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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,001,916 | OWR-11139-009 | Asymptotics of Intermediate Jet-Bundle Cohomology | How does
$$h^0\bigl(X_k,\mathcal O_{X_k}(m)\otimes\pi_k^*\mathcal O(-A)\bigr)$$
behave asymptotically when intermediate cohomology groups are present, and can this prove the generalized Green–Griffiths–Lang conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11139-009",
"literature-status:open",
"owr-year:2011"
] | The required asymptotic control of intermediate cohomology of jet-differential bundles is a central unresolved technical problem in the generalized Green--Griffiths--Lang program. | [
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | How does
$$h^0\bigl(X_k,\mathcal O_{X_k}(m)\otimes\pi_k^*\mathcal O(-A)\bigr)$$
behave asymptotically when intermediate cohomology groups are present, and can this prove the generalized Green–Griffiths–Lang conjecture? | How does h^0(X_k,O_{X_k}(m) tensor pi_k^*O(-A)) behave asymptotically when intermediate cohomology groups are present, and can this prove the generalized Green--Griffiths--Lang conjecture? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,917 | OWR-11139-010 | Normality of Varieties of Minimal Rational Tangents | Is the variety of minimal rational tangents $\mathcal C_x$ normal at a general point $x\in X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11139-010",
"literature-status:open",
"owr-year:2011"
] | The normality of the VMRT at a general point is explicitly posed as a central conjecture, and the located literature still treats it as unresolved in general. | [
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | Is the variety of minimal rational tangents $\mathcal C_x$ normal at a general point $x\in X$? | Normality conjecture: the variety of minimal rational tangents C_x at a general point x of X is normal. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,918 | OWR-11139-011 | The Yau–Tian–Donaldson Correspondence for Polarized Manifolds | Does a polarized manifold $(X,L)$ admit a constant-scalar-curvature Kähler metric in $c_1(L)$ if and only if $(X,L)$ is K-stable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,011 | 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-11139-011",
"literature-status:partially-solved",
"owr-year:2011"
] | The Yau--Tian--Donaldson correspondence is proved in major settings, including smooth Fano manifolds, and cscK existence is characterized analytically in important cases; the full polarized-manifold statement in the excerpt remains open. | [
{
"url": "https://arxiv.org/abs/1210.7494",
"label": "Chen--Donaldson--Sun, Kahler--Einstein metrics and stability"
},
{
"url": "https://arxiv.org/abs/1801.00656",
"label": "Chen--Cheng, cscK existence results"
},
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | Does a polarized manifold $(X,L)$ admit a constant-scalar-curvature Kähler metric in $c_1(L)$ if and only if $(X,L)$ is K-stable? | Yau--Tian--Donaldson conjecture: a polarized manifold (X,L) admits a constant-scalar-curvature Kahler metric in c_1(L) if and only if (X,L) is K-stable. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,919 | OWR-11139-012 | Conical Kähler–Einstein Metrics and Ricci Lower Bounds | Let $X$ be a Fano manifold, let $D$ be a smooth anticanonical divisor, and let $R(X)$ be the supremum of $t$ for which some Kähler metric $\omega\in c_1(X)$ satisfies $\operatorname{Ric}(\omega)>t\omega$. Does
$$\operatorname{Ric}(\omega_\beta)=\beta\omega_\beta+(1-\beta)\{D\}$$
admit a cone-singularity solution for ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | solved | null | 2,011 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://arxiv.org/abs/1102.1196",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no: the existence half fails)**. C. Li (OWR 47/2011, p. 2703, Conjecture 3) states Donaldson's conjecture ([arXiv:1102.1196](https://arxiv.org/abs/1102.1196), Conj. 1): along a smooth anticanonical D in a Fano manifold X, a Kähler–Einstein metric with cone angle 2... | [
"owr",
"oberwolfach-reports",
"OWR-11139-012",
"literature-status:partially-solved",
"owr-year:2011"
] | The conical Kahler--Einstein conjecture is proved in toric and other substantial settings, including existence below the greatest Ricci lower bound under additional hypotheses, but not in the full generality stated. | [
{
"url": "https://arxiv.org/abs/1207.4839",
"label": "Song--Wang, greatest Ricci lower bound and conical metrics"
},
{
"url": "https://arxiv.org/abs/1207.5011",
"label": "Chen--Donaldson--Sun, conical Kahler--Einstein metric revisited"
},
{
"url": "https://doi.org/10.4171/owr/2011/47",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | Let $X$ be a Fano manifold, let $D$ be a smooth anticanonical divisor, and let $R(X)$ be the supremum of $t$ for which some Kähler metric $\omega\in c_1(X)$ satisfies $\operatorname{Ric}(\omega)>t\omega$. Does
$$\operatorname{Ric}(\omega_\beta)=\beta\omega_\beta+(1-\beta)\{D\}$$
admit a cone-singularity solution for ... | Let X be a Fano manifold, D a smooth anticanonical divisor, and R(X) the supremum of t for which some Kahler metric omega in c_1(X) satisfies Ric(omega)>t omega. Conjecture: Ric(omega_beta)=beta omega_beta+(1-beta){D} has a cone-singularity solution for beta in (0,R(X)); if R(X)<1, it has no solution for beta in (R(X),... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,920 | OWR-11139-014 | Mirror Symmetry for Relative Hodge Numbers | Mirror Hodge-number conjecture: For a mirror pair $(\widetilde X_\sigma,w)$ and $(\widetilde X_{\sigma^\vee},w^\vee)$,
$$h^{p,q}(\widetilde X_\sigma,w)=h^{n-p,q}(\widetilde X_{\sigma^\vee},w^\vee)$$
when both spaces are smooth, with orbifold Hodge numbers used in the orbifold case. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,011 | 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-11139-014",
"literature-status:partially-solved",
"owr-year:2011"
] | Gross--Katzarkov--Ruddat prove the expected Hodge-number exchange for their toric hypersurface construction, while the broader orbifold and general mirror formulation remains only partially established. | [
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.aim.2016.03.035",
"label": "published mirror-symmetry theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | Mirror Hodge-number conjecture: For a mirror pair $(\widetilde X_\sigma,w)$ and $(\widetilde X_{\sigma^\vee},w^\vee)$,
$$h^{p,q}(\widetilde X_\sigma,w)=h^{n-p,q}(\widetilde X_{\sigma^\vee},w^\vee)$$
when both spaces are smooth, with orbifold Hodge numbers used in the orbifold case. | Mirror Hodge-number conjecture: for a mirror pair (X_tilde_sigma,w) and (X_tilde_sigma_dual,w_dual), h^{p,q}(X_tilde_sigma,w) equals h^{n-p,q}(X_tilde_sigma_dual,w_dual) when both spaces are smooth, with orbifold Hodge numbers used in the orbifold case. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,921 | OWR-11139-015 | Hochschild Homology of Landau–Ginzburg Mirrors | For a mirror pair $S$ and $(S^\vee,F_{S^\vee})$, is the Hochschild homology $HH^k(S)$ isomorphic to the cohomology $H^k(S^\vee,\mathbb C)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,011 | 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-11139-015",
"literature-status:partially-solved",
"owr-year:2011"
] | The conjecture is proved for curves and an example of a quintic surface in the cited work, but no general theorem covering the stated mirror construction was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1202.4042",
"label": "Gross--Katzarkov--Ruddat"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | For a mirror pair $S$ and $(S^\vee,F_{S^\vee})$, is the Hochschild homology $HH^k(S)$ isomorphic to the cohomology $H^k(S^\vee,\mathbb C)$? | Conjecture: for a mirror pair S and (S_dual,F_S_dual), the Hochschild homology HH^k(S) is isomorphic to the cohomology H^k(S_dual,C). | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,922 | OWR-11139-018 | Abelian-Quotient Models from High-Rank Group Actions | Let $X$ be a projective minimal terminal variety of dimension $n$, and let $G\leq\operatorname{Aut}(X)$ act so that its induced action on $\operatorname{NS}_{\mathbb C}(X)$ is not virtually solvable. Suppose that, after passage to finite index and quotient by the radical $R(G)$, the group embeds as a Zariski-dense subg... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11139-018",
"literature-status:open",
"owr-year:2011"
] | The question remains open beyond the lattice cases covered by Cantat--Zeghib; no general theorem establishing the stated birational classification was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1011.4768",
"label": "Cantat--Zeghib lattice case"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | Let $X$ be a projective minimal terminal variety of dimension $n$, and let $G\leq\operatorname{Aut}(X)$ act so that its induced action on $\operatorname{NS}_{\mathbb C}(X)$ is not virtually solvable. Suppose that, after passage to finite index and quotient by the radical $R(G)$, the group embeds as a Zariski-dense subg... | Under the hypotheses of Theorem 3, if H has real rank n-1 without assuming n=3, is X birational to a quotient of an abelian variety of dimension n? | corrected_verified | The hypotheses suppressed by the extracted theorem reference were restored from the official report, producing a self-contained version of the higher-dimensional question. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,923 | OWR-11446-001 | Simultaneous Exact Tests for Contingency Tables | How can many contingency tables, especially 2 by 2 and 2 by 3 tables, be analyzed simultaneously using exact tests and suitable multiple-testing methods? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Very High Dimensional Semiparametric Models (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/48, pp. 2745--2779](https://doi.org/10.4171/owr/2011/48)
## Literature review (checked 2026-08... | 3 | open | null | 2,011 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The phrase was extracted from a contribution title and abstract that present methods and results, not a standalone open conjecture. No separ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11446-001",
"literature-status:open",
"owr-year:2011"
] | This is a talk title followed by a description of multiple-testing methods, not a standalone mathematical conjecture; no definite open claim is extracted. | [
{
