition regular for two colours, but partition regularity for arbitrary finite colourings remains open. | [
{
"url": "https://www.cambridge.org/core/journals/forum-of-mathematics-pi/article/partition-regularity-of-pythagorean-pairs/BE259EB45DC64E7BDE1649C6693F2A2E",
"label": "Partition regularity of Pythagorean pairs"
},
{
"url": "https://doi.org/10.4171/owr/2017/51",
"label": "Oberwolfach Report 51, ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | Is the Pythagorean equation $x^2+y^2=z^2$ partition regular on $\mathbb{N}$, meaning that every finite coloring of $\mathbb{N}$ has a nontrivial monochromatic solution? | Is the Pythagorean equation x^2+y^2=z^2 partition regular on \mathbb N, meaning that every finite coloring of \mathbb N has a nontrivial monochromatic solution? | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,642 | OWR-15956-008 | Critical Mean Values of Dirichlet Polynomials | Let $D(s)=\sum_{n\leq N}a_nn^{-s}$ with $|a_n|\leq1$. In the critical range $T^{1/2}<N<T$ with $N^\kappa=T$, is $\int_0^T|D(it)|^{2\kappa}\,dt\ll T^{2+\varepsilon}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 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-15956-008",
"literature-status:open",
"owr-year:2017"
] | The extracted claim is the conjectured Dirichlet-polynomial mean-value bound in the critical range; the Hardy--Littlewood majorant implication is unavailable because that majorant conjecture is false, and the displayed bound itself remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2017/51",
"label": "Oberwolfach Report 51, Dirichlet-polynomial discussion"
},
{
"url": "https://ems.press/content/serial-article-files/46710",
"label": "Oberwolfach Report 51, full text"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | Let $D(s)=\sum_{n\leq N}a_nn^{-s}$ with $|a_n|\leq1$. In the critical range $T^{1/2}<N<T$ with $N^\kappa=T$, is $\int_0^T|D(it)|^{2\kappa}\,dt\ll T^{2+\varepsilon}$? | For D(s)=\sum_{n\leq N}a_n n^{-s} with |a_n|\leq1, and in the critical range T^{1/2}<N<T with N^\kappa=T, is it true that \int_0^T|D(it)|^{2\kappa}dt\ll T^{2+\varepsilon}? | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,643 | OWR-15956-009 | Fourier Uniqueness from Spherical Zero Sets | Let $f\in\mathcal S(\mathbb R^n)$. If $f$ vanishes on every sphere $|x|=r_j$ and its Fourier transform $\widehat f$ vanishes on every sphere $|\xi|=\rho_j$, where $r_j,\rho_j\to\infty$, must $f\equiv0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 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-15956-009",
"literature-status:open",
"owr-year:2017"
] | For arbitrary increasing radius sequences, the simultaneous Fourier-uniqueness question remains open; published results establish only structured special cases such as radii near square roots of integers. | [
{
"url": "https://doi.org/10.4171/owr/2017/51",
"label": "Oberwolfach Report 51, Hedenmalm problem"
},
{
"url": "https://arxiv.org/abs/2103.12015",
"label": "Ramos--Stoller, Perturbed Fourier uniqueness in higher dimensions"
},
{
"url": "https://doi.org/10.1007/s11854-025-0376-1",
"l... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | Let $f\in\mathcal S(\mathbb R^n)$. If $f$ vanishes on every sphere $|x|=r_j$ and its Fourier transform $\widehat f$ vanishes on every sphere $|\xi|=\rho_j$, where $r_j,\rho_j\to\infty$, must $f\equiv0$? | If f\in\mathcal S(\mathbb R^n) vanishes on every sphere |x|=r_j and its Fourier transform vanishes on every sphere |\xi|=\rho_j, where both radius sequences tend to infinity, must f\equiv0? | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,644 | OWR-15956-010 | Zero-Free Dirichlet Polynomials on the Unit Line | For
$$
D(s)=1+2^{-s}+3^{-s}+5^{-s},
$$
is $D(s)\neq0$ whenever $\operatorname{Re}(s)=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 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-15956-010",
"literature-status:open",
"owr-year:2017"
] | The finite Dirichlet polynomial D(s)=1+2^{-s}+3^{-s}+5^{-s} is the simplest unresolved case of the Erdos--Ingham nonvanishing question on Re(s)=1. | [
{
"url": "https://eudml.org/doc/207489",
"label": "Erdos--Ingham, Arithmetical Tauberian theorems"
},
{
"url": "https://www.erdosproblems.com/latex/967",
"label": "Erdos Problems, problem 967"
},
{
"url": "https://doi.org/10.4171/owr/2017/51",
"label": "Oberwolfach Report 51, open-pr... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | For
$$
D(s)=1+2^{-s}+3^{-s}+5^{-s},
$$
is $D(s)\neq0$ whenever $\operatorname{Re}(s)=1$? | For D(s)=1+2^{-s}+3^{-s}+5^{-s}, is D(s)\ne0 for every \operatorname{Re}(s)=1? Equivalently, is every nondecreasing f:\mathbb R_{>0}\to\mathbb R_{>0} satisfying f(x)+f(x/2)+f(x/3)+f(x/5)=(61/30+o(1))x necessarily f(x)=(1+o(1))x? | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,645 | OWR-15956-011 | Rigidity of a Multiplicative Functional Equation | If $f:\mathbb R_{>0}\to\mathbb R_{>0}$ is nondecreasing and
$$
f(x)+f(x/2)+f(x/3)+f(x/5)=\left(\frac{61}{30}+o(1)\right)x
$$
as $x\to\infty$, must $f(x)=(1+o(1))x$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 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-15956-011",
"literature-status:open",
"owr-year:2017"
] | This Tauberian formulation is equivalent to the preceding nonvanishing question, and the finite case with divisors 2, 3, and 5 remains unresolved. | [
{
"url": "https://eudml.org/doc/207489",
"label": "Erdos--Ingham, Arithmetical Tauberian theorems"
},
{
"url": "https://www.erdosproblems.com/latex/967",
"label": "Erdos Problems, problem 967"
},
{
"url": "https://doi.org/10.4171/owr/2017/51",
"label": "Oberwolfach Report 51, open-pr... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | If $f:\mathbb R_{>0}\to\mathbb R_{>0}$ is nondecreasing and
$$
f(x)+f(x/2)+f(x/3)+f(x/5)=\left(\frac{61}{30}+o(1)\right)x
$$
as $x\to\infty$, must $f(x)=(1+o(1))x$? | If f:\mathbb R_{>0}\to\mathbb R_{>0} is nondecreasing and f(x)+f(x/2)+f(x/3)+f(x/5)=(61/30+o(1))x as x\to\infty, must f(x)=(1+o(1))x? | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,646 | OWR-15956-012 | Odd-Density Limits for Multiplicative Functions | Let $f:\mathbb N\to\mathbb R_{\geq0}$ be multiplicative, and set
$$
F(x)=\sum_{n\leq x}f(n),\qquad F_2(x)=\sum_{\substack{n\leq x\\ n\text{ odd}}}f(n).
$$
If $F(\lambda x)=(1+o(1))F(x)$ for every fixed $\lambda>0$, does $\lim_{x\to\infty}F_2(x)/F(x)$ exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem () | null | null | [Discussion #4 literature review, 2026-09-29] . The record copies the printed hypothesis F(λx) = (1+o(1))F(x). | [
"owr",
"oberwolfach-reports",
"OWR-15956-012",
"literature-status:open",
"owr-year:2017"
] | The Hilberdink question asks whether slow variation of the summatory function forces the odd-part ratio to converge to the predicted Euler-factor value; the report and subsequent search revealed no general proof or counterexample. | [
{
"url": "https://doi.org/10.4171/owr/2017/51",
"label": "Oberwolfach Report 51, Hilberdink problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | Let $f:\mathbb N\to\mathbb R_{\geq0}$ be multiplicative, and set
$$
F(x)=\sum_{n\leq x}f(n),\qquad F_2(x)=\sum_{\substack{n\leq x\\ n\text{ odd}}}f(n).
$$
If $F(\lambda x)=(1+o(1))F(x)$ for every fixed $\lambda>0$, does $\lim_{x\to\infty}F_2(x)/F(x)$ exist? | Let f:\mathbb N\to\mathbb R_{\geq0} be multiplicative, F(x)=\sum_{n\leq x}f(n), and F_2(x)=\sum_{\substack{n\leq x\\n odd}}f(n). If F(\lambda x)=(1+o(1))F(x) for every fixed \lambda>0, does \lim_{x\to\infty}F_2(x)/F(x) exist? | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,647 | OWR-15956-013 | Contractivity Abscissas of Dirichlet Partial Sums | For $f(s)=\sum_{n\geq1}a_nn^{-s}\in H^\infty(\mathbb C_0)$, define
$$
\sigma_N(f)=\inf\left\{\sigma>0:\lVert S_N(f)\rVert_{H^\infty(\mathbb C_\sigma)}\leq\lVert f\rVert_{H^\infty(\mathbb C_\sigma)}\right\},
\qquad
\sigma_N=\sup_f\sigma_N(f),
$$
where $\mathbb C_\sigma=\{s\in\mathbb C:\operatorname{Re}(s)>\sigma\}$. Is ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069](https://doi.org/10.4171/owr/2017/51)
... | 3 | open | null | 2,017 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem () | null | null | [Discussion #4 literature review, 2026-09-29] . The printed definition puts the H^∞(C_σ) norm of f on the right-hand side. | [
"owr",
"oberwolfach-reports",
"OWR-15956-013",
"literature-status:open",
"owr-year:2017"
] | The Bayart question about whether the half-plane threshold sigma_N tends to zero for partial sums of bounded Dirichlet series remains stated as open in the available literature. | [
{
"url": "https://doi.org/10.4171/owr/2017/51",
"label": "Oberwolfach Report 51, Bayart problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/51 | null | null | null | For $f(s)=\sum_{n\geq1}a_nn^{-s}\in H^\infty(\mathbb C_0)$, define
$$
\sigma_N(f)=\inf\left\{\sigma>0:\lVert S_N(f)\rVert_{H^\infty(\mathbb C_\sigma)}\leq\lVert f\rVert_{H^\infty(\mathbb C_\sigma)}\right\},
\qquad
\sigma_N=\sup_f\sigma_N(f),
$$
where $\mathbb C_\sigma=\{s\in\mathbb C:\operatorname{Re}(s)>\sigma\}$. Is ... | For f(s)=\sum_{n\geq1}a_n n^{-s}\in H^\infty(C_0), define \sigma_N(f)=\inf\{\sigma>0:\|S_N(f)\|_{H^\infty(C_\sigma)}\leq\|f\|_{H^\infty(C_\sigma)}\} and \sigma_N=\sup_f\sigma_N(f). Is \sigma_N\to0 as N\to\infty? | 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: Interplay between Number Theory and Analysis for Dirichlet Series (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/51, pp. 3035--3069 |
30,003,648 | OWR-15957-001 | Extremal Copositive Rays and Completely Positive Factorizations | For the copositive cone, can the extremal generating rays be completely characterized? For the completely positive cone, can the supporting hyperplanes be completely characterized, and can a general completely positive matrix $A$ be given explicitly as $A=\sum_{i=1}^r b_i b_i^T$ with $b_i\in\mathbb R_+^n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120](https://doi.org/10.4171/owr/2017/52)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,017 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15957-001",
"literature-status:open",
"owr-year:2017"
] | The copositive cone has known complete descriptions only in low dimensions; a general characterization of its extremal rays remains open, as does the unrestricted completely-positive factorization problem. | [
{
"url": "https://doi.org/10.4171/owr/2017/52",
"label": "Oberwolfach Report 52, copositive and completely positive cones"
},
{
"url": "https://doi.org/10.1016/j.laa.2017.02.017",
"label": "Dutour Sikirić--Schürmann--Vallentin, rational cp factorizations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/52 | null | null | null | For the copositive cone, can the extremal generating rays be completely characterized? For the completely positive cone, can the supporting hyperplanes be completely characterized, and can a general completely positive matrix $A$ be given explicitly as $A=\sum_{i=1}^r b_i b_i^T$ with $b_i\in\mathbb R_+^n$? | For the copositive cone, can the extremal generating rays be completely characterized? For the completely positive cone, can the supporting hyperplanes be completely characterized, and can a general completely positive matrix A be given explicitly as A=\sum_{i=1}^r b_i b_i^T with b_i\in\mathbb R_+^n? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120 |
30,003,649 | OWR-15957-002 | Rational and Integral Completely Positive Factorizations | Does every rational completely positive matrix have a rational completely positive factorization? Does every $2\times2$ integral completely positive matrix have an integral completely positive factorization? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120](https://doi.org/10.4171/owr/2017/52)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,017 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | [Discussion #4 update, 2026-10-13] Literature-status update for OWR-15957-002 (not a new result by me). | [
"owr",
"oberwolfach-reports",
"OWR-15957-002",
"literature-status:partially-solved",
"owr-year:2017"
] | Every rational interior completely positive matrix has a rational cp factorization, and every integral 2 by 2 completely positive matrix has an integral factorization; the boundary case for arbitrary rational completely positive matrices remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.laa.2017.02.017",
"label": "Dutour Sikirić--Schürmann--Vallentin, rational cp factorizations"
},
{
"url": "https://doi.org/10.1007/s10107-020-01467-4",
"label": "A simplex algorithm for rational cp-factorization"
},
{
"url": "https://doi.org/10.4171/ow... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/52 | null | null | null | Does every rational completely positive matrix have a rational completely positive factorization? Does every $2\times2$ integral completely positive matrix have an integral completely positive factorization? | Does every rational completely positive matrix have a rational completely positive factorization? Does every 2\times2 integral completely positive matrix have an integral completely positive factorization? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120 |
30,003,650 | OWR-15957-003 | Extremal Completely Positive Plus-Rank | For a nonzero symmetric matrix $A\in S^n$, let $\operatorname{cp}(A)$ be its completely positive rank and $\operatorname{cp}^+(A)$ its completely positive plus-rank. What is the maximum finite value of $\operatorname{cp}^+(A)-\operatorname{cp}(A)$, and what is the maximum finite value of $\operatorname{cp}^+(A)$ on $S^... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120](https://doi.org/10.4171/owr/2017/52)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,017 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15957-003",
"literature-status:open",
"owr-year:2017"
] | The cited cp-plus-rank paper proves bounds and generic equality but leaves both the maximal finite difference from cp-rank and the exact maximal cp-plus-rank unresolved. | [
{
"url": "https://doi.org/10.1016/j.laa.2015.05.021",
"label": "Bomze--Dickinson--Still, cp-rank and cp-plus-rank"
},
{
"url": "https://doi.org/10.4171/owr/2017/52",