"url": "https://doi.org/10.4171/owr/2011/48",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/48 | null | null | null | null | How can many contingency tables, especially 2 by 2 and 2 by 3 tables, be analyzed simultaneously using exact tests and suitable multiple-testing methods? | unrecoverable | The phrase was extracted from a contribution title and abstract that present methods and results, not a standalone open conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Very High Dimensional Semiparametric Models (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/48, pp. 2745--2779 |
30,001,924 | OWR-11447-001 | Semiclassical Measures and Exceptional Eigenmodes | What are the possible semiclassical measures, and do they include all classically invariant measures? What is the rate of convergence to Liouville measure, and can exceptional eigenmodes exhibit the behavior of exceptional invariant measures? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Quantum Ergodicity (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/49, pp. 2781--2835](https://doi.org/10.4171/owr/2011/49)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,011 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11447-001",
"literature-status:open",
"owr-year:2011"
] | The question asks whether exceptional eigenmodes occur; arithmetic cases are proved, while the general negative-curvature case remains open. | [
{
"url": "https://doi.org/10.4171/owr/2011/49",
"label": "original OWR report"
},
{
"url": "https://www.ams.org/journals/notices/202310/noti2801/noti2801.html",
"label": "current QUE survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/49 | null | null | null | What are the possible semiclassical measures, and do they include all classically invariant measures? What is the rate of convergence to Liouville measure, and can exceptional eigenmodes exhibit the behavior of exceptional invariant measures? | What are the possible semiclassical measures, and do they include all classically invariant measures? What is the rate of convergence to Liouville measure, and can exceptional eigenmodes exhibit the behavior of exceptional invariant measures? | exact | The statement is internally readable; retained byte-for-byte. | null | null | null | null | null | Arbeitsgemeinschaft: Quantum Ergodicity (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/49, pp. 2781--2835 |
30,001,925 | OWR-11447-002 | Quantum Variance Conjectures for Matrix Elements | For an observable $A$, do the off-diagonal matrix elements satisfy $|A_{jk}|^2=S(0)/(2\pi\hbar\rho(E))$, hence scale as $\hbar^{d-1}$? Are the diagonal matrix elements Gaussian with mean $\{A\}$ and variance $gS(0)/(2\pi\hbar\rho(E))$, where $g=2$ in the presence of time-reversal symmetry and $g=1$ otherwise? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Quantum Ergodicity (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/49, pp. 2781--2835](https://doi.org/10.4171/owr/2011/49)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,011 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11447-002",
"literature-status:partially-solved",
"owr-year:2011"
] | The Feingold--Peres-type variance predictions remain beyond general proofs; rigorous work gives upper bounds and special arithmetic cases, so the stated conjectures are only partially supported. | [
{
"url": "https://doi.org/10.4171/owr/2011/49",
"label": "original OWR report"
},
{
"url": "https://www.math.tau.ac.il/~rudnick/papers/shortwindows.pdf",
"label": "Kurlberg--Rosen--Rudnick"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/49 | null | null | null | For an observable $A$, do the off-diagonal matrix elements satisfy $|A_{jk}|^2=S(0)/(2\pi\hbar\rho(E))$, hence scale as $\hbar^{d-1}$? Are the diagonal matrix elements Gaussian with mean $\{A\}$ and variance $gS(0)/(2\pi\hbar\rho(E))$, where $g=2$ in the presence of time-reversal symmetry and $g=1$ otherwise? | Quantum variance conjectures: non-diagonal matrix elements have variance proportional to S(0) times hbar^(d-1) divided by 2 pi rho(E), while diagonal matrix elements are Gaussian about their classical mean with variance g S(0) times hbar^(d-1) divided by 2 pi rho(E), where g is 2 with time-reversal symmetry and 1 other... | corrected_verified | The official report was checked and the variance formulas, density-of-states factor, classical mean, and symmetry factor were restored. | null | null | null | null | null | Arbeitsgemeinschaft: Quantum Ergodicity (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/49, pp. 2781--2835 |
30,001,926 | OWR-11447-003 | Quantum Unique Ergodicity on Negatively Curved Manifolds | Quantum unique ergodicity conjecture: eigenmodes of manifolds with negative sectional curvature become equidistributed in the high-energy limit. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Quantum Ergodicity (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/49, pp. 2781--2835](https://doi.org/10.4171/owr/2011/49)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,011 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11447-003",
"literature-status:partially-solved",
"owr-year:2011"
] | QUE is proved for important arithmetic systems and constrained models, but remains open for general negatively curved manifolds. | [
{
"url": "https://doi.org/10.4171/owr/2011/49",
"label": "original OWR report"
},
{
"url": "https://www.ams.org/journals/notices/202310/noti2801/noti2801.html",
"label": "current QUE survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/49 | null | null | null | Quantum unique ergodicity conjecture: eigenmodes of manifolds with negative sectional curvature become equidistributed in the high-energy limit. | Quantum unique ergodicity conjecture: eigenmodes of manifolds with negative sectional curvature become equidistributed in the high-energy limit. | exact | The statement is internally readable; retained byte-for-byte. | null | null | null | null | null | Arbeitsgemeinschaft: Quantum Ergodicity (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/49, pp. 2781--2835 |
30,001,927 | OWR-11448-001 | Many-Body Localization at Positive Density | For systems of infinitely many interacting particles at positive density, what is the precise localization regime and is it stable under interactions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Correlations and Interactions for Random Quantum Systems (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/50, pp. 2837--2890](https://doi.org/10.4171/owr/2011/50)
## Literature review (ch... | 3 | open | null | 2,011 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11448-001",
"literature-status:open",
"owr-year:2011"
] | The report explicitly identifies localization at positive density in infinitely many-particle systems as an open problem; later literature does not supply a general resolution. | [
{
"url": "https://doi.org/10.4171/owr/2011/50",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/50 | null | null | null | For systems of infinitely many interacting particles at positive density, what is the precise localization regime and is it stable under interactions? | For systems of infinitely many interacting particles at positive density, what is the precise localization regime and is it stable under interactions? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Correlations and Interactions for Random Quantum Systems (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/50, pp. 2837--2890 |
30,001,928 | OWR-11448-002 | Classification of Gapped Ground-State Phases | What is a gapped ground-state phase for an infinite quantum spin system, when phases are defined by differentiable paths of sufficiently short-range interactions with a uniform positive spectral gap? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Correlations and Interactions for Random Quantum Systems (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/50, pp. 2837--2890](https://doi.org/10.4171/owr/2011/50)
## Literature review (ch... | 3 | partially_solved | null | 2,011 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11448-002",
"literature-status:partially-solved",
"owr-year:2011"
] | The question has a rigorous phase definition and substantial one-dimensional classifications, but no general classification of gapped ground-state phases in the stated setting is known. | [
{
"url": "https://doi.org/10.4171/owr/2011/50",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1102.0842",
"label": "automorphic equivalence theorem"
},
{
"url": "https://arxiv.org/abs/1212.3718",
"label": "one-dimensional classification"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/50 | null | null | null | What is a gapped ground-state phase for an infinite quantum spin system, when phases are defined by differentiable paths of sufficiently short-range interactions with a uniform positive spectral gap? | What is a gapped ground-state phase for an infinite quantum spin system, when phases are defined by differentiable paths of sufficiently short-range interactions with a uniform positive spectral gap? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Correlations and Interactions for Random Quantum Systems (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/50, pp. 2837--2890 |
30,001,929 | OWR-11450-003 | Predicting SAT-Solver Hardness from Formula Structure | What explains the success of SAT solvers, how can one determine whether a particular propositional formula is hard or tractable, and can formula space complexity serve as a useful measure of hardness? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/52, pp. 2963--3002](https://doi.org/10.4171/owr/2011/52)
## Literature review (... | 3 | partially_solved | null | 2,011 | 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-11450-003",
"literature-status:partially-solved",
"owr-year:2011"
] | Proof-complexity research establishes many time--space tradeoffs and lower bounds, but the broad question of predicting SAT-solver hardness and tractability remains open. | [
{
"url": "https://doi.org/10.4171/owr/2011/52",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1008.1789",
"label": "Ben-Sasson--Nordström"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/52 | null | null | null | What explains the success of SAT solvers, how can one determine whether a particular propositional formula is hard or tractable, and can formula space complexity serve as a useful measure of hardness? | What explains the spectacular success of SAT solvers, how can one determine whether a particular propositional formula is hard or tractable, and can the space complexity of the formula serve as a useful measure of its hardness? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/52, pp. 2963--3002 |