"label": "Oberwolfach Report 52, open questions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/52 | null | null | null | For a nonzero symmetric matrix $A\in S^n$, let $\operatorname{cp}(A)$ be its completely positive rank and $\operatorname{cp}^+(A)$ its completely positive plus-rank. What is the maximum finite value of $\operatorname{cp}^+(A)-\operatorname{cp}(A)$, and what is the maximum finite value of $\operatorname{cp}^+(A)$ on $S^... | What is the maximum finite difference between the cp-plus-rank and the cp-rank of a matrix, and what is the maximum finite cp-plus-rank of matrices in S^n? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120 |
30,003,651 | OWR-15957-004 | Complexity of Completely Positive Matrix Recognition and Rank | Is membership in the cone $\operatorname{CP}_n$ of completely positive matrices in the complexity class NP? How can the completely positive rank of a given matrix in $\operatorname{CP}_n$ be computed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120](https://doi.org/10.4171/owr/2017/52)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,017 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15957-004",
"literature-status:open",
"owr-year:2017"
] | Membership in the completely positive cone is NP-hard and exact cp-rank computation is still open; the record's stronger NP-membership and computation questions therefore remain unresolved. | [
{
"url": "https://doi.org/10.1007/s10589-022-00417-4",
"label": "Completely positive factorization by a Riemannian smoothing method"
},
{
"url": "https://doi.org/10.4171/owr/2017/52",
"label": "Oberwolfach Report 52, complexity questions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/52 | null | null | null | Is membership in the cone $\operatorname{CP}_n$ of completely positive matrices in the complexity class NP? How can the completely positive rank of a given matrix in $\operatorname{CP}_n$ be computed? | Is membership in the cone CP_n of completely positive matrices in the complexity class NP, and how can the cp-rank of a given completely positive matrix be computed? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120 |
30,003,652 | OWR-15957-005 | Copositive Hierarchies for the Kissing-Number Problem | How do copositive and completely positive approximation hierarchies compare with other known hierarchies for bounding the kissing number? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120](https://doi.org/10.4171/owr/2017/52)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,017 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15957-005",
"literature-status:open",
"owr-year:2017"
] | Convergent copositive-kernel hierarchies for the kissing number have been developed, but the requested general relationship between those hierarchies and other approximations is not settled. | [
{
"url": "https://doi.org/10.1016/j.endm.2017.10.052",
"label": "Kuryatnikova--Vera, approximating copositive kernels"
},
{
"url": "https://doi.org/10.4171/owr/2017/52",
"label": "Oberwolfach Report 52, open question"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/52 | null | null | null | How do copositive and completely positive approximation hierarchies compare with other known hierarchies for bounding the kissing number? | What is the connection between the copositive/completely positive hierarchies developed here and other existing approximations for the kissing-number problem? | corrected_verified | The official report was checked. The source-dependent phrase “developed here” was replaced by a direct comparison question without altering its mathematical scope. | null | null | null | null | null | Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120 |
30,003,653 | OWR-15957-006 | Ordered-Median Facility Location | Given $n$ sites, a nonnegative cost matrix $C=(c_{j\ell})$, and $p<n$ facilities, choose $X\subseteq\{1,\ldots,n\}$ with $|X|=p$ to minimize the ordered weighted cost $\sum_{k=1}^n\lambda_k c_{\sigma_X(k)}(X)$, where $c_j(X)=\min_{\ell\in X}c_{j\ell}$ and $\sigma_X$ sorts these costs. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120](https://doi.org/10.4171/owr/2017/52)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,017 | 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-15957-006",
"literature-status:open",
"owr-year:2017"
] | The extracted passage is a facility-location problem definition rather than a resolved conjecture; no specific mathematical claim is stated that can be classified as solved. | [
{
"url": "https://doi.org/10.4171/owr/2017/52",
"label": "Oberwolfach Report 52, facility-location presentation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/52 | null | null | null | Given $n$ sites, a nonnegative cost matrix $C=(c_{j\ell})$, and $p<n$ facilities, choose $X\subseteq\{1,\ldots,n\}$ with $|X|=p$ to minimize the ordered weighted cost $\sum_{k=1}^n\lambda_k c_{\sigma_X(k)}(X)$, where $c_j(X)=\min_{\ell\in X}c_{j\ell}$ and $\sigma_X$ sorts these costs. | Given n sites, a nonnegative cost matrix C=(c_{j\ell}), and p<n facilities, choose X\subseteq\{1,\ldots,n\} with |X|=p to minimize the ordered weighted cost \sum_{k=1}^n\lambda_k c_{\sigma_X(k)}(X), where c_j(X)=\min_{\ell\in X}c_{j\ell} and \sigma_X sorts these costs. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120 |
30,003,654 | OWR-15957-007 | Certificates of Polynomial Nonnegativity in Copositive Optimization | For polynomials nonnegative on an unbounded set $S\cap h^{-1}(0)$, under what hypotheses can certificates expressed through polynomials nonnegative on $S$ and the ideal $(h)$ be used to extend copositive-polynomial formulations and polynomial-optimization methods? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120](https://doi.org/10.4171/owr/2017/52)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,017 | 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-15957-007",
"literature-status:open",
"owr-year:2017"
] | The extracted sentence asks only about a possible generalization of a certificate and does not specify a theorem; the claim is therefore unresolved and is normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2017/52",
"label": "Oberwolfach Report 52, certificate discussion"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/52 | null | null | null | For polynomials nonnegative on an unbounded set $S\cap h^{-1}(0)$, under what hypotheses can certificates expressed through polynomials nonnegative on $S$ and the ideal $(h)$ be used to extend copositive-polynomial formulations and polynomial-optimization methods? | What role can the proposed certificate of polynomial non-negativity play in generalizing the associated copositive-polynomial and optimization results to other contexts? | corrected_verified | The official report was checked. The reconstruction identifies the certificate, its domain, and its intended optimization generalization instead of relying on “proposed” and “associated” source references. | null | null | null | null | null | Copositivity and Complete Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/52, pp. 3071--3120 |
30,003,655 | OWR-15958-001 | Constant-Color Proof-Theoretic Finite Ramsey Theorems | Can the proof-theoretic finite Ramsey theorem be formulated with a constant number of colors while retaining the optimal induction fragment $I\Sigma_{n-2}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183](https://doi.org/10.4171/owr/2017/53)
## Literature review (... | 3 | open | null | 2,017 | 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-15958-001",
"literature-status:open",
"owr-year:2017"
] | Proof-length results establish the stated lower-fragment phenomenon, but the remaining question of retaining the optimal induction fragment while using a constant number of colours is still open. | [
{
"url": "https://doi.org/10.1016/j.apal.2017.01.004",
"label": "Freund, Proof lengths for instances of the Paris--Harrington principle"
},
{
"url": "https://doi.org/10.4171/owr/2017/53",
"label": "Oberwolfach Report 53, proof theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/53 | null | null | null | Can the proof-theoretic finite Ramsey theorem be formulated with a constant number of colors while retaining the optimal induction fragment $I\Sigma_{n-2}$? | Can one retain the optimal fragment I\Sigma_{n-2} while making the number of colors constant in the proof-theoretic finite Ramsey theorem construction? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183 |
30,003,656 | OWR-15958-003 | Wraith Redundancy for Algebraic Theories | For an algebraic theory $T$, does every $T$-redundant sentence hold in the generic model of $T$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183](https://doi.org/10.4171/owr/2017/53)
## Literature review (... | 3 | solved | null | 2,017 | 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 | {
"source_url": "https://arxiv.org/abs/1712.07743",
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (no)**. U. Buchholtz (joint with M. Bezem and T. Coquand; OWR 53/2017, p. 3136) leaves open whether, for an algebraic theory T, every T-redundant sentence holds in the generic model (BBC, [arXiv:1712.07743](https://arxiv.org/abs/1712.07743), Sec. 7; [Indag. Math. 2... | [
"owr",
"oberwolfach-reports",
"OWR-15958-003",
"literature-status:open",
"owr-year:2017"
] | The general Wraith question is disproved, but the extracted open problem concerns algebraic coherent theories, for which the positive answer remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.indag.2018.06.004",
"label": "Bezem--Buchholtz--Coquand, Syntactic forcing models for coherent logic"
},
{
"url": "https://doi.org/10.4171/owr/2017/53",
"label": "Oberwolfach Report 53, algebraic-theory open problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/53 | null | null | null | For an algebraic theory $T$, does every $T$-redundant sentence hold in the generic model of $T$? | Although Wraith's question has a negative answer in general, does it have a positive answer for algebraic theories; that is, does every T-redundant sentence hold in the generic model of an algebraic theory T? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183 |
30,003,657 | OWR-15958-004 | Shared Conceptual Foundations of Mathematics | Can a common core of conceptual foundations for mathematics be developed whose concepts are acceptable across several major philosophical approaches? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183](https://doi.org/10.4171/owr/2017/53)
## Literature review (... | 3 | open | null | 2,017 | 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-15958-004",
"literature-status:open",
"owr-year:2017"
] | The core conceptual foundations of mathematics proposal is explicitly presented as a question of feasibility and no subsequent mathematical resolution of that question was found. | [
{
"url": "https://doi.org/10.4171/owr/2017/53",
"label": "Oberwolfach Report 53, Aczel talk"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/53 | null | null | null | Can a common core of conceptual foundations for mathematics be developed whose concepts are acceptable across several major philosophical approaches? | Can there be a core Conceptual Foundations of Mathematics consisting of concepts acceptable across several philosophical approaches? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183 |
30,003,658 | OWR-15958-005 | Fixed Complexity Separations in Bounded Arithmetic | Is there a fixed $k$ such that $T_{2n+1}(\alpha)$ can be separated from $T_{2n}(\alpha)$ by a $\forall\Sigma_k^b(\alpha)$ sentence? In particular, is there a $\forall\Sigma_1^b(\alpha)$ sentence provable in some $T_{2n}(\alpha)$ but not in $\mathrm{APC}_2(\alpha)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183](https://doi.org/10.4171/owr/2017/53)
## Literature review (... | 3 | open | null | 2,017 | 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-15958-005",
"literature-status:open",
"owr-year:2017"
] | The bounded-arithmetic separation between successive T-levels by a fixed-complexity universal bounded formula remains a central open problem; later work gives partial separations but not the requested general result. | [
{
"url": "https://arxiv.org/abs/1812.10771",
"label": "Kolodziejczyk--Thapen, Approximate counting and NP search problems"
},
{
"url": "https://doi.org/10.4171/owr/2017/53",
"label": "Oberwolfach Report 53, bounded arithmetic"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/53 | null | null | null | Is there a fixed $k$ such that $T_{2n+1}(\alpha)$ can be separated from $T_{2n}(\alpha)$ by a $\forall\Sigma_k^b(\alpha)$ sentence? In particular, is there a $\forall\Sigma_1^b(\alpha)$ sentence provable in some $T_{2n}(\alpha)$ but not in $\mathrm{APC}_2(\alpha)$? | For some fixed k, can T_{2n+1}(\alpha) be separated from T_{2n}(\alpha) by a \forall\Sigma^b_k(\alpha) sentence? In particular, is there a \forall\Sigma^b_1(\alpha) sentence provable in some T_{2n}(\alpha) but not in APC_2(\alpha)? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183 |
30,003,659 | OWR-15958-006 | Completeness of Cut-Free Kozen Modal Calculus | Is Kozen's axiomatization of the modal $\mu$-calculus complete after the cut rule is removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183](https://doi.org/10.4171/owr/2017/53)
## Literature review (... | 3 | open | null | 2,017 | 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-15958-006",
"literature-status:open",
"owr-year:2017"
] | Kozen's original system is complete with cut, and complete cut-free systems exist in other formalisms, but completeness of the original system after removing cut remains open. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/50824d0c-d5f5-4a10-8518-36ade258b3e3/download",
"label": "Afshari--Leigh, Finitary proof systems for Kozen's mu"
},
{
"url": "https://doi.org/10.4171/owr/2017/53",
"label": "Oberwolfach Report 53, cut elimination"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/53 | null | null | null | Is Kozen's axiomatization of the modal $\mu$-calculus complete after the cut rule is removed? | Is Kozen's axiomatization of the modal \mu-calculus without the cut rule complete? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183 |