30,001,930 | OWR-11451-002 | Polynomial Diameter Bounds for Polyhedra | Can the diameter of a polyhedron $P=\{x\in\mathbb{R}^n:Ax\leq b\}$, with $m$ defining inequalities and dimension $n$, be bounded by a polynomial in $m$ and $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076](https://doi.org/10.4171/owr/2011/53)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11451-002",
"literature-status:open",
"owr-year:2011"
] | The polynomial diameter bound remains open; primary work has improved the upper bound to quasipolynomial forms, but no polynomial bound is known. | [
{
"url": "https://doi.org/10.4171/owr/2011/53",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/S00454-014-9601-X",
"label": "Eisenbrand--Haehnle--Razborov--Rothvoss"
},
{
"url": "https://doi.org/10.1137/140962310",
"label": "Todd's improved bound"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/53 | null | null | null | Can the diameter of a polyhedron $P=\{x\in\mathbb{R}^n:Ax\leq b\}$, with $m$ defining inequalities and dimension $n$, be bounded by a polynomial in $m$ and $n$? | Can the diameter of a polyhedron P = {x in R^n : Ax <= b}, with m defining inequalities and dimension n, be bounded by a polynomial in m and n? | corrected_verified | The official report states this polynomial diameter question in the same variables; only mathematical typography was normalized. | null | null | null | null | null | Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076 |
30,001,931 | OWR-11451-004 | Integer Carathéodory Property for Intersecting Matroid Base Polytopes | Does the intersection of two base polytopes of strongly base orderable matroids have the Integer Carathéodory Property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076](https://doi.org/10.4171/owr/2011/53)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11451-004",
"literature-status:open",
"owr-year:2011"
] | The generalization from gammoids to intersections of other matroids remains open; the cited ICP theorem does not cover this intersection question. | [
{
"url": "https://doi.org/10.4171/owr/2011/53",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1004.4552",
"label": "Gijswijt--Regts ICP theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/53 | null | null | null | Does the intersection of two base polytopes of strongly base orderable matroids have the Integer Carathéodory Property? | Does the intersection of two base polytopes of strongly base orderable matroids have the Integer Caratheodory Property? | corrected_verified | The official report poses this as the first of three distinct Integer Carathéodory questions. | null | null | null | null | null | Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076 |
30,001,932 | OWR-11451-005 | Composite Repetition of Three Matroid Questions | Does the intersection of two base polytopes of strongly base orderable matroids have the Integer Caratheodory Property; does the r-arborescence polytope have this property; and can matroids admit a more intuitive greedy decomposition into affinely independent integral vectors? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076](https://doi.org/10.4171/owr/2011/53)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report contains three separate questions, but this extraction conflates all three and repeats the first two records in this chu) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11451-005",
"literature-status:open",
"owr-year:2011"
] | The 2012 paper states these as open questions; the cited results do not prove the ICP for intersections of strongly base-orderable matroids or the requested greedy decomposition. | [
{
"url": "https://doi.org/10.4171/owr/2011/53",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1004.4552",
"label": "Gijswijt--Regts ICP theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/53 | null | null | null | null | Does the intersection of two base polytopes of strongly base orderable matroids have the Integer Caratheodory Property; does the r-arborescence polytope have this property; and can matroids admit a more intuitive greedy decomposition into affinely independent integral vectors? | unrecoverable | The official report contains three separate questions, but this extraction conflates all three and repeats the first two records in this chunk while paraphrasing the third only vaguely. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076 |
30,001,933 | OWR-11451-006 | Integer Carathéodory Property for Arborescence Polytopes | Does the $r$-arborescence polytope—the common-base polytope of the graphic matroid and the appropriate partition matroid—have the Integer Carathéodory Property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076](https://doi.org/10.4171/owr/2011/53)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11451-006",
"literature-status:open",
"owr-year:2011"
] | The r-arborescence ICP question remains explicitly open in recent polyhedral literature; no proof or counterexample resolving it was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/53",
"label": "original OWR report"
},
{
"url": "https://dial.uclouvain.be/pr/boreal/object/boreal%3A312886/datastream/PDF_01/view",
"label": "recent box-TDI survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/53 | null | null | null | Does the $r$-arborescence polytope—the common-base polytope of the graphic matroid and the appropriate partition matroid—have the Integer Carathéodory Property? | Does the r-arborescence polytope have the Integer Caratheodory Property, and can matroids admit a more intuitive greedy decomposition into affinely independent integral vectors? | corrected_verified | The official report confirms that this is the second Integer Carathéodory question and supplies the matroid-intersection description needed to identify the polytope. | null | null | null | null | null | Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076 |
30,001,934 | OWR-11451-007 | Greedy Decomposition of the Spanning-Tree Polytope | Does the spanning-tree polytope $P$ admit greedy decomposition, meaning that for every positive integer $k$ and integral $w\in kP$, there is an integral $x\in P$ for which $\max\{\lambda:w-\lambda x\in(k-\lambda)P\}$ is an integer? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076](https://doi.org/10.4171/owr/2011/53)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11451-007",
"literature-status:open",
"owr-year:2011"
] | The 2011 report poses this as Question 3; the checked literature did not locate a proof or counterexample. | [
{
"url": "https://doi.org/10.4171/owr/2011/53",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/53 | null | null | null | Does the spanning-tree polytope $P$ admit greedy decomposition, meaning that for every positive integer $k$ and integral $w\in kP$, there is an integral $x\in P$ for which $\max\{\lambda:w-\lambda x\in(k-\lambda)P\}$ is an integer? | Does the spanning tree polytope admit greedy decomposition, meaning that for every positive integer k and integral w in kP there is an integral x in P for which the maximum lambda with w minus lambda x in (k minus lambda)P is an integer? | corrected_verified | The official report poses this as the third, distinct matroid-polytope question; the formula and quantifiers are preserved. | null | null | null | null | null | Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076 |
30,001,935 | OWR-11451-008 | Flows in Signed Graphs and Binary Matroids | For a signed graph or binary matroid with nonnegative edge weights satisfying the cut condition, does there exist an integer flow, a fractional flow, and, when the weights are Eulerian, an integer flow? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076](https://doi.org/10.4171/owr/2011/53)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,011 | 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 | [Discussion #4 update, 2026-10-16] The unrestricted cut-sufficiency statement in this record has a classical negative answer, even with Eulerian weights. Guenin gives the example in [*Binary Clutters and Multicommodity Flows*, Optima 71 (March 2004), p. 4](https://mathopt.zib.de/Optima-Issues/optima71.pdf): take K(2,3)... | [
"owr",
"oberwolfach-reports",
"OWR-11451-008",
"literature-status:partially-solved",
"owr-year:2011"
] | The report records Q1--Q3 for signed graphs and binary matroids; special signed-graph cases are known, but the general questions remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2011/53",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1008.2136",
"label": "flow-cut gaps"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/53 | null | null | null | For a signed graph or binary matroid with nonnegative edge weights satisfying the cut condition, does there exist an integer flow, a fractional flow, and, when the weights are Eulerian, an integer flow? | For a signed graph or binary matroid with nonnegative edge weights satisfying the cut condition, does there exist an integer flow, a fractional flow, and, when the weights are Eulerian, an integer flow? | exact | The official report explicitly asks the three flow-existence questions under the cut and Eulerian hypotheses. | null | null | null | null | null | Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076 |
30,001,936 | OWR-11451-009 | Seymour One-Flowing Conjecture | Does Seymour’s $1$-flowing conjecture hold: does the max-flow min-cut relation hold for every binary matroid with no minor isomorphic to $\operatorname{AG}(3,2)$, $T_{11}$, or $T_{11}^*$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076](https://doi.org/10.4171/owr/2011/53)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,011 | 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-11451-009",
"literature-status:partially-solved",
"owr-year:2011"
] | The report calls this Seymour's 1-flowing conjecture; later work characterizes highly connected cases, but the excluded-minor conjecture is not fully resolved. | [
{
"url": "https://doi.org/10.4171/owr/2011/53",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1137/16M1077283",
"label": "binary matroid templates"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/53 | null | null | null | Does Seymour’s $1$-flowing conjecture hold: does the max-flow min-cut relation hold for every binary matroid with no minor isomorphic to $\operatorname{AG}(3,2)$, $T_{11}$, or $T_{11}^*$? | Does the 1-flowing conjecture hold: does the max-flow min-cut relation hold for every binary matroid with no minor in the excluded-minor set consisting of AG(3,2), T_11, and its dual? | corrected_verified | The official report states Seymour’s conjecture with precisely these three excluded minors. | null | null | null | null | null | Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076 |
30,001,937 | OWR-11451-010 | Minimum Size of Cone Lifts | Given a nested family of cones $(K_k)$, determine the least $k$ for which a cone $C$ can be represented as $C=\pi(K_k\cap L)$ for an affine subspace $L$ and a linear map $\pi$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076](https://doi.org/10.4171/owr/2011/53)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11451-010",
"literature-status:open",
"owr-year:2011"
] | The report poses the general cone-lift representation and least-size questions; no general classification or resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/53",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/53 | null | null | null | Given a nested family of cones $(K_k)$, determine the least $k$ for which a cone $C$ can be represented as $C=\pi(K_k\cap L)$ for an affine subspace $L$ and a linear map $\pi$. | Given a full-dimensional closed convex cone K in R^m and a convex set C in R^n, when does C equal the linear image of K intersected with an affine subspace, and for a cone family K_k what is the least k for which such a lift exists? | corrected_verified | The official report proves the preceding general characterization of cone lifts and leaves only the minimum-size question open. | null | null | null | null | null | Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076 |
30,001,938 | OWR-11451-013 | Unique Games Conjecture | Is the Unique Games constraint-satisfaction problem computationally hard as asserted by the Unique Games Conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076](https://doi.org/10.4171/owr/2011/53)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate of canonical problem CS-001 | [
"CS-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11451-013",
"literature-status:open",
"owr-year:2011"
] | The extracted fragment refers to the Unique Games Conjecture, which remains unresolved in current primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2011/53",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2404.16024",
"label": "Unique Games research"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/53 | null | null | null | Is the Unique Games constraint-satisfaction problem computationally hard as asserted by the Unique Games Conjecture? | Is the Unique Games Conjecture true, namely that the Unique Games constraint-satisfaction problem is computationally hard, and can semidefinite programming hierarchies resolve or characterize this hardness? | corrected_verified | The official report presents the Unique Games Conjecture as the open claim; its discussion of semidefinite-programming hierarchies reports results rather than a second problem. | null | null | null | null | null | Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076 |
30,001,939 | OWR-11451-014 | Nondeterministic Polynomial Characterization of Seymour Graphs | Can one find a nondeterministic polynomial-time characterization of Seymour graphs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076](https://doi.org/10.4171/owr/2011/53)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11451-014",
"literature-status:open",
"owr-year:2011"
] | The report and later excluded-minor work give co-NP characterizations, but an NP characterization or equivalent resolution remains open. | [
{
"url": "https://doi.org/10.4171/owr/2011/53",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/978-3-642-20807-2_1",
"label": "Seymour graph characterization"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/53 | null | null | null | Can one find a nondeterministic polynomial-time characterization of Seymour graphs? | Can one find a nondeterministic polynomial-time characterization of Seymour graphs? | exact | The official report states this question verbatim as an open characterization problem. | null | null | null | null | null | Combinatorial Optimization (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/53, pp. 3003--3076 |
30,001,940 | OWR-11453-001 | Dissipative Noether Theory and Quantum Fluid Energies | For the two energy functionals arising from the dissipative variational formulation of quantum fluid dynamics, are there other transformations yielding new energy functionals, how can a dissipative Noether theory be developed on the space of measures, can the theory be applied to classical fluid dynamics and identify m... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/55, pp. 3145--3216](https://doi.org/10.4171/owr/2011/55)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11453-001",
"literature-status:open",
"owr-year:2011"
] | The report lists four open questions about dissipative Noether theory, fluid dynamics, and optimal transport formulations; no complete resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/55",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/55 | null | null | null | For the two energy functionals arising from the dissipative variational formulation of quantum fluid dynamics, are there other transformations yielding new energy functionals, how can a dissipative Noether theory be developed on the space of measures, can the theory be applied to classical fluid dynamics and identify m... | For the two energy functionals arising from the dissipative variational formulation of quantum fluid dynamics, are there other transformations yielding new energy functionals, how can a dissipative Noether theory be developed on the space of measures, can the theory be applied to classical fluid dynamics and identify m... | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Variational Methods for Evolution (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/55, pp. 3145--3216 |
30,001,941 | OWR-11453-002 | Sharp Free-Energy Decay for Fast Diffusion | For the fast-diffusion solution $u(t,\cdot)$ and its free-energy functional $\mathcal F_\sigma$, can one obtain sharp estimates for the decay of $\mathcal F_\sigma[u(t,\cdot)]$ for every $t\geq0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/55, pp. 3145--3216](https://doi.org/10.4171/owr/2011/55)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11453-002",
"literature-status:open",
"owr-year:2011"
] | The source explicitly calls sharp all-time decay estimates an open question; later results give bounds but do not settle the stated sharp problem. | [
{
"url": "https://doi.org/10.4171/owr/2011/55",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/55 | null | null | null | For the fast-diffusion solution $u(t,\cdot)$ and its free-energy functional $\mathcal F_\sigma$, can one obtain sharp estimates for the decay of $\mathcal F_\sigma[u(t,\cdot)]$ for every $t\geq0$? | For the fast diffusion solution u(t, dot) and its free-energy functional F_sigma, can one obtain sharp estimates for the decay of F_sigma[u(t, dot)] for every time t greater than or equal to zero? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Variational Methods for Evolution (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/55, pp. 3145--3216 |
30,001,942 | OWR-11453-003 | Uniqueness for Periodic Semigeostrophic Systems | Are distributional solutions unique for the two-dimensional periodic semi-geostrophic system and for its dual system? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/55, pp. 3145--3216](https://doi.org/10.4171/owr/2011/55)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11453-003",
"literature-status:open",
"owr-year:2011"
] | The source explicitly says uniqueness of distributional solutions is unknown for both SG and SGD; no complete resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/55",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/55 | null | null | null | Are distributional solutions unique for the two-dimensional periodic semi-geostrophic system and for its dual system? | Are distributional solutions unique for the two-dimensional periodic semi-geostrophic system and for its dual system? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Variational Methods for Evolution (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/55, pp. 3145--3216 |
30,001,943 | OWR-11454-001 | Minimal Singularity Classes for Functorial Resolution | What is the smallest class $\mathcal S$ of singularities containing all normal-crossings singularities such that every variety $X$ admits a proper birational or bimeromorphic morphism from a variety $X'$ having only singularities in $\mathcal S$, with the morphism an isomorphism over the normal-crossings locus of $X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286](https://doi.org/10.4171/owr/2011/56)
## Literature review (... | 3 | partially_solved | null | 2,011 | 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-11454-001",
"literature-status:partially-solved",
"owr-year:2011"
] | The smallest class is determined in low dimensions and low codimension, while the higher-dimensional problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2011/56",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.aim.2012.08.002",
"label": "minimal singularities"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/56 | null | null | null | What is the smallest class $\mathcal S$ of singularities containing all normal-crossings singularities such that every variety $X$ admits a proper birational or bimeromorphic morphism from a variety $X'$ having only singularities in $\mathcal S$, with the morphism an isomorphism over the normal-crossings locus of $X$? | What is the smallest class S of singularities containing all normal-crossings singularities such that every variety X admits a proper birational or bimeromorphic morphism from a variety X prime with only singularities in S, which is an isomorphism over the normal-crossings locus of X? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286 |
30,001,944 | OWR-11454-002 | Witten Spinor Proofs on Nonspin Asymptotically Flat Manifolds | Can Witten's proof of the positive mass theorem be adapted to asymptotically flat nonspin manifolds using singular spin structures and Witten spinors? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286](https://doi.org/10.4171/owr/2011/56)
## Literature review (... | 3 | partially_solved | null | 2,011 | 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-11454-002",
"literature-status:partially-solved",
"owr-year:2011"