30,003,660 | OWR-15958-007 | Strong-Induction Admissibility in Cut-Free Modal Calculus | Is the strong-induction rule admissible in Kozen's cut-free system for the modal $\mu$-calculus? Equivalently, is the corresponding quantifier-contraction inference admissible? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183](https://doi.org/10.4171/owr/2017/53)
## Literature review (... | 3 | open | null | 2,017 | 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"
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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-15958-007",
"literature-status:open",
"owr-year:2017"
] | The strong-induction admissibility condition is identified as equivalent to the unresolved completeness question for Kozen's cut-free system; current cut-free results use strengthened or alternative systems. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/50824d0c-d5f5-4a10-8518-36ade258b3e3/download",
"label": "Afshari--Leigh, Finitary proof systems for Kozen's mu"
},
{
"url": "https://doi.org/10.4171/owr/2017/53",
"label": "Oberwolfach Report 53, cut elimination"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/53 | null | null | null | Is the strong-induction rule admissible in Kozen's cut-free system for the modal $\mu$-calculus? Equivalently, is the corresponding quantifier-contraction inference admissible? | Is the strong-induction rule admissible in Kozen's cut-free system for the modal \mu-calculus, equivalently is the corresponding quantifier-contraction inference admissible? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183 |
30,003,661 | OWR-15958-008 | Pathwise Connected Choice in Dimension Two | Is pathwise connected choice in dimension $2$ strongly Weihrauch equivalent to Weak König's Lemma, as connected choice is in dimensions at least $2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183](https://doi.org/10.4171/owr/2017/53)
## Literature review (... | 3 | open | null | 2,017 | 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"
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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-15958-008",
"literature-status:open",
"owr-year:2017"
] | The dimension two pathwise connected choice case is explicitly still open; the corresponding geometric reduction is known in dimension three and higher. | [
{
"url": "https://people.math.wisc.edu/~jsmiller8/Papers/BFT.pdf",
"label": "Brattka--Le Roux--Miller--Pauly"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/53 | null | null | null | Is pathwise connected choice in dimension $2$ strongly Weihrauch equivalent to Weak König's Lemma, as connected choice is in dimensions at least $2$? | Is pathwise connected choice in dimension two strongly Weihrauch equivalent to Weak Koenig's Lemma, as connected choice is from dimension two onwards? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183 |
30,003,662 | OWR-15958-009 | Uniform Quantitative Rates for Provably Convergent Sequences | For natural classes of provably convergent sequences, which uniform rates, moduli, or other quantitative forms of convergence can be extracted? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183](https://doi.org/10.4171/owr/2017/53)
## Literature review (... | 3 | partially_solved | null | 2,017 | 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-15958-009",
"literature-status:partially-solved",
"owr-year:2017"
] | Proof-theoretic work establishes uniform metastability and uniform jump bounds for broad classes of provably convergent sequences, but no universal effective rate answers the unrestricted question. | [
{
"url": "https://ems.press/content/serial-article-files/46716",
"label": "OWR Report 53/2017"
},
{
"url": "https://mca2017.mcofamericas.org/sites/mca2017/files/abstracts/ibm-ht.pdf",
"label": "Howard--Towsner abstract"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/53 | null | null | null | For natural classes of provably convergent sequences, which uniform rates, moduli, or other quantitative forms of convergence can be extracted? | For classes of provably convergent sequences, what uniform rates or other quantitative forms of convergence can be established? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183 |
30,003,663 | OWR-15959-001 | Variational Principle for Complete GENERIC Thermodynamics | Does there exist a variational principle embodying the complete GENERIC structure of nonequilibrium thermodynamics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/54, pp. 3185--3261](https://doi.org/10.4171/owr/2017/54)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report shows that this record repeats the first half of the two-part GENERIC variational-principle problem retained in full as ) | [
"OWR-15959-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15959-001",
"literature-status:partially-solved",
"owr-year:2017"
] | Variational formulations exist for important irreversible systems and GENERIC structure-preserving integrators, but a variational principle embodying the complete nonequilibrium GENERIC structure is not established in general. | [
{
"url": "https://doi.org/10.1515/jnet-2017-0034",
"label": "GENERIC integrators"
},
{
"url": "https://arxiv.org/abs/1502.02122",
"label": "Glavatskiy, Lagrangian irreversible thermodynamics"
},
{
"url": "https://ems.press/content/serial-article-files/46718",
"label": "OWR Report 54/... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/54 | null | null | null | null | Does there exist a variational principle embodying the complete GENERIC structure of nonequilibrium thermodynamics? | unrecoverable | The official report shows that this record repeats the first half of the two-part GENERIC variational-principle problem retained in full as OWR-15959-002. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Variational Methods for Evolution (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/54, pp. 3185--3261 |
30,003,664 | OWR-15959-002 | Variational GENERIC Structure and Preserving Integrators | Does there exist a variational principle that embodies the complete GENERIC structure of nonequilibrium thermodynamics, including its reversible Poisson and irreversible dissipative parts? If so, can its discretization yield structure-preserving GENERIC integrators? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/54, pp. 3185--3261](https://doi.org/10.4171/owr/2017/54)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 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"
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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... | [
"OWR-15959-001"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15959-002",
"literature-status:partially-solved",
"owr-year:2017"
] | Structure-preserving GENERIC integrators and variational descriptions of selected irreversible systems are available, while the requested complete GENERIC variational principle remains unresolved. | [
{
"url": "https://doi.org/10.1515/jnet-2017-0034",
"label": "GENERIC integrators"
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{
"url": "https://arxiv.org/abs/1502.02122",
"label": "Glavatskiy, Lagrangian irreversible thermodynamics"
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{
"url": "https://ems.press/content/serial-article-files/46718",
"label": "OWR Report 54/... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/54 | null | null | null | Does there exist a variational principle that embodies the complete GENERIC structure of nonequilibrium thermodynamics, including its reversible Poisson and irreversible dissipative parts? If so, can its discretization yield structure-preserving GENERIC integrators? | Does a variational principle embody the complete GENERIC structure, and can it be used to construct structure-preserving GENERIC integrators? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Variational Methods for Evolution (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/54, pp. 3185--3261 |
30,003,665 | OWR-15959-003 | Gradient Flow of Wasserstein-Quantization Supports | For $N$-point Wasserstein quantization of a density supported on a compact subset of $\mathbb R^d$, how does the support set evolve under steepest descent, and how does this discrete evolution compare with the Wasserstein gradient flow of the limiting energy? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/54, pp. 3185--3261](https://doi.org/10.4171/owr/2017/54)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 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"
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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-15959-003",
"literature-status:partially-solved",
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] | The optimal-measure asymptotics and gradient-flow viewpoint have been developed in one dimension and for selected two-dimensional settings, but the general evolution and Wasserstein-flow comparison remain open. | [
{
"url": "https://arxiv.org/abs/1711.01652",
"label": "A gradient flow perspective on quantization"
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{
"url": "https://doi.org/10.1016/j.anihpc.2017.12.003",
"label": "Quantization in space dimension two"
},
{
"url": "https://ems.press/content/serial-article-files/46718",
"label": ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/54 | null | null | null | For $N$-point Wasserstein quantization of a density supported on a compact subset of $\mathbb R^d$, how does the support set evolve under steepest descent, and how does this discrete evolution compare with the Wasserstein gradient flow of the limiting energy? | For N-point Wasserstein quantization of a density on a compact subset of R^d, how does the support set evolve under steepest descent, and how does this compare with the Wasserstein gradient flow of the limiting energy? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Variational Methods for Evolution (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/54, pp. 3185--3261 |
30,003,666 | OWR-15959-004 | Continuum Stability of Gradient Flows on Geometric Graphs | Under which hypotheses do gradient-flow evolution equations on geometric graphs converge to a continuum evolution as the number of sample points $n\to\infty$ and the connectivity scale $\varepsilon\to0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/54, pp. 3185--3261](https://doi.org/10.4171/owr/2017/54)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 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"
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"level": 3,
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15959-004",
"literature-status:partially-solved",
"owr-year:2017"
] | Discrete Wasserstein spaces and several graph gradient-flow models have continuum-limit theorems, but stability for the full geometric-graph evolution problem under the stated limits is not settled. | [
{
"url": "https://link.springer.com/article/10.1007/s00205-021-01631-w",
"label": "Nonlocal interaction equations on graphs"
},
{
"url": "https://ems.press/content/serial-article-files/46718",
"label": "OWR Report 54/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/54 | null | null | null | Under which hypotheses do gradient-flow evolution equations on geometric graphs converge to a continuum evolution as the number of sample points $n\to\infty$ and the connectivity scale $\varepsilon\to0$? | How and when can one establish stability of gradient-flow evolution equations on geometric graphs as the number of points n tends to infinity and the connectivity parameter epsilon tends to zero? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Variational Methods for Evolution (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/54, pp. 3185--3261 |
30,003,667 | OWR-15959-005 | Stable Wasserstein Gradient Flow Algorithms for Data Analysis | Which clustering or classification algorithms can be formulated as Wasserstein gradient flows, and can such algorithms be designed to remain stable as the sample size $n\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/54, pp. 3185--3261](https://doi.org/10.4171/owr/2017/54)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15959-005",
"literature-status:partially-solved",
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] | Wasserstein variational clustering, interacting-particle optimization, and gradient-flow learning methods provide positive instances, but a general characterization and stability-preserving algorithmic theory is not known. | [
{
"url": "https://proceedings.mlr.press/v162/xu22d.html",
"label": "Accurate quantization by interacting particles"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC6377175/",
"label": "Variational Wasserstein clustering"
},
{
"url": "https://arxiv.org/abs/2010.12760",
"label": ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/54 | null | null | null | Which clustering or classification algorithms can be formulated as Wasserstein gradient flows, and can such algorithms be designed to remain stable as the sample size $n\to\infty$? | Which clustering or classification algorithms can be described as Wasserstein gradient flows, and can one design such algorithms with stability as n tends to infinity? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Variational Methods for Evolution (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/54, pp. 3185--3261 |
30,003,668 | OWR-15960-001 | Euclidean Reconstruction of Relativistic Quantum Field Theories | Given a Euclidean classical field theory, when does analytic continuation from Euclidean time to real time produce a sensible relativistic quantum field theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reflection Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/55, pp. 3263--3343](https://doi.org/10.4171/owr/2017/55)
## Literature review (checked 2026-08-21)
**Status:** part... | 3 | partially_solved | null | 2,017 | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15960-001",
"literature-status:partially-solved",
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] | Osterwalder--Schrader reconstruction gives a Lorentzian theory for Euclidean data satisfying the axioms, but reconstruction from an arbitrary Euclidean theory and the full inverse Wick-rotation problem remain unresolved. | [
{
"url": "https://doi.org/10.1007/BF01645738",
"label": "Osterwalder--Schrader axioms"