] | Schoen--Yau and Degeratu--Stern provide important partial results, but a full Witten-style proof for higher-dimensional nonspin manifolds remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2011/56",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1112.0194",
"label": "Witten spinors on nonspin manifolds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/56 | null | null | null | Can Witten's proof of the positive mass theorem be adapted to asymptotically flat nonspin manifolds using singular spin structures and Witten spinors? | Can Witten's proof of the positive mass theorem be adapted to asymptotically flat nonspin manifolds using singular spin structures and Witten spinors? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286 |
30,001,945 | OWR-11454-003 | Chain-Independent Homology Growth over Arbitrary Fields | For which groups $G$ does
$$\lim_i\frac{b_1(G_i;K)}{[G:G_i]}$$
exist for every inverse system of finite-index normal subgroups $G_i$ with trivial intersection, independently of the system and the field $K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286](https://doi.org/10.4171/owr/2011/56)
## Literature review (... | 3 | partially_solved | null | 2,011 | 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-11454-003",
"literature-status:partially-solved",
"owr-year:2011"
] | Lueck approximation settles the finitely presented rational case, and Ershov--Lueck prove important characteristic-p inequalities, but the stated independence for all groups, chains, and fields remains open. | [
{
"url": "https://doi.org/10.4171/owr/2011/56",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1206.0474",
"label": "first L2-Betti approximation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/56 | null | null | null | For which groups $G$ does
$$\lim_i\frac{b_1(G_i;K)}{[G:G_i]}$$
exist for every inverse system of finite-index normal subgroups $G_i$ with trivial intersection, independently of the system and the field $K$? | For which groups G does the limit of b_1(G/G_i;K) divided by the index [G:G_i] exist for every inverse system of finite-index normal subgroups G_i with trivial intersection, independently of the system and the field K? | corrected_verified | The numerator was repaired from the erroneous quotient-group Betti number to the subgroup Betti number shown in the official report. | null | null | null | null | null | Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286 |
30,001,946 | OWR-11454-004 | Topological Isolation of Singularities in Witt Bordism | Can every $\mathbb Q$-Witt space be shown, by a purely topological construction, to be $\mathbb Q$-Witt bordant to a $\mathbb Q$-Witt space with at worst isolated singularities? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286](https://doi.org/10.4171/owr/2011/56)
## Literature review (... | 3 | open | null | 2,011 | 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-11454-004",
"literature-status:open",
"owr-year:2011"
] | The bordism fact is known algebraically, but the requested purely topological construction is posed as an open question. | [
{
"url": "https://doi.org/10.4171/owr/2011/56",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/56 | null | null | null | Can every $\mathbb Q$-Witt space be shown, by a purely topological construction, to be $\mathbb Q$-Witt bordant to a $\mathbb Q$-Witt space with at worst isolated singularities? | Can every Q-Witt space be shown by a purely topological construction to be Q-Witt bordant to a Q-Witt space with at worst isolated singularities? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286 |
30,001,947 | OWR-11454-005 | Nontrivial Witt Pairings in $\mathbb Z_2$-Witt Spaces | Does there exist a compact $\mathbb Z$-oriented $\mathbb Z_2$-Witt space of dimension $4j+2$ whose middle-dimensional pairing represents the nontrivial element of the Witt group $W(\mathbb Z_2)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286](https://doi.org/10.4171/owr/2011/56)
## Literature review (... | 3 | open | null | 2,011 | 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-11454-005",
"literature-status:open",
"owr-year:2011"
] | The source explicitly leaves the existence of a Z-oriented compact Z2-Witt space with the nontrivial Witt pairing unsettled. | [
{
"url": "https://doi.org/10.4171/owr/2011/56",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/56 | null | null | null | Does there exist a compact $\mathbb Z$-oriented $\mathbb Z_2$-Witt space of dimension $4j+2$ whose middle-dimensional pairing represents the nontrivial element of the Witt group $W(\mathbb Z_2)$? | Does there exist a compact Z-oriented Z_2-Witt space of dimension 4j+2 whose middle-dimensional pairing represents the nontrivial element of the Witt group W(Z_2)? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286 |
30,001,948 | OWR-11454-006 | Topological $\widehat A$-Classes on Witt Spaces | For a Witt space $X$, under what hypotheses can the homology $\widehat A$-class be defined topologically, how does it depend on a positive-scalar-curvature metric on the links, and is it the Chern character of a suitable $K$-homology class defined by the spin Dirac operator? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286](https://doi.org/10.4171/owr/2011/56)
## Literature review (... | 3 | open | null | 2,011 | 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-11454-006",
"literature-status:open",
"owr-year:2011"
] | The question about metric dependence and identification with a spin-Dirac K-homology Chern character remains unresolved in the cited stratified-space literature. | [
{
"url": "https://doi.org/10.4171/owr/2011/56",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/56 | null | null | null | For a Witt space $X$, under what hypotheses can the homology $\widehat A$-class be defined topologically, how does it depend on a positive-scalar-curvature metric on the links, and is it the Chern character of a suitable $K$-homology class defined by the spin Dirac operator? | For a Witt space X, under what hypotheses can the homology A-hat class be defined topologically, how does it depend on a positive-scalar-curvature metric on the links, and is it the Chern character of a suitable K-homology class defined by the spin Dirac operator? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286 |
30,001,949 | OWR-11454-007 | Even-Codimension Stratifications of Codimension-Two Embeddings | Let $M$ be a simply connected piecewise-linear manifold with a homotopy equivalence $M\simeq N$, and hence an embedding $M\hookrightarrow N\times D^2$. Can this embedding be stratified using only strata of even codimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286](https://doi.org/10.4171/owr/2011/56)
## Literature review (... | 3 | open | null | 2,011 | 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-11454-007",
"literature-status:open",
"owr-year:2011"
] | The report poses this embedding-stratification question; the checked literature supplies related even-codimension theories but no answer to this specific construction. | [
{
"url": "https://doi.org/10.4171/owr/2011/56",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/56 | null | null | null | Let $M$ be a simply connected piecewise-linear manifold with a homotopy equivalence $M\simeq N$, and hence an embedding $M\hookrightarrow N\times D^2$. Can this embedding be stratified using only strata of even codimension? | If M is a simply connected piecewise-linear manifold and M is homotopy equivalent to N, so that M embeds in N times D^2, can this embedding be stratified using only strata of even codimension? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Stratified Spaces: Joining Analysis, Topology and Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/56, pp. 3217--3286 |
30,001,950 | OWR-11568-002 | Positive-Ricci Cohomogeneity Manifolds with Exceptional Orbits | Can one find manifolds with more than two non-principal orbits that admit an invariant metric of positive Ricci curvature in cohomogeneities other than 3 and 5? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Manifolds with Lower Curvature Bounds (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/01, pp. 5--42](https://doi.org/10.4171/owr/2012/01)
## Literature review (checked 202... | 3 | open | null | 2,012 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11568-002",
"literature-status:open",
"owr-year:2012"
] | Positive-Ricci examples with many non-principal orbits were constructed in cohomogeneities 3 and 5, but the stated question for other cohomogeneities remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/01",
"label": "original OWR report"
},
{
"url": "https://mural.maynoothuniversity.ie/id/eprint/6970/1/DW-many_isolated.pdf",
"label": "many isolated singular orbits"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/01 | null | null | null | Can one find manifolds with more than two non-principal orbits that admit an invariant metric of positive Ricci curvature in cohomogeneities other than 3 and 5? | Can one find manifolds with more than two non-principal orbits that admit an invariant metric of positive Ricci curvature in cohomogeneities other than 3 and 5? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Mini-Workshop: Manifolds with Lower Curvature Bounds (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/01, pp. 5--42 |
30,001,951 | OWR-11568-004 | Complex Structures on Polyhedral Kähler Manifolds | If a nonnegatively curved, nonflat polyhedral manifold $M$ has irreducible holonomy and $b_2(M)>0$, does $M$ have a natural holomorphic structure, is it biholomorphic to $\mathbb{CP}^n$, and is its metric a singular Kähler metric? More generally, does every polyhedral Kähler manifold $M^{2n}$ have a natural complex str... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Manifolds with Lower Curvature Bounds (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/01, pp. 5--42](https://doi.org/10.4171/owr/2012/01)
## Literature review (checked 202... | 3 | partially_solved | null | 2,012 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11568-004",
"literature-status:partially-solved",
"owr-year:2012"
] | The conjecture is proved in dimensions at most four and related six-dimensional results are available, but the general higher-dimensional statement remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/01",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2510.17447",
"label": "polyhedral Kahler metrics"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/01 | null | null | null | If a nonnegatively curved, nonflat polyhedral manifold $M$ has irreducible holonomy and $b_2(M)>0$, does $M$ have a natural holomorphic structure, is it biholomorphic to $\mathbb{CP}^n$, and is its metric a singular Kähler metric? More generally, does every polyhedral Kähler manifold $M^{2n}$ have a natural complex str... | Conjecture: If a non-negatively curved, non-flat polyhedral manifold M has irreducible holonomy and b_2(M)>0, then M has a natural holomorphic structure, is biholomorphic to \mathbb{CP}^n, and its metric is a singular Kähler metric; moreover, every polyhedral Kähler manifold M^{2n} should have a natural complex structu... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Manifolds with Lower Curvature Bounds (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/01, pp. 5--42 |
30,001,952 | OWR-11568-005 | Torus Quotients with Second Betti Number One | Does there exist an algebraic torus quotient $Y=A/G$ by a freely acting finite group $G$ such that $b_2(Y)=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Manifolds with Lower Curvature Bounds (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/01, pp. 5--42](https://doi.org/10.4171/owr/2012/01)
## Literature review (checked 202... | 3 | partially_solved | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "needs_review",
"evidence": "published"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11568-005",
"literature-status:open",
"owr-year:2012"
] | Lutowski proves that a non-torus flat Kähler manifold has reducible holonomy. This is a relevant obstruction: a decomposition of the complex holonomy representation gives independent invariant (1,1)-forms and hence $b_2\ge2$. The source asks about dimensions above three, whereas the extracted statement omits dimension ... | [
{
"url": "https://doi.org/10.5486/pmd.2021.8881",
"label": "R. Lutowski, Flat manifolds with homogeneous holonomy representation (2021)"
},
{
"url": "https://arxiv.org/abs/1803.07177",
"label": "Lutowski — primary manuscript"
},
{
"url": "https://doi.org/10.4171/owr/2012/01",
"label"... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2012/01 | null | null | null | Does there exist an algebraic torus quotient $Y=A/G$ by a freely acting finite group $G$ such that $b_2(Y)=1$? | Does there exist an algebraic torus quotient Y=A/G by a freely acting finite group G such that b_2(Y)=1? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Manifolds with Lower Curvature Bounds (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/01, pp. 5--42 |
30,001,953 | OWR-11568-006 | Hopf Conjecture | Does every closed even-dimensional Riemannian manifold with positive sectional curvature have positive Euler characteristic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Manifolds with Lower Curvature Bounds (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/01, pp. 5--42](https://doi.org/10.4171/owr/2012/01)
## Literature review (checked 202... | 3 | open | null | 2,012 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11568-006",
"literature-status:open",
"owr-year:2012"
] | The extraction is only contextual discussion of the positive curvature conjecture and the Hopf conjecture, without a complete claim to verify; no resolution can be assigned. | [
{
"url": "https://doi.org/10.4171/owr/2012/01",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/01 | null | null | null | Does every closed even-dimensional Riemannian manifold with positive sectional curvature have positive Euler characteristic? | Hopf conjecture: Every closed Riemannian manifold of even dimension with positive sectional curvature has positive Euler characteristic. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Manifolds with Lower Curvature Bounds (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/01, pp. 5--42 |
30,001,954 | OWR-11568-007 | Elliptic Genera of Positively Curved Spin Manifolds | Let $(M,g)$ be a closed Riemannian spin manifold with $\operatorname{sec}(M)>0$. Is its elliptic genus constant as a modular function, namely $\phi(M)=\operatorname{sign}(M)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Manifolds with Lower Curvature Bounds (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/01, pp. 5--42](https://doi.org/10.4171/owr/2012/01)
## Literature review (checked 202... | 3 | partially_solved | null | 2,012 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11568-007",
"literature-status:partially-solved",
"owr-year:2012"
] | The general elliptic genus question remains unresolved, while symmetry and homogeneous cases have vanishing results for additional coefficients. | [
{
"url": "https://doi.org/10.4171/owr/2012/01",
"label": "original Oberwolfach report"
},
{
"url": "https://nyjm.albany.edu/j/2017/23-11p.pdf",
"label": "positive curvature and elliptic genus"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/01 | null | null | null | Let $(M,g)$ be a closed Riemannian spin manifold with $\operatorname{sec}(M)>0$. Is its elliptic genus constant as a modular function, namely $\phi(M)=\operatorname{sign}(M)$? | Let (M,g) be a closed Riemannian Spin manifold with sectional curvature sec(M)>0. Is its elliptic genus constant as a modular function, namely \phi(M)=\operatorname{sign}(M)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Manifolds with Lower Curvature Bounds (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/01, pp. 5--42 |
30,001,955 | OWR-11569-001 | Bolza Surface Maximization of the First Eigenvalue | Is the first eigenvalue on the Teichmüller space of genus-$2$ surfaces maximized by the Bolza surface? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Boundary Value Problems and Spectral Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/02, pp. 43--76](https://doi.org/10.4171/owr/2012/02)
## Literature review (ch... | 3 | open | null | 2,012 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11569-001",
"literature-status:open",
"owr-year:2012"
] | The extracted statement ends after the words we conjecture that the first and does not contain a complete mathematical problem; no resolution is verifiable. | [
{
"url": "https://doi.org/10.4171/owr/2012/02",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/02 | null | null | null | Is the first eigenvalue on the Teichmüller space of genus-$2$ surfaces maximized by the Bolza surface? | Conjecture: The first eigenvalue in the Teichmüller space of genus-2 surfaces is maximized by the Bolza surface. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Boundary Value Problems and Spectral Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/02, pp. 43--76 |
30,001,956 | OWR-11570-001 | Bowen's Formula for Nonirreducible Dynamical Systems | For which large classes of non-irreducible systems does Bowen's formula hold, and is there a variation of Bowen's formula encompassing an even broader class of systems? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129](https://doi.org/10.4171/owr/2012/03)
## Literature revie... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11570-001",
"literature-status:open",
"owr-year:2012"
] | The report asks for extensions of Bowen formula to broad non irreducible systems; available results cover special classes but do not establish the requested broad scope. | [
{
"url": "https://doi.org/10.4171/owr/2012/03",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/03 | null | null | null | For which large classes of non-irreducible systems does Bowen's formula hold, and is there a variation of Bowen's formula encompassing an even broader class of systems? | For which large classes of non-irreducible systems does Bowen's formula hold, and is there a variation of Bowen's formula encompassing an even broader class of systems? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129 |
30,001,957 | OWR-11570-002 | Entropy Production on Folded Hyperbolic Fractals | Find other folded fractals $\Lambda$ that are hyperbolic for noninvertible maps $f$, together with families of $f$-invariant measures $\mu$ on $\Lambda$ whose entropy production is negative or positive. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129](https://doi.org/10.4171/owr/2012/03)
## Literature revie... | 3 | partially_solved | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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-11570-002",
"literature-status:partially-solved",
"owr-year:2012"
] | The cited construction already supplies negative inverse SRB entropy, and general entropy production formulas cover broad folded systems; finding further fractals and invariant families remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/03",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1104.2342",
"label": "entropy production for folded systems"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/03 | null | null | null | Find other folded fractals $\Lambda$ that are hyperbolic for noninvertible maps $f$, together with families of $f$-invariant measures $\mu$ on $\Lambda$ whose entropy production is negative or positive. | Find other folded fractals \Lambda that are hyperbolic for non-invertible maps f, together with families of f-invariant measures \mu on \Lambda whose entropy production is negative or positive. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129 |
30,001,958 | OWR-11570-003 | Explicit Invariant Densities for Even Continued Fractions | For the set $E_{\mathrm{even}}$ of irrational numbers in $[0,1]$ with all continued-fraction entries even, whose Gauss-map invariant measure $\mu$ is equivalent to its Hausdorff-dimension packing measure $P_h$, find a closed explicit formula for the real-analytic extension of $d\mu/dP_h$ to $[0,1]$, or prove that no su... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129](https://doi.org/10.4171/owr/2012/03)
## Literature revie... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11570-003",
"literature-status:open",
"owr-year:2012"
] | The extracted text repeats the preceding problem and then ends before the actual noise induced phenomenon question; no complete claim is available to verify. | [
{
"url": "https://doi.org/10.4171/owr/2012/03",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/03 | null | null | null | For the set $E_{\mathrm{even}}$ of irrational numbers in $[0,1]$ with all continued-fraction entries even, whose Gauss-map invariant measure $\mu$ is equivalent to its Hausdorff-dimension packing measure $P_h$, find a closed explicit formula for the real-analytic extension of $d\mu/dP_h$ to $[0,1]$, or prove that no su... | For the set E_{\mathrm{even}} of irrational numbers in [0,1] with all continued-fraction entries even, whose Gauss-map invariant measure \mu is equivalent to its Hausdorff-dimension packing measure P_h, find a closed explicit formula for the real-analytic extension of d\mu/dP_h to [0,1], or prove that no such formula e... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129 |