},
{
"url": "https://ems.press/content/serial-article-files/46717",
"label": "OWR Report 55/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/55 | null | null | null | Given a Euclidean classical field theory, when does analytic continuation from Euclidean time to real time produce a sensible relativistic quantum field theory? | Given a Euclidean classical field theory, when does analytic continuation from Euclidean time to real time produce a sensible relativistic quantum field theory? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Reflection Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/55, pp. 3263--3343 |
30,003,669 | OWR-15960-002 | Symmetry Identities Beyond Renormalization-Group Methods | Can symmetry-generated identities help study models for which standard renormalization-group techniques do not apply? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reflection Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/55, pp. 3263--3343](https://doi.org/10.4171/owr/2017/55)
## Literature review (checked 2026-08-21)
**Status:** part... | 3 | partially_solved | null | 2,017 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15960-002",
"literature-status:partially-solved",
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] | Reflection-positivity analogues have been constructed in bi-free probability, including bi-free products preserving reflection positivity, but the broad free-probability analogue requested in the problem is not classified. | [
{
"url": "https://arxiv.org/abs/2312.06813",
"label": "Speicher, Bi-Free Probability and Reflection Positivity"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/8df8b5cb-72c1-4ca0-929f-dca03ec9bec0/content",
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/55 | null | null | null | Can symmetry-generated identities help study models for which standard renormalization-group techniques do not apply? | Can symmetry-generated identities help study models for which standard renormalization-group techniques do not apply? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Reflection Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/55, pp. 3263--3343 |
30,003,670 | OWR-15960-003 | Osterwalder–Schrader Positivity in Free Probability | Do analogues of Osterwalder–Schrader positivity exist in free probability or for noncommuting random variables? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reflection Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/55, pp. 3263--3343](https://doi.org/10.4171/owr/2017/55)
## Literature review (checked 2026-08-21)
**Status:** part... | 3 | partially_solved | null | 2,017 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
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"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15960-003",
"literature-status:partially-solved",
"owr-year:2017"
] | Bi-free reflection positivity supplies a concrete positive analogue of Osterwalder--Schrader positivity, while a general theory covering the full free-probability setting remains open. | [
{
"url": "https://arxiv.org/abs/2312.06813",
"label": "Speicher, Bi-Free Probability and Reflection Positivity"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/8df8b5cb-72c1-4ca0-929f-dca03ec9bec0/content",
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/55 | null | null | null | Do analogues of Osterwalder–Schrader positivity exist in free probability or for noncommuting random variables? | Do analogues of Osterwalder-Schrader positivity exist in free probability and for noncommuting random variables? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Reflection Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/55, pp. 3263--3343 |
30,003,671 | OWR-15960-004 | Nontriviality of Local Algebras from Deformed Borchers Triples | Are the local von Neumann algebras generated by the deformed Borchers triples nontrivial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reflection Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/55, pp. 3263--3343](https://doi.org/10.4171/owr/2017/55)
## Literature review (checked 2026-08-21)
**Status:** open... | 3 | open | null | 2,017 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
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"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15960-004",
"literature-status:open",
"owr-year:2017"
] | The extracted record is truncated before stating a definite mathematical claim, so no reliable resolution can be established from the available literature. | [
{
"url": "https://ems.press/content/serial-article-files/46717",
"label": "OWR Report 55/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/55 | null | null | null | Are the local von Neumann algebras generated by the deformed Borchers triples nontrivial? | Are the local von Neumann algebras generated by the deformed Borchers triples nontrivial? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Reflection Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/55, pp. 3263--3343 |
30,003,672 | OWR-15960-006 | Relative Commutants and Möbius Nets for Finite-Group Inclusions | Let $(N_0\subset M_0,\Omega_0)$ be a standard half-sided modular inclusion, and form the free-product inclusion $(N\subset M,\Omega)$ from finitely many isomorphic copies indexed by a finite set $K$. Determine the relative commutant $N'\cap M$. If it is nontrivial, which Möbius-covariant net does the inclusion define? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reflection Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/55, pp. 3263--3343](https://doi.org/10.4171/owr/2017/55)
## Literature review (checked 2026-08-21)
**Status:** open... | 3 | open | null | 2,017 | 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-15960-006",
"literature-status:open",
"owr-year:2017"
] | For finite free-product half-sided modular inclusions, the relative commutant problem is explicitly still unknown; nontrivial relative commutants are known in related finite Möbius-net constructions. | [
{
"url": "https://aif.centre-mersenne.org/item/10.5802/aif.3269.pdf",
"label": "Free products in AQFT"
},
{
"url": "https://ems.press/content/serial-article-files/46717",
"label": "OWR Report 55/2017"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/55 | null | null | null | Let $(N_0\subset M_0,\Omega_0)$ be a standard half-sided modular inclusion, and form the free-product inclusion $(N\subset M,\Omega)$ from finitely many isomorphic copies indexed by a finite set $K$. Determine the relative commutant $N'\cap M$. If it is nontrivial, which Möbius-covariant net does the inclusion define? | When the finite group K has finite cardinality, what is the intersection N' cap M, and what Mobius-covariant net does it define if it is nontrivial? | corrected_verified | The official report was checked. The reconstruction restores the free-product half-sided modular inclusion and finite indexing set needed by the two source questions. | null | null | null | null | null | Reflection Positivity (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/55, pp. 3263--3343 |
30,003,673 | OWR-15961-001 | Uniqueness of Higher-Dimensional Critical Minimizers | In spatial dimension $N>1$, for the fair-competition aggregation–diffusion model at critical interaction strength $\chi=\chi_c$, is the global minimizer of the free-energy functional unique up to dilations? In the subcritical rescaled problem, are stationary states global minimizers and are those minimizers unique? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical and Quantum Mechanical Models of Many-Particle Systems (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/56, pp. 3345--3425](https://doi.org/10.4171/owr/2017/56)
## Literature re... | 3 | open | null | 2,017 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 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-15961-001",
"literature-status:open",
"owr-year:2017"
] | Uniqueness of the global minimizer modulo dilations is proved in the Newtonian and one-dimensional cases, but remains open in the higher-dimensional fair-competition regime. | [
{
"url": "https://arxiv.org/abs/1610.00939",
"label": "Equilibria in the fair-competition regime"
},
{
"url": "https://arxiv.org/abs/1905.07788",
"label": "Uniqueness of stationary Keller--Segel states"
},
{
"url": "https://oa.tib.eu/renate/bitstreams/63dd963a-2f59-4c50-b626-ffc98e104dc8... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/56 | null | null | null | In spatial dimension $N>1$, for the fair-competition aggregation–diffusion model at critical interaction strength $\chi=\chi_c$, is the global minimizer of the free-energy functional unique up to dilations? In the subcritical rescaled problem, are stationary states global minimizers and are those minimizers unique? | In higher dimensions, is the global minimizer of the critical rescaled functional unique modulo dilations? | corrected_verified | The official report was checked. The reconstruction distinguishes the critical unrescaled minimization problem from the subcritical rescaled problem, both left open beyond one dimension. | null | null | null | null | null | Classical and Quantum Mechanical Models of Many-Particle Systems (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/56, pp. 3345--3425 |
30,003,674 | OWR-15961-002 | Quantum Optimal Transport for Mean-Field Dynamics | Can the pseudo-metric used for quantum mean-field dynamics be formulated through a quantum analogue of optimal transport, such as a Benamou-Brenier variational formula? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical and Quantum Mechanical Models of Many-Particle Systems (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/56, pp. 3345--3425](https://doi.org/10.4171/owr/2017/56)
## Literature re... | 3 | partially_solved | null | 2,017 | 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"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15961-002",
"literature-status:partially-solved",
"owr-year:2017"
] | Quantum optimal-transport metrics and quantum Benamou--Brenier-type formulas have been developed for finite-dimensional algebras, but a general quantum optimal-transport formulation remains incomplete. | [
{
"url": "https://doi.org/10.1007/s10955-020-02682-1",
"label": "Quantum statistical learning"
},
{
"url": "https://arxiv.org/abs/2105.06922",
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{
"url": "https://oa.tib.eu/renate/bitstreams/63dd963a-2f59-4c50-b626-ffc98e104dc8/download",
"label"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/56 | null | null | null | Can the pseudo-metric used for quantum mean-field dynamics be formulated through a quantum analogue of optimal transport, such as a Benamou-Brenier variational formula? | Can the pseudo-metric used for quantum mean-field dynamics be formulated through a quantum analogue of optimal transport, such as a Benamou-Brenier variational formula? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Classical and Quantum Mechanical Models of Many-Particle Systems (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/56, pp. 3345--3425 |
30,003,675 | OWR-15962-001 | Epidemic Phase Transitions on General Weighted Networks | For sequences of finite weighted networks with an SIS stationary infected count, does a separation between sublinear and linear infection at two virulence thresholds imply analogous phase-transition behavior in general networks? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470](https://doi.org/10.4171/owr/2017/57)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,017 | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report shows that this is an overview-level summary of the explicit SIS phase-transition conjecture retained as OWR-15962-002. ) | [
"OWR-15962-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15962-001",
"literature-status:open",
"owr-year:2017"
] | The phase transition is understood for the general susceptible-infected model, but the conjectured analogous transitions for other epidemic-type models remain unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46721",
"label": "OWR Report 57/2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/57 | null | null | null | null | For sequences of finite weighted networks with an SIS stationary infected count, does a separation between sublinear and linear infection at two virulence thresholds imply analogous phase-transition behavior in general networks? | unrecoverable | The official report shows that this is an overview-level summary of the explicit SIS phase-transition conjecture retained as OWR-15962-002. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470 |
30,003,676 | OWR-15962-002 | Sharp Virulence Thresholds for Stationary SIS Infection | For each $n$, consider a finite connected weighted network with recovery rates $\mu_v$, and let $X^{(n)}_{\theta,\varepsilon}$ be the stationary number of infected vertices in the SIS process whose infection rate at $v$ is $$\varepsilon+\theta\sum_{y\ \mathrm{infected}}w_{vy}.$$ Assume that there are $0<\theta_*<\theta... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470](https://doi.org/10.4171/owr/2017/57)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open 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-15962-001"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15962-002",
"literature-status:open",
"owr-year:2017"
] | The Aldous SIS threshold conjecture, including sublinear versus linear infection under the stated virulence and degree conditions, remains an open problem. | [
{
"url": "https://ems.press/content/serial-article-files/46721",
"label": "OWR Report 57/2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/57 | null | null | null | For each $n$, consider a finite connected weighted network with recovery rates $\mu_v$, and let $X^{(n)}_{\theta,\varepsilon}$ be the stationary number of infected vertices in the SIS process whose infection rate at $v$ is $$\varepsilon+\theta\sum_{y\ \mathrm{infected}}w_{vy}.$$ Assume that there are $0<\theta_*<\theta... | Under the stated SIS threshold assumptions, do there exist intermediate virulence values theta_n such that infection is sublinear below theta_n and linear above theta_n, with high probability, for every fixed margin? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470 |
30,003,677 | OWR-15962-003 | Strategic Starting Vertices in Competing First-Passage Percolation | In competing first-passage percolation on a finite-variance configuration model, can a weaker type capture a positive fraction of the vertices when it starts from high-degree vertices and the stronger type starts from a low-degree vertex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470](https://doi.org/10.4171/owr/2017/57)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,017 | 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": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15962-003",
"literature-status:open",
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] | Known competing first-passage results treat uniformly random starts and related regimes, while the high-degree-versus-low-degree initial placement question remains a stated further problem. | [
{
"url": "https://arxiv.org/abs/1711.02902",
"label": "Competing first passage percolation on random graphs"
},
{
"url": "https://ems.press/content/serial-article-files/46721",
"label": "OWR Report 57/2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/57 | null | null | null | In competing first-passage percolation on a finite-variance configuration model, can a weaker type capture a positive fraction of the vertices when it starts from high-degree vertices and the stronger type starts from a low-degree vertex? | In competing first-passage percolation on a finite-variance configuration model, can a weaker type capture a positive fraction of vertices by starting at high-degree vertices while the stronger type starts at a low-degree vertex? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470 |
30,003,678 | OWR-15962-004 | Recurrence of High-Dimensional Scale-Free Percolation | Consider scale-free percolation on $\mathbb Z^d$ in a parameter regime with a unique infinite cluster, $\gamma>2$, and $\alpha>2d$. In dimensions $d\geq3$, is the simple random walk on the infinite cluster recurrent or transient? Resolve the analogous open regime for long-range percolation as well. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470](https://doi.org/10.4171/owr/2017/57)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,017 | 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-15962-004",
"literature-status:open",
"owr-year:2017"
] | Transience versus recurrence in the stated strong-decay d-dimensional scale-free percolation regime was explicitly unresolved, and later long-range-percolation advances do not settle this exact scale-free model question. | [
{
"url": "https://doi.org/10.1214/16-AAP1270",
"label": "Scale-free percolation and long-range percolation"
},
{
"url": "https://arxiv.org/abs/2312.04099",
"label": "Continuity and shape theorem for long-range percolation"
},
{
"url": "https://ems.press/content/serial-article-files/46721... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/57 | null | null | null | Consider scale-free percolation on $\mathbb Z^d$ in a parameter regime with a unique infinite cluster, $\gamma>2$, and $\alpha>2d$. In dimensions $d\geq3$, is the simple random walk on the infinite cluster recurrent or transient? Resolve the analogous open regime for long-range percolation as well. | In regime (ii) of the stated theorem, does transience or recurrence occur in dimensions d at least 3, including for long-range percolation? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470 |
30,003,679 | OWR-15962-005 | Sharp Polynomial-Time Upper Bounds for Minimum Bisection | Construct polynomial-time computable bounds $\operatorname{UB}(G)$ for the minimum-bisection objective $\operatorname{OPT}(G)$ such that $\operatorname{OPT}(G)\leq\operatorname{UB}(G)$ for every graph $G$ and $\operatorname{UB}(G)$ is asymptotically sharp on random graphs. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470](https://doi.org/10.4171/owr/2017/57)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,017 | 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-15962-005",
"literature-status:partially-solved",
"owr-year:2017"
] | Polynomial-time semidefinite programs give rigorous upper bounds with the correct leading-order scale for sparse random graphs, but the requested generally sharp approximation to the optimum remains open. | [
{
"url": "https://arxiv.org/abs/1504.05910",
"label": "Semidefinite programs on sparse random graphs"
},
{
"url": "https://arxiv.org/abs/1411.1698",
"label": "On the Max-Cut of sparse random graphs"
},
{
"url": "https://ems.press/content/serial-article-files/46721",
"label": "OWR Rep... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/57 | null | null | null | Construct polynomial-time computable bounds $\operatorname{UB}(G)$ for the minimum-bisection objective $\operatorname{OPT}(G)$ such that $\operatorname{OPT}(G)\leq\operatorname{UB}(G)$ for every graph $G$ and $\operatorname{UB}(G)$ is asymptotically sharp on random graphs. | What polynomial-time computable upper bounds UB(G) for the minimum-bisection objective OPT(G) are valid for every graph and asymptotically tight on random graphs? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470 |
30,003,680 | OWR-15962-007 | Information–Computation Gaps in Sparse Linear Regression | In sparse high-dimensional linear regression, when the sample size $n$ lies between the information-theoretic threshold $n_*$ and the algorithmic threshold $n_{\mathrm{alg}}$, is the signal $\beta_*$ information-theoretically recoverable, and is efficient recovery possible? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470](https://doi.org/10.4171/owr/2017/57)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,017 | 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-15962-007",
"literature-status:partially-solved",
"owr-year:2017"
] | Information-theoretic thresholds, all-or-nothing behavior, and algorithmic barriers are established in important sparse-regression regimes, but the full information-versus-efficient-recovery question is not resolved. | [
{
"url": "https://arxiv.org/abs/1701.04455",
"label": "High-dimensional regression with binary coefficients"
},
{
"url": "https://arxiv.org/abs/1711.04952",
"label": "Sparse regression algorithmic barriers"
},
{
"url": "https://arxiv.org/abs/1903.05046",
"label": "All-or-nothing in s... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/57 | null | null | null | In sparse high-dimensional linear regression, when the sample size $n$ lies between the information-theoretic threshold $n_*$ and the algorithmic threshold $n_{\mathrm{alg}}$, is the signal $\beta_*$ information-theoretically recoverable, and is efficient recovery possible? | When the sample size n lies between the information-theoretic threshold n-star and the algorithmic threshold n-alg in sparse high-dimensional linear regression, is there enough information to recover beta-star, and can an efficient recovery algorithm be constructed? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Network Models: Structure and Function (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/57, pp. 3427--3470 |
30,003,681 | OWR-15963-001 | Historical Research Questions on Embodied Mathematics | What mathematics is involved in mathematical instruments, what does it mean for a material artefact to embody mathematics, and how do non-mathematicians engage with embodied mathematics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560](ht... | 3 | open | null | 2,017 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"name": "miscellaneous",
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"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report presents these as framing questions for historical, philosophical, and educational inquiry rather than as a standalone m) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15963-001",
"literature-status:open",
"owr-year:2017"
] | Research on embodied mathematics and material encounters supplies case studies and conceptual frameworks, but the broad questions about mathematical embodiment and non-mathematicians engagement have no general resolution. | [
{
"url": "https://ems.press/content/serial-article-files/46722",
"label": "OWR Report 58/2019"
},
{
"url": "https://link.springer.com/article/10.1007/s10649-015-9657-4",
"label": "Material encounters and media events"
},
{
"url": "https://link.springer.com/article/10.1007/s11858-019-0104... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/58 | null | null | null | null | What mathematics is involved in mathematical instruments, what does it mean for a material artefact to embody mathematics, and how do non-mathematicians engage with embodied mathematics? | unrecoverable | The official report presents these as framing questions for historical, philosophical, and educational inquiry rather than as a standalone mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560 |
30,003,682 | OWR-15963-003 | Historical Proposal for Concrete Infinitesimal Analysis | Can infinitesimal analysis be given a rigorous yet concrete foundation using a calculus based on historical geometric insights? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560](ht... | 3 | partially_solved | null | 2,017 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The source is a historical and foundational research proposal about machine-based calculus, not a sufficiently specified mathematical conjec) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15963-003",
"literature-status:partially-solved",
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] | Tractional and constructive approaches provide rigorous partial formalisms, but no generally accepted concrete foundation of infinitesimal analysis based on the proposed historical constructions has been completed. | [
{
"url": "https://ems.press/content/serial-article-files/46722",
"label": "OWR Report 58/2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/58 | null | null | null | null | Can infinitesimal analysis be given a rigorous yet concrete foundation using a calculus based on historical geometric insights? | unrecoverable | The source is a historical and foundational research proposal about machine-based calculus, not a sufficiently specified mathematical conjecture or construction problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560 |
30,003,683 | OWR-15963-004 | Historical Study of Instruments in Medieval Monasteries | What motivated monks to study mathematical instruments, and how were those instruments studied and used in monasteries? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560](ht... | 3 | open | null | 2,017 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 source poses historical questions about evidence, motivations, and practice in medieval monasteries rather than a mathematical problem. ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15963-004",
"literature-status:open",
"owr-year:2017"
] | This broad historical question has no complete account in the literature of monastic motivations, study, and use of instruments; it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2017/58",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/58 | null | null | null | null | What motivated monks to study mathematical instruments, and how were those instruments studied and used in monasteries? | unrecoverable | The source poses historical questions about evidence, motivations, and practice in medieval monasteries rather than a mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560 |
30,003,684 | OWR-15963-005 | Historical Uses of Portable Astronomical Instruments | What were portable astronomical instruments used for in late-medieval England, and how much were they actually carried around? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560](ht... | 3 | open | null | 2,017 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "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 source asks an archaeological and historical question about the use and portability of medieval instruments, not a mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15963-005",
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{
"url": "https://doi.org/10.4171/owr/2017/58",
"label": "Oberwolfach report"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/58 | null | null | null | null | What were portable astronomical instruments used for in late-medieval England, and how much were they actually carried around? | unrecoverable | The source asks an archaeological and historical question about the use and portability of medieval instruments, not a mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560 |
30,003,685 | OWR-15963-006 | Historical Classification of Optical Diagrams as Instruments | Were early modern optical diagrams mathematical instruments? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560](ht... | 3 | open | null | 2,017 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "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 source develops a historiographical classification question about optical diagrams rather than a mathematical problem. No separate clean) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15963-006",
"literature-status:open",
"owr-year:2017"
] | The record itself notes that the definition is partly arbitrary and supplies no settled criterion that resolves the definitional question. | [
{
"url": "https://doi.org/10.4171/owr/2017/58",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/58 | null | null | null | null | Were early modern optical diagrams mathematical instruments? | unrecoverable | The source develops a historiographical classification question about optical diagrams rather than a mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560 |
30,003,686 | OWR-15986-001 | Graph-Cototal Enumeration Degrees and Punctiform Decompositions | Is every almost-total enumeration degree graph-cototal? Equivalently, does the Hilbert cube $[0,1]^\omega$ admit a countable decomposition into punctiform spaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41](https://doi.org/10.4171/owr/2018/1)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,018 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15986-001",