30,001,959 | OWR-11570-004 | Rigorous Noise-Induced Phenomena in Random Dynamical Systems | Give mathematically complete proofs for various noise-induced phenomena observed in numerical experiments for random dynamical systems, including i.i.d. random dynamics of complex polynomials on the Riemann sphere. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129](https://doi.org/10.4171/owr/2012/03)
## Literature revie... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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-11570-004",
"literature-status:open",
"owr-year:2012"
] | This is an explicitly broad request for rigorous proofs of noise induced phenomena, and the extracted statement supplies no resolved theorem or finite target. | [
{
"url": "https://doi.org/10.4171/owr/2012/03",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/03 | null | null | null | Give mathematically complete proofs for various noise-induced phenomena observed in numerical experiments for random dynamical systems, including i.i.d. random dynamics of complex polynomials on the Riemann sphere. | Give mathematically complete proofs for various noise-induced phenomena observed in numerical experiments for random dynamical systems, including i.i.d. random dynamics of complex polynomials on the Riemann sphere. | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129 |
30,001,960 | OWR-11570-005 | Decay of Correlations in Random Quadratic Maps | For the random quadratic system $T_\lambda(x)=\lambda x(1-x)$ with i.i.d. parameters $\lambda_i\in[1,4]$ distributed by an absolutely continuous probability measure $P$, does the system have random decay of correlations, equivalently, is it relatively exact? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129](https://doi.org/10.4171/owr/2012/03)
## Literature revie... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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-11570-005",
"literature-status:open",
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] | The extraction contains only the tail of the random quadratic map problem and does not state a complete proposition; the requested general result is therefore unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2012/03",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/03 | null | null | null | For the random quadratic system $T_\lambda(x)=\lambda x(1-x)$ with i.i.d. parameters $\lambda_i\in[1,4]$ distributed by an absolutely continuous probability measure $P$, does the system have random decay of correlations, equivalently, is it relatively exact? | For the random quadratic system T_\lambda(x)=\lambda x(1-x) with i.i.d. parameters \lambda_i\in[1,4] distributed by an absolutely continuous probability measure P, does the system have random decay of correlations, equivalently, is it relatively exact? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129 |
30,001,961 | OWR-11570-006 | Local-Energy Classes of Summable Lattice-Gas Interactions | For translation-invariant lattice-gas interactions $\Phi$ on $\mathbb{N}^{\mathbb{Z}^d}$, let $\mathcal{A}_S$ consist of the local energy functions generated by interactions in $S=\{\Phi:\sum_{\Lambda\ni0}\lVert\Phi_\Lambda\rVert_\infty<\infty\}$, and let $\mathcal{R}_d=\{f:\sum_{n\geq1}n^d\delta_n(f)<\infty\}$. Given ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129](https://doi.org/10.4171/owr/2012/03)
## Literature revie... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11570-006",
"literature-status:open",
"owr-year:2012"
] | The known theory gives real analyticity of the radial Julia dimension in hyperbolic parameters, but the supremum and monotonicity questions in the report remain open. | [
{
"url": "https://doi.org/10.4171/owr/2012/03",
"label": "original Oberwolfach report"
},
{
"url": "https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/real-analyticity-of-hausdorff-dimension-of-finer-julia-sets-of-exponential-family/40CE052F557F04507E762ABE161CF857"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/03 | null | null | null | For translation-invariant lattice-gas interactions $\Phi$ on $\mathbb{N}^{\mathbb{Z}^d}$, let $\mathcal{A}_S$ consist of the local energy functions generated by interactions in $S=\{\Phi:\sum_{\Lambda\ni0}\lVert\Phi_\Lambda\rVert_\infty<\infty\}$, and let $\mathcal{R}_d=\{f:\sum_{n\geq1}n^d\delta_n(f)<\infty\}$. Given ... | For translation-invariant lattice-gas interactions \Phi on \mathbb{N}^{\mathbb{Z}^d}, let \mathcal A_S be the class of local energy functions generated by interactions in S=\{\Phi:\sum_{\Lambda\ni0}\|\Phi_\Lambda\|_\infty<\infty\}, and let \mathcal R_d=\{f:\sum_{n\ge1}n^d\delta_n(f)<\infty\}. Given the known inclusions... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129 |
30,001,962 | OWR-11570-007 | Radial Julia Dimensions of Exponential Maps | For $f_\lambda(z)=\lambda e^z$ with hyperbolic parameter $\lambda$, determine the supremum of $\dim_H(J_r(f_\lambda))$ over all hyperbolic parameters, and determine whether the function $\lambda\mapsto\dim_H(J_r(f_\lambda))$ is increasing on $(0,1/e)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129](https://doi.org/10.4171/owr/2012/03)
## Literature revie... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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-11570-007",
"literature-status:open",
"owr-year:2012"
] | The extraction ends at the setup of the lattice gas Banach spaces and omits the actual question; no mathematical resolution can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2012/03",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/03 | null | null | null | For $f_\lambda(z)=\lambda e^z$ with hyperbolic parameter $\lambda$, determine the supremum of $\dim_H(J_r(f_\lambda))$ over all hyperbolic parameters, and determine whether the function $\lambda\mapsto\dim_H(J_r(f_\lambda))$ is increasing on $(0,1/e)$. | For f_\lambda(z)=\lambda e^z with hyperbolic parameter \lambda, determine the supremum of \dim_H(J_r(f_\lambda)) over all hyperbolic parameters, and determine whether the function \lambda\mapsto\dim_H(J_r(f_\lambda)) is increasing on (0,1/e). | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/03, pp. 77--129 |
30,001,963 | OWR-11571-001 | Recovering Tacit Mathematical Skills from Historical Sources | How can historians recover skills, arts, or knowledge that were not specified or explicated in mathematical sources? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-001",
"literature-status:open",
"owr-year:2012"
] | This is a historiographical question about recovering tacit mathematical skills, not a resolved mathematical theorem; no definitive answer was located. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | How can historians recover skills, arts, or knowledge that were not specified or explicated in mathematical sources? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,964 | OWR-11571-002 | Tacit and Explicit Knowledge in Mathematical Practice | How tacit is tacit knowledge in mathematical practice, and how can historians distinguish and recover it from explicit knowledge and incomplete sources? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-002",
"literature-status:open",
"owr-year:2012"
] | This is a broad conceptual question about tacit knowledge, with no determinate theorem or demonstrably settled answer in the cited literature. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | How tacit is tacit knowledge in mathematical practice, and how can historians distinguish and recover it from explicit knowledge and incomplete sources? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,965 | OWR-11571-003 | Tacit Knowledge in Mathematical History | Can historical events in the development of mathematics be understood more plausibly by treating tacit knowledge as a form of knowledge? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-003",
"literature-status:open",
"owr-year:2012"
] | The extracted question asks for a historical interpretation of tacit knowledge and is not a claim that can be marked solved or disproved. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | Can historical events in the development of mathematics be understood more plausibly by treating tacit knowledge as a form of knowledge? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,966 | OWR-11571-004 | Explicit and Tacit Knowledge in Mathematical Instruments | In mathematical instruments and their accompanying texts, what knowledge was selected to be explained and what knowledge remained tacit? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-004",
"literature-status:open",
"owr-year:2012"
] | The text is an open historiographical question about what knowledge was made explicit; no unique settled answer is asserted by the literature. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | In mathematical instruments and their accompanying texts, what knowledge was selected to be explained and what knowledge remained tacit? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,967 | OWR-11571-005 | Bicycle Mechanics and Tacit Mathematical Knowledge | What are the historical relationships between bicycle riding, tacit knowledge, mathematical knowledge, and mathematical theories of the bicycle; what tacit knowledge shaped those theories; and what does this reveal about the role of mathematics in mechanics around the turn of the twentieth century? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-005",
"literature-status:open",
"owr-year:2012"
] | These are research questions about bicycle mechanics and tacit knowledge, not a single theorem with a known resolution; they remain open as posed. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | What are the historical relationships between bicycle riding, tacit knowledge, mathematical knowledge, and mathematical theories of the bicycle; what tacit knowledge shaped those theories; and what does this reveal about the role of mathematics in mechanics around the turn of the twentieth century? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,968 | OWR-11571-006 | Modeling and Solving Bicycle Motion | In developing a mathematical theory of bicycle motion, how should one choose coordinates, parameters, and variables; derive the differential equations; choose useful approximations; solve the equations analytically, numerically, or graphically; and draw practical conclusions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-006",