"literature-status:open",
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] | The report explicitly presents the almost-total versus graph-cototal question and its punctiform-decomposition equivalent as open; no later resolution was located. | [
{
"url": "https://doi.org/10.4171/owr/2018/1",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/1 | null | null | null | Is every almost-total enumeration degree graph-cototal? Equivalently, does the Hilbert cube $[0,1]^\omega$ admit a countable decomposition into punctiform spaces? | Is every almost-total enumeration degree graph-cototal? Equivalently, does the Hilbert cube [0,1]^{\omega} admit a countable decomposition into punctiform spaces? | 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 | Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41 |
30,003,687 | OWR-15986-002 | Algorithmic Randomness and Uniform Distribution | How is algorithmic randomness related to the classical theory of uniform distribution of sequences of real numbers? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41](https://doi.org/10.4171/owr/2018/1)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,018 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15986-002",
"literature-status:partially-solved",
"owr-year:2018"
] | Avigad proved several implications and separations between algorithmic randomness notions and uniform distribution, but the broad relationship asked for in the record is not exhausted. | [
{
"url": "https://arxiv.org/abs/1203.4126",
"label": "Avigad, Uniform distribution and algorithmic randomness"
},
{
"url": "https://doi.org/10.4171/owr/2018/1",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/1 | null | null | null | How is algorithmic randomness related to the classical theory of uniform distribution of sequences of real numbers? | How is algorithmic randomness related to the classical theory of uniform distribution of sequences of real numbers? | 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 | Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41 |
30,003,688 | OWR-15986-003 | Finite Families with Two-Element Rogers Semilattices | For each $n\geq2$, does there exist a finite family $\mathcal S$ of $\Sigma_n^0$ sets whose Rogers semilattice has exactly two elements $\alpha$ and $\beta$, where $\alpha$ is Friedberg and every numbering $\gamma$ not equivalent to $\alpha$ satisfies $\beta\leq\gamma$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41](https://doi.org/10.4171/owr/2018/1)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,018 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15986-003",
"literature-status:open",
"owr-year:2018"
] | The extracted record omits the properties and family being quantified, so no definite claim can be verified; it is therefore normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2018/1",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/1 | null | null | null | For each $n\geq2$, does there exist a finite family $\mathcal S$ of $\Sigma_n^0$ sets whose Rogers semilattice has exactly two elements $\alpha$ and $\beta$, where $\alpha$ is Friedberg and every numbering $\gamma$ not equivalent to $\alpha$ satisfies $\beta\leq\gamma$? | Does there exist a finite family of\mathop{\Sigma}\nolimits^0_n sets with the stated Rogers-semilattice property, and does there exist a family with these properties at all? | 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 | Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41 |
30,003,689 | OWR-15986-004 | Final Segments of Difference-C.E. Degrees | Which finite final segments occur in the degrees of d.c.e. sets? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41](https://doi.org/10.4171/owr/2018/1)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,018 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15986-004",
"literature-status:partially-solved",
"owr-year:2018"
] | Lempp and collaborators proved that every finite distributive lattice occurs as a final segment, but the complete classification of finite final segments of the d.c.e. degrees remains unresolved. | [
{
"url": "https://arxiv.org/abs/2403.04254",
"label": "Lempp et al., Finite final segments"
},
{
"url": "https://doi.org/10.4171/owr/2018/1",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/1 | null | null | null | Which finite final segments occur in the degrees of d.c.e. sets? | Which finite final segments occur in the degrees of d.c.e. sets? | 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 | Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41 |
30,003,690 | OWR-15986-005 | Composite of Randomness and Hindman-Theorem Questions | Does there exist a Martin-Löf random real x such that, for all sufficiently large N, the discrepancy of (2^n x)_{n\geq 1} is O((\log N)/N)? For which n does there exist a computable instance of Hindman's theorem for two colors restricted to sums of length n with no \Sigma^0_n solution? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41](https://doi.org/10.4171/owr/2018/1)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,018 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official open-problem section shows that this extraction concatenates independent questions on low discrepancy of a Martin–Löf random re) | null | null | [Discussion #4 unrefereed claim, 2026-10-15] I have released an unrefereed preprint, **On a Question of Becher and Slaman: For Kurtz Random x the Discrepancy of (2^n x) Is Not O((log N)/N)** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23400059) | [
"owr",
"oberwolfach-reports",
"OWR-15986-005",
"literature-status:partially-solved",
"owr-year:2018"
] | The exact-two-sum two-color case now has a computable instance with no Sigma two solution, while the general n question in the record and the stated Martin-Lof discrepancy question remain unresolved. | [
{
"url": "https://math.uchicago.edu/~drh/Papers/hindman.html",
"label": "Csima et al., exact-two-sum Hindman theorem"
},
{
"url": "https://doi.org/10.4171/owr/2018/1",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/1 | null | null | null | null | Does there exist a Martin-Löf random real x such that, for all sufficiently large N, the discrepancy of (2^n x)_{n\geq 1} is O((\log N)/N)? For which n does there exist a computable instance of Hindman's theorem for two colors restricted to sums of length n with no \Sigma^0_n solution? | unrecoverable | The official open-problem section shows that this extraction concatenates independent questions on low discrepancy of a Martin–Löf random real and computable instances of restricted Hindman's theorem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41 |
30,003,691 | OWR-15986-006 | Composite of Randomness and Scott-Sentence Questions | Does there exist a Martin-Löf random real with discrepancy O((\log N)/N) for (2^n x)_{n\geq 1}, and does there exist a computable finitely presented group with no d-\Sigma^0_2 Scott sentence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41](https://doi.org/10.4171/owr/2018/1)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,018 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official open-problem section shows that this extraction concatenates the low-discrepancy question with a separate computable-group Scot) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15986-006",
"literature-status:open",
"owr-year:2018"
] | The cited exact-two-sum result settles only the n equals two case; the higher-n Hindman question and the finitely presented group Scott-sentence question remain open. | [
{
"url": "https://homepages.math.uic.edu/~mht/papers/fggroups.pdf",
"label": "Harrison-Trainor and Ho, finitely generated groups"
},
{
"url": "https://doi.org/10.4171/owr/2018/1",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/1 | null | null | null | null | Does there exist a Martin-Löf random real with discrepancy O((\log N)/N) for (2^n x)_{n\geq 1}, and does there exist a computable finitely presented group with no d-\Sigma^0_2 Scott sentence? | unrecoverable | The official open-problem section shows that this extraction concatenates the low-discrepancy question with a separate computable-group Scott-sentence question. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41 |
30,003,692 | OWR-15986-007 | Composite of Three Independent Computability Questions | Are the reductions List2N \leq_W UCNN strict? Are computably compact computably Hausdorff spaces also computably regular? Does there exist a model of ZF with a cofinal maximal chain of Turing degrees of order type \omega_1 but no well-ordering of the reals? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41](https://doi.org/10.4171/owr/2018/1)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | partially_solved | null | 2,018 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1017/jsl.2020.12",
"checked_at": "2026-10-02",
"kind": "partial",
"evidence": "published"
} | Unrecoverable OWR statement (The official open-problem section shows that this extraction combines independent questions about Weihrauch degrees, computable regularity, ) | null | null | [Discussion #4 literature review, 2026-10-02] **partially_solved** (two of three questions answered). The record bundles three items of the problem list in OWR 1/2018 (p. 36). A. Pauly's Question 2, whether List\_{2^ℕ} ≤\_W UC\_{ℕ^ℕ} is strict, was answered yes during the workshop by T. Kihara, as the report says; a pu... | [
"owr",
"oberwolfach-reports",
"OWR-15986-007",
"literature-status:open",
"owr-year:2018"
] | The first subquestion was answered yes and the compact-Hausdorff regularity claim was disproved, but the cited consistency result gives a cofinal chain rather than the requested cofinal maximal chain; that final question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/1",
"label": "Oberwolfach report"
},
{
"url": "https://ems.press/content/serial-article-files/46899",
"label": "Schroder, Effectively Hausdorff spaces"
},
{
"url": "https://doi.org/10.1090/S0002-9939-2014-11868-5",
"label": "Wang, Wu, and Yu... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/1 | null | null | null | null | Are the reductions List2N \leq_W UCNN strict? Are computably compact computably Hausdorff spaces also computably regular? Does there exist a model of ZF with a cofinal maximal chain of Turing degrees of order type \omega_1 but no well-ordering of the reals? | unrecoverable | The official open-problem section shows that this extraction combines independent questions about Weihrauch degrees, computable regularity, and models of ZF; two of the component questions were answered during or before publication of the report. No separate clean statement is promoted, and the original record remains ... | null | null | null | null | null | Computability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/1, pp. 5--41 |
30,003,693 | OWR-15987-001 | Combinatorial Determination of Arrangement Milnor-Fiber Betti Numbers | Are the Betti numbers $b_i(F)$ of the Milnor fiber $F$ of a complex hyperplane arrangement determined by the arrangement's combinatorial data $d_{\mathcal A}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 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-15987-001",
"literature-status:open",
"owr-year:2018"
] | The same-combinatorics arrangement-group problem was resolved, but the record explicitly leaves the Betti-number question for Milnor fibers open. | [
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Are the Betti numbers $b_i(F)$ of the Milnor fiber $F$ of a complex hyperplane arrangement determined by the arrangement's combinatorial data $d_{\mathcal A}$? | Are the Betti numbers b_i(F) of the Milnor fiber of a complex hyperplane arrangement determined by its combinatorial data d_A? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,694 | OWR-15987-002 | Combinatorial Determination of Milnor-Fiber Monodromy | Let $\mathcal{A}$ be a central hyperplane arrangement in $\mathbb{C}^n$ with Milnor fiber $F$ and algebraic monodromy homomorphism $h : H^1(F; \mathbb{C}) \to H^1(F; \mathbb{C})$. Is the first-cohomology monodromy homomorphism $H^1(F) \to H^1(F)$ combinatorially determined by the intersection lattice / arrangement data... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 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-15987-002",
"literature-status:open",
"owr-year:2018"
] | The report explicitly calls it open whether the Milnor-fiber H one monodromy is determined by the arrangement intersection data, and no resolution was located. | [
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Let $\mathcal{A}$ be a central hyperplane arrangement in $\mathbb{C}^n$ with Milnor fiber $F$ and algebraic monodromy homomorphism $h : H^1(F; \mathbb{C}) \to H^1(F; \mathbb{C})$. Is the first-cohomology monodromy homomorphism $H^1(F) \to H^1(F)$ combinatorially determined by the intersection lattice / arrangement data... | Is the monodromy homomorphism H^1(F) \to H^1(F) of the Milnor fiber determined by the arrangement data d_A? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,695 | OWR-15987-003 | Polynomial Degree of IA-Group Homology Functors | For every $k\geq0$, is the functor $H_k(\operatorname{IA}_\bullet)$ from the category $S(\mathbb Z)$ to abelian groups weakly polynomial of degree at most $3k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15987-003",
"literature-status:open",
"owr-year:2018"
] | The extracted statement is explicitly presented as Djament's conjecture; the searched literature did not establish the asserted weak polynomial degree for all homological degrees. | [
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1093/imrn/rnx099",
"label": "Djament and Vespa, weak polynomial functors"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | For every $k\geq0$, is the functor $H_k(\operatorname{IA}_\bullet)$ from the category $S(\mathbb Z)$ to abelian groups weakly polynomial of degree at most $3k$? | Conjecture: for every k\geq 0, the functor H_k(IA_{\bullet}) from S(\mathbb{Z}) to Ab is weak polynomial of degree at most 3k. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,696 | OWR-15987-004 | Continuous Choices of Points on Smooth Cubic Curves | Classify the multisections of the universal family of smooth plane cubic curves: for which integers $n$ can one continuously choose $n$ distinct unlabeled points on every smooth cubic, and how are all such choices classified up to homotopy? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | partially_solved | null | 2,018 | 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... | [
"OWR-15987-005"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15987-004",
"literature-status:partially-solved",
"owr-year:2018"
] | Nonexistence for many degrees, uniqueness at degree nine, nonexistence at degree eighteen, and newer rigidity at degree twenty-seven are known, but the classification for every positive degree remains open. | [
{
"url": "https://arxiv.org/abs/2101.03824",
"label": "Banerjee and Chen, cubic plane curves"
},
{
"url": "https://arxiv.org/abs/2607.14128",
"label": "Yao, rigidity of cubic multisections"
},
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Classify the multisections of the universal family of smooth plane cubic curves: for which integers $n$ can one continuously choose $n$ distinct unlabeled points on every smooth cubic, and how are all such choices classified up to homotopy? | What are all the possible ways to continuously choose n distinct unlabeled points on every smooth cubic plane curve as the curve varies in a family? | corrected_verified | The official report was checked. This record is the canonical form of the source multisection-classification problem. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,697 | OWR-15987-005 | Duplicate Universal Smooth-Cubic Multisection Problem | Classify the multisections of the universal smooth-cubic-curve bundle; in particular, is there no multisection of degree n<9? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | partially_solved | null | 2,018 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report contains one classification problem for multisections of the universal smooth cubic family, represented canonically by O) | [
"OWR-15987-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15987-005",
"literature-status:partially-solved",
"owr-year:2018"
] | The degree-below-nine conjecture is proved, degree nine is unique up to homotopy, degree eighteen is impossible, and many constructions are known, but the requested full classification remains open. | [
{
"url": "https://arxiv.org/abs/1806.10207",
"label": "Chen, obstructions for cubic plane curves"
},
{
"url": "https://arxiv.org/abs/2101.03824",
"label": "Banerjee and Chen, cubic plane curves"
},
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | null | Classify the multisections of the universal smooth-cubic-curve bundle; in particular, is there no multisection of degree n<9? | unrecoverable | The official report contains one classification problem for multisections of the universal smooth cubic family, represented canonically by OWR-15987-004. This record repeats that problem and appends a degree-below-nine claim already proved in the same report. No separate clean statement is promoted; the original record... | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,698 | OWR-15987-007 | Closed Formulas for Braid-Matroid Kazhdan–Lusztig Polynomials | Find a simple closed formula for the Kazhdan–Lusztig polynomials of braid matroids. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | partially_solved | null | 2,018 | 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-15987-007",
"literature-status:partially-solved",
"owr-year:2018"
] | Explicit generating and combinatorial results now determine the top coefficient and substantially advance computation, but a simple closed formula for the full braid-matroid polynomials is still not established. | [
{
"url": "https://arxiv.org/abs/2303.02253",
"label": "Ferroni and Larson, braid matroid polynomials"
},
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Find a simple closed formula for the Kazhdan–Lusztig polynomials of braid matroids. | Find a simple closed formula for the braid-matroid Kazhdan--Lusztig polynomials. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,699 | OWR-15987-008 | Coefficient Complexity of Braid-Matroid Kazhdan–Lusztig Polynomials | Can the known flag-Whitney-number and Stirling-number formulas for coefficients of braid-matroid Kazhdan–Lusztig polynomials be converted into effective complexity bounds and computations of the remaining coefficients of $P(B_n,t)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | partially_solved | null | 2,018 | 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-15987-008",
"literature-status:partially-solved",
"owr-year:2018"
] | Ferroni and Larson proved the previously conjectured top-coefficient formula, but the complexity questions and a complete explicit formula requested in the record remain open. | [
{
"url": "https://arxiv.org/abs/2303.02253",
"label": "Ferroni and Larson, braid matroid polynomials"
},
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Can the known flag-Whitney-number and Stirling-number formulas for coefficients of braid-matroid Kazhdan–Lusztig polynomials be converted into effective complexity bounds and computations of the remaining coefficients of $P(B_n,t)$? | Do Theorems 2, 3, and 4 imply information about the complexity of the coefficients of braid-matroid Kazhdan--Lusztig polynomials? Could they help compute the conjectured top coefficient of P(B_n,t)? | corrected_verified | The official report was checked. The reconstruction replaces references to numbered theorems with the combinatorial formulas they concern and omits the now-resolved top-coefficient clause. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,700 | OWR-15987-009 | Coefficient Formulas for Polynomial Roots | Find and understand formulas for the roots of $P(z)=z^n+a_1z^{n-1}+\cdots+a_n$ in terms of its coefficients. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | partially_solved | null | 2,018 | 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-15987-009",
"literature-status:partially-solved",
"owr-year:2018"
] | The impossibility of radical formulas from degree five onward and classical reductions such as Bring's are established, but the broader request for formulas and understanding of roots is not completely resolved. | [
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1803.04063",
"label": "Farb and Wolfson, resolvent degree"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Find and understand formulas for the roots of $P(z)=z^n+a_1z^{n-1}+\cdots+a_n$ in terms of its coefficients. | Find and understand formulas for the roots of P(z)=z^n+a_1z^{n-1}+\cdots+a_n in terms of its coefficients. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,701 | OWR-15987-010 | Resolvent Degree of Polynomial Root Covers | Let $\widetilde{\mathcal P}_n\to\mathcal P_n$ be the finite cover from monic degree-$n$ polynomials with a chosen root to all monic degree-$n$ polynomials. Determine its resolvent degree $\operatorname{RD}(\widetilde{\mathcal P}_n/\mathcal P_n)$; in particular, decide Hilbert's sextic, thirteenth, and octic conjectures... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 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-15987-010",
"literature-status:open",
"owr-year:2018"
] | The general resolvent-degree problem and Hilbert's sextic, thirteenth, and octic conjectures remain open; only upper bounds are known for the displayed target values. | [
{
"url": "https://arxiv.org/abs/2406.15954",
"label": "Edens and Reichstein, Hilbert thirteen in prime characteristic"
},
{
"url": "https://arxiv.org/abs/1803.04063",
"label": "Farb and Wolfson, resolvent degree"
},
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Let $\widetilde{\mathcal P}_n\to\mathcal P_n$ be the finite cover from monic degree-$n$ polynomials with a chosen root to all monic degree-$n$ polynomials. Determine its resolvent degree $\operatorname{RD}(\widetilde{\mathcal P}_n/\mathcal P_n)$; in particular, decide Hilbert's sextic, thirteenth, and octic conjectures... | For the finite map of monic degree-n polynomials with a chosen root to the space P_n of monic degree-n polynomials, compute its resolvent degree RD; in particular, decide Hilbert's sextic, 13th, and octic conjectures. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,702 | OWR-15987-011 | Global Resolvent Degree of General Polynomial Equations | Determine the global resolvent degree of solving general polynomial equations, including whether the parameter reductions conjectured by Hilbert are optimal. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 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-15987-011",
"literature-status:open",
"owr-year:2018"
] | The global algebraic reduction problem remains open even though Kolmogorov and Arnold solved the continuous analogue and removed local topological obstructions. | [
{
"url": "https://arxiv.org/abs/2406.15954",
"label": "Edens and Reichstein, Hilbert thirteen in prime characteristic"
},
{
"url": "https://arxiv.org/abs/1803.04063",
"label": "Farb and Wolfson, resolvent degree"
},
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Determine the global resolvent degree of solving general polynomial equations, including whether the parameter reductions conjectured by Hilbert are optimal. | Determine the global resolvent degree of solving general polynomial equations, including whether the parameter reductions conjectured by Hilbert are optimal. | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,703 | OWR-15987-013 | Equality of the Andreadakis and Representation-Ring Filtrations | Let $A_n(k)$ be the Andreadakis–Johnson filtration of $\operatorname{Aut}(F_n)$, and let $D_n(k)$ be the kernel of its action on $J/J^{k+1}$, where $J$ is the augmentation ideal of the universal $\operatorname{SL}_2(\mathbb C)$-representation ring of $F_n$. Is
$$A_n(k)=D_n(k)$$
for every $k\geq1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15987-013",
"literature-status:open",
"owr-year:2018"
] | The equality of the two displayed families is stated only as a conjecture in the record, and no later proof or counterexample was located. | [
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Let $A_n(k)$ be the Andreadakis–Johnson filtration of $\operatorname{Aut}(F_n)$, and let $D_n(k)$ be the kernel of its action on $J/J^{k+1}$, where $J$ is the augmentation ideal of the universal $\operatorname{SL}_2(\mathbb C)$-representation ring of $F_n$. Is
$$A_n(k)=D_n(k)$$
for every $k\geq1$? | Conjecture: A_n(k)=D_n(k) for every k\geq 1. | corrected_verified | The official report was checked. The reconstruction restores both filtrations and the representation-ring augmentation ideal needed to interpret the conjectured equality. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,704 | OWR-15987-014 | Finite Generation of Graph-Configuration Homology Functors | Does the finite-generation result for the functor $G\mapsto H_q(\operatorname{Conf}_k(G))$ extend from $q\leq1$ to every $q\geq0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 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-15987-014",
"literature-status:open",
"owr-year:2018"
] | Finite generation is proved for graph homology in degree at most one and for the stated FI-graph families, but whether it holds for all homological degrees in the general graph category remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1805.05316",
"label": "Ramos, FI-algebras and graph configuration spaces"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Does the finite-generation result for the functor $G\mapsto H_q(\operatorname{Conf}_k(G))$ extend from $q\leq1$ to every $q\geq0$? | Does the finite-generation result for the functor G\mapsto H_q(\operatorname{Conf}_k(G)) extend from q\leq 1 to every q\geq 0? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,705 | OWR-15987-016 | Symmetric-Group Characters Determined by Reflection Length | Give a simple description of the characters $\chi(g)$ of $S_n$ that depend only on the reflection length $\ell(g)$, equivalently only on the number of cycles of $g$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 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-15987-016",
"literature-status:open",
"owr-year:2018"
] | The report explicitly leaves open a satisfactory description of the S_n characters depending only on cycle count; the cited partial character results do not resolve that classification problem. | [
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach Report 2/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Give a simple description of the characters $\chi(g)$ of $S_n$ that depend only on the reflection length $\ell(g)$, equivalently only on the number of cycles of $g$. | Give a simple description of the characters \chi(g) of S_n that depend only on the reflection length \ell(g), equivalently only on the number of cycles of g. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,706 | OWR-15987-017 | Finitely Generated Categories for Slowly Growing Braid Representations | Is there a category playing the role for braid groups $B_n$ that FI plays for symmetric groups $S_n$, such that every slowly growing sequence of $B_n$-representations arises from a finitely generated module over that category? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-15987-018"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15987-017",
"literature-status:open",
"owr-year:2018"
] | The FI-type classification conjecture for slowly growing braid-group representations remains unresolved in general; known linear-growth cases do not establish the proposed analogue for all slow growth. | [
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach Report 2/2018"
},
{
"url": "https://arxiv.org/abs/math/0502118",
"label": "Marin, braid-group representations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Is there a category playing the role for braid groups $B_n$ that FI plays for symmetric groups $S_n$, such that every slowly growing sequence of $B_n$-representations arises from a finitely generated module over that category? | Is there an analogue for the braid group B_n of the FI-module theorem describing all slowly growing representations of S_n? Conjecturally, all slowly growing representations of B_n arise from finitely generated modules over a suitable category. | corrected_verified | The official problem-session report was checked. This is the canonical, more complete extraction of its conjecture about slowly growing braid-group representations. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,707 | OWR-15987-018 | Duplicate FI-Type Stability Problem for Braid Groups | Is there an analogue of the polynomial-growth FI-module representation theorem when S_n is replaced by the braid group B_n? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report states one conjectural FI-type classification of slowly growing braid-group representations, represented canonically by ) | [
"OWR-15987-017"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15987-018",
"literature-status:open",
"owr-year:2018"
] | This is the same unresolved braid-group analogue question stated in the report: the known linear-growth remark does not settle the general FI-like structure for B_n. | [
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach Report 2/2018"
},
{
"url": "https://arxiv.org/abs/math/0502118",
"label": "Marin, braid-group representations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | null | Is there an analogue of the polynomial-growth FI-module representation theorem when S_n is replaced by the braid group B_n? | unrecoverable | The official report states one conjectural FI-type classification of slowly growing braid-group representations, represented canonically by OWR-15987-017. This record is a shorter restatement of the same question. No separate clean statement is promoted; the original record remains publicly visible and retained for pro... | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,708 | OWR-15987-019 | Homological Stability for Indefinite Orthogonal Groups | For a maximal ordered field $k$ and the inclusion $O_n(k)\times O_i(k)\hookrightarrow O_{n,i}(k)$, does the induced map on discrete group homology $H_d(-,\mathbb Z)$ become an isomorphism for $n$ sufficiently large relative to $d$ and $i$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | partially_solved | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15987-019",
"literature-status:partially-solved",
"owr-year:2018"
] | Homological stability for broad families of orthogonal groups is proved, but the exact mixed-form inclusion over a maximal ordered field and the full stated range of i are not thereby completely settled. | [
{
"url": "https://arxiv.org/abs/1812.08742",
"label": "Sprehn--Wahl, classical-group stability"
},
{
"url": "https://arxiv.org/abs/2206.00981",
"label": "Schlichting--Sood, orthogonal stability"
},
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach Report 2/2018"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | For a maximal ordered field $k$ and the inclusion $O_n(k)\times O_i(k)\hookrightarrow O_{n,i}(k)$, does the induced map on discrete group homology $H_d(-,\mathbb Z)$ become an isomorphism for $n$ sufficiently large relative to $d$ and $i$? | For a maximal ordered field k and the inclusion O_n(k)\times O_i(k)\hookrightarrow O_{n,i}(k), does the induced map on discrete group homology H_d(-,\mathbb{Z}) become an isomorphism for n sufficiently large relative to d and i? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,709 | OWR-15987-020 | Recovering Toric Arrangement Posets from Complement Cohomology | For a central toric arrangement $A$ with layer poset $L$ and complement $M(A)$, does the cohomology algebra $H^\bullet(M(A))$ determine $L$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 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-15987-020",
"literature-status:open",
"owr-year:2018"
] | The poset determines the rational cohomology algebra, and integral counterexamples show limits of the converse framework, but no result establishes that the rational algebra recovers the toric layer poset. | [
{
"url": "https://arxiv.org/abs/1804.05767",
"label": "Pagaria, Two Examples of Toric Arrangements"
},
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach Report 2/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | For a central toric arrangement $A$ with layer poset $L$ and complement $M(A)$, does the cohomology algebra $H^\bullet(M(A))$ determine $L$? | For a central toric arrangement A with layer poset L and complement M(A), does the cohomology algebra H^\bullet(M(A)) determine L? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,710 | OWR-15987-021 | Periodicity of Twisted Outer-Automorphism-Group Cohomology | For each fixed $i$ and prime $p$, determine whether $H^i(\operatorname{Out}(F_n),(\mathbb Z/p\mathbb Z)^n)$ is eventually periodic as $n$ increases; if so, ask the same question for coefficients given by a polynomial functor or a VIC-module. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15987-021",
"literature-status:open",
"owr-year:2018"
] | The exact eventual-periodicity question for H^i(Out(F_n),(Z/pZ)^n), and its polynomial-functor or VIC variants, remains unresolved; rational representation-stability results do not answer this modular question. | [
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach Report 2/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | For each fixed $i$ and prime $p$, determine whether $H^i(\operatorname{Out}(F_n),(\mathbb Z/p\mathbb Z)^n)$ is eventually periodic as $n$ increases; if so, ask the same question for coefficients given by a polynomial functor or a VIC-module. | For each fixed i and prime p, determine whether H^i(\operatorname{Out}(F_n),(\mathbb Z/p\mathbb Z)^n) is eventually periodic as n increases; if so, ask the same question for coefficients given by a polynomial functor or a VIC-module. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,711 | OWR-15987-022 | Schwarz Genus of the Flex-Point Cover | Let $X$ be the space of smooth complex homogeneous cubic polynomials in three variables modulo $\mathbb C^\times$, and let $Y=\{(F,p):p\in\mathbb{CP}^2\text{ is a flex of }F=0\}$. The map $Y\to X$ is a degree-nine covering; determine its Schwarz genus. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 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-15987-022",
"literature-status:open",
"owr-year:2018"
] | For the flex cover of the moduli space of smooth plane cubics, the Schwarz genus is bounded below by 8 and above by 9; the literature leaves the choice between 8 and 9 open. | [
{
"url": "https://arxiv.org/abs/2306.17303",
"label": "Chen--Wan, flex-point topological complexity"
},
{
"url": "https://doi.org/10.1090/proc/17184",
"label": "Chen--Wan, Proceedings of the AMS"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Let $X$ be the space of smooth complex homogeneous cubic polynomials in three variables modulo $\mathbb C^\times$, and let $Y=\{(F,p):p\in\mathbb{CP}^2\text{ is a flex of }F=0\}$. The map $Y\to X$ is a degree-nine covering; determine its Schwarz genus. | Let X be the space of smooth complex homogeneous cubic polynomials in three variables modulo \mathbb C^\times, and let Y=\{(F,p):p\in\mathbb{CP}^2 is a flex of F=0\}. The map Y\to X is a degree-nine covering; determine its Schwarz genus. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,712 | OWR-15987-025 | Representation Stability and Compactifications for Braid Milnor Fibers | For the Milnor fiber $F_n=\{(x_1,\ldots,x_n):\prod_{i<j}(x_i-x_j)^2=1\}$, determine $H^*(F_n,\mathbb Q)$ as an $(S_n\times\mu_{n(n-1)})$-module; determine whether a category analogous to FI makes $H^i(F_n,\mathbb Q)$ a finitely generated module; and determine whether $M_{d,n}$ has a natural compactification. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | partially_solved | null | 2,018 | 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-15987-025",
"literature-status:partially-solved",
"owr-year:2018"
] | Miller and Tosteson proved representation stability and computed stable integral homology for the pure-braid Milnor fibers, answering the finite-generation direction, but the full S_n times root-of-unity module structure and compactification questions remain open. | [
{
"url": "https://doi.org/10.1090/tran/8466",
"label": "Miller--Tosteson, Transactions of the AMS"
},
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach Report 2/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | For the Milnor fiber $F_n=\{(x_1,\ldots,x_n):\prod_{i<j}(x_i-x_j)^2=1\}$, determine $H^*(F_n,\mathbb Q)$ as an $(S_n\times\mu_{n(n-1)})$-module; determine whether a category analogous to FI makes $H^i(F_n,\mathbb Q)$ a finitely generated module; and determine whether $M_{d,n}$ has a natural compactification. | For the Milnor fiber F_n=\{(x_1,\ldots,x_n):\prod_{i<j}(x_i-x_j)^2=1\}, determine H^*(F_n,\mathbb Q) as an (S_n\times\mu_{n(n-1)})-module; determine whether a category analogous to FI makes H^i(F_n,\mathbb Q) a finitely generated module; and determine whether M_{d,n} has a natural compactification. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,713 | OWR-15987-026 | Homology of Free-Lie Current Algebras over Square-Zero Extensions | Let $E$ and $V$ be finite-dimensional complex vector spaces, let $A=\mathbb C\oplus E$ with $E^2=0$, and let $\mathfrak g=\operatorname{Lie}(V)$ be the free Lie algebra. Determine the Lie algebra homology $H_*(\mathfrak g\otimes A)$, preferably as a sum of polynomial functors in $E$ and $V$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123](https://doi.org/10.4171/owr/2018/2)
## Literature review (checked 20... | 3 | open | null | 2,018 | 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-15987-026",
"literature-status:open",
"owr-year:2018"
] | General formulas exist for important low-degree cases of current Lie-algebra homology, but no general computation of H_*(g tensor A) for the stated broad class is available. | [
{
"url": "https://arxiv.org/abs/0808.0217",
"label": "Zusmanovich, current Lie algebras"
},
{
"url": "https://doi.org/10.4171/owr/2018/2",
"label": "Oberwolfach Report 2/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/2 | null | null | null | Let $E$ and $V$ be finite-dimensional complex vector spaces, let $A=\mathbb C\oplus E$ with $E^2=0$, and let $\mathfrak g=\operatorname{Lie}(V)$ be the free Lie algebra. Determine the Lie algebra homology $H_*(\mathfrak g\otimes A)$, preferably as a sum of polynomial functors in $E$ and $V$. | Let E and V be finite-dimensional complex vector spaces, let A=\mathbb C\oplus E with E^2=0, and let \mathfrak g=\operatorname{Lie}(V) be the free Lie algebra. Determine the Lie algebra homology H_*(\mathfrak g\otimes A), preferably as a sum of polynomial functors in E and V. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topology of Arrangements and Representation Stability (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/2, pp. 43--123 |
30,003,714 | OWR-15988-001 | Curvature Bias in Statistics on Quotient Spaces | For statistical estimators on quotient spaces, determine when curvature-induced bias occurs, whether it affects analyses beyond the mean shape, how large it is in applications, and when and how it should be corrected. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistics for Data with Geometric Structure (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/3, pp. 125--186](https://doi.org/10.4171/owr/2018/3)
## Literature review (checked 2026-08-21... | 3 | partially_solved | null | 2,018 | 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-15988-001",
"literature-status:partially-solved",
"owr-year:2018"
] | Asymptotic bias of Fréchet means on quotient-shaped spaces has been quantified, with Taylor expansions and bootstrap or correction procedures, but its scope across other statistical analyses and practical necessity is not fully settled. | [
{
"url": "https://doi.org/10.1137/16M1084493",
"label": "Miolane--Holmes--Pennec, asymptotic bias"
},
{
"url": "https://doi.org/10.4171/owr/2018/3",
"label": "Oberwolfach Report 3/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/3 | null | null | null | For statistical estimators on quotient spaces, determine when curvature-induced bias occurs, whether it affects analyses beyond the mean shape, how large it is in applications, and when and how it should be corrected. | For statistical estimators on quotient spaces, determine when curvature-induced bias occurs, whether it is confined to the mean shape or also affects other analyses, how important it is in practice, whether it should be corrected, and how to correct it. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Statistics for Data with Geometric Structure (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/3, pp. 125--186 |
30,003,715 | OWR-15988-002 | Singular Curvature and Stickiness of Fréchet Means | Are curvature-dependent corrections to Fréchet means and covariances on Riemannian manifolds precursors of stickiness of the mean in singular-curvature limits? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistics for Data with Geometric Structure (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/3, pp. 125--186](https://doi.org/10.4171/owr/2018/3)
## Literature review (checked 2026-08-21... | 3 | open | null | 2,018 | 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-15988-002",
"literature-status:open",
"owr-year:2018"
] | The proposed link between singular curvature and stickiness of the Fréchet mean, together with the global flag-based unexplained-variance criterion, remains a conjectural research direction rather than a proved criterion. | [
{
"url": "https://doi.org/10.4171/owr/2018/3",
"label": "Oberwolfach Report 3/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/3 | null | null | null | Are curvature-dependent corrections to Fréchet means and covariances on Riemannian manifolds precursors of stickiness of the mean in singular-curvature limits? | Conjecture: the curvature-dependent corrections to Fr\acute et means and covariances in Riemannian manifolds are precursors of stickiness of the mean in limiting cases where the curvature becomes singular. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Statistics for Data with Geometric Structure (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/3, pp. 125--186 |
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