"literature-status:open",
"owr-year:2012"
] | The extracted text lists methodological questions about modeling and solving mechanics problems, without a finite mathematical claim or established resolution. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | In developing a mathematical theory of bicycle motion, how should one choose coordinates, parameters, and variables; derive the differential equations; choose useful approximations; solve the equations analytically, numerically, or graphically; and draw practical conclusions? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,969 | OWR-11571-007 | Interpreting Obscure Medieval Mathematical Algorithms | How can algorithms in medieval mathematical texts that are obscure to modern readers be understood, and what elements guarantee their correctness? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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"
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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 history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-007",
"literature-status:open",
"owr-year:2012"
] | The questions concern interpretation and correctness of medieval algorithms; the extraction provides no single formal claim whose resolution could be verified. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | How can algorithms in medieval mathematical texts that are obscure to modern readers be understood, and what elements guarantee their correctness? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,970 | OWR-11571-008 | Tacit Steps and Textual Corruption in Medieval Algorithms | When a medieval mathematical algorithm omits steps, is the tacit formulation intentional and meant to transmit the knowledge clearly, or does it arise from some other cause such as textual corruption? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-008",
"literature-status:open",
"owr-year:2012"
] | The extracted question is a conceptual inquiry about authorial tacit formulation, not a resolved mathematical proposition. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | When a medieval mathematical algorithm omits steps, is the tacit formulation intentional and meant to transmit the knowledge clearly, or does it arise from some other cause such as textual corruption? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,971 | OWR-11571-009 | Omitted Steps in Historical Mathematical Algorithms | Why did the author of a mathematical algorithm omit some steps: by deliberate choice, or because the surviving text is corrupted? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-009",
"literature-status:open",
"owr-year:2012"
] | This is a historical question about omitted steps and textual corruption; no determinate answer is established by the extracted report passage. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | Why did the author of a mathematical algorithm omit some steps: by deliberate choice, or because the surviving text is corrupted? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,972 | OWR-11571-010 | Mathematical Signs and Model-Theoretic Semantics | What is the connection between the realm of signs used in mathematical practice and the realm of unused signs studied by model theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-010",
"literature-status:open",
"owr-year:2012"
] | The question concerns the relation between mathematical signs and model theory in a philosophical context; it is not a settled theorem or false claim. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | What is the connection between the realm of signs used in mathematical practice and the realm of unused signs studied by model theory? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,973 | OWR-11571-011 | Practices of Nineteenth-Century Mathematical Education | What mathematical practices were students encouraged to master in nineteenth-century mathematical education, and what methods, priorities, and evaluation criteria governed that training? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-011",
"literature-status:open",
"owr-year:2012"
] | The extracted question asks about mathematical practices in nineteenth century training and remains an interpretive historical research question. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | What mathematical practices were students encouraged to master in nineteenth-century mathematical education, and what methods, priorities, and evaluation criteria governed that training? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,974 | OWR-11571-012 | Mathematical Learning as Evidence of Tacit Knowledge | What does taking the learning of mathematics as a point of departure add to the investigation of tacit and explicit mathematical knowledge? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-012",
"literature-status:open",
"owr-year:2012"
] | The question asks what is gained by studying learning as a historical source; it has no determinate mathematical truth value or settled resolution. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | What does taking the learning of mathematics as a point of departure add to the investigation of tacit and explicit mathematical knowledge? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,975 | OWR-11571-013 | Polanyi's Tacit Knowledge in Mathematical History | Does Polanyi's concept of tacit knowledge help explain the historical development of mathematics, and how does tacit knowledge relate to explicit mathematical knowledge? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-013",
"literature-status:open",
"owr-year:2012"
] | The extracted text poses a broad historical question about Polanyi and mathematical development, with no definitive answer that would justify solved or Disproved. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | Does Polanyi's concept of tacit knowledge help explain the historical development of mathematics, and how does tacit knowledge relate to explicit mathematical knowledge? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,976 | OWR-11571-014 | Rigor and Antiformalism in Mathematics | How can the apparent tension between the modern demand for rigor and criticism of formalism be explained? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-014",
"literature-status:open",
"owr-year:2012"
] | This is a philosophical historiographical question about rigor and formalism, not a resolved mathematical assertion; it remains open as extracted. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | How can the apparent tension between the modern demand for rigor and criticism of formalism be explained? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,977 | OWR-11571-015 | Tree Metaphors for Mathematical Development | In the tree metaphor for mathematics, are the roots or the branches essential, or does the mathematical organism depend on the interaction of all its parts? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 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 official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-015",
"literature-status:open",
"owr-year:2012"
] | The extracted passage is a botanical analogy, not a mathematical claim or formal open problem; no mathematical resolution can be assigned. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | In the tree metaphor for mathematics, are the roots or the branches essential, or does the mathematical organism depend on the interaction of all its parts? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,978 | OWR-11571-017 | Logical Strength and Usefulness in Number Theory | Should number theorists care whether their abstract structures imply strongly inaccessible cardinals, and can logic yield useful number-theoretic results or clarify the strength of Fermat's Last Theorem over Peano Arithmetic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210](https://doi.org/10.4171/owr/2012/04)
## Literature review (checked 2026-0... | 3 | open | null | 2,012 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather tha) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11571-017",
"literature-status:open",
"owr-year:2012"
] | This is a broad foundational question about the usefulness of strong axioms and formal independence, not a single precisely stated theorem; no resolution applies to the extracted text. | [
{
"url": "https://doi.org/10.4171/owr/2012/04",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/04 | null | null | null | null | Should number theorists care whether their abstract structures imply strongly inaccessible cardinals, and can logic yield useful number-theoretic results or clarify the strength of Fermat's Last Theorem over Peano Arithmetic? | unrecoverable | The official history-of-mathematics workshop report treats this as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/04, pp. 131--210 |
30,001,979 | OWR-11573-001 | Equivalent-Dynamics Construction Report | How can one construct an equivalent dynamics that is obtained much more quickly than by naively discretizing the governing equation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Analysis and Probability in Physics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/06, pp. 281--349](https://doi.org/10.4171/owr/2012/06)
## Literature review (checked 2026... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official contribution introduces the desire for faster equivalent dynamics and then supplies the construction and results; the extracted) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11573-001",
"literature-status:open",
"owr-year:2012"
] | The extraction is a methodological question about obtaining faster equivalent dynamics and supplies no precise equation, hypotheses, or target theorem; it remains open as extracted. | [
{
"url": "https://doi.org/10.4171/owr/2012/06",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/06 | null | null | null | null | How can one construct an equivalent dynamics that is obtained much more quickly than by naively discretizing the governing equation? | unrecoverable | The official contribution introduces the desire for faster equivalent dynamics and then supplies the construction and results; the extracted sentence is expository motivation, not a separately posed open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for prov... | null | null | null | null | null | Interplay of Analysis and Probability in Physics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/06, pp. 281--349 |
30,001,980 | OWR-11573-002 | Ballistic-Annihilation Scaling-Limit Report | Can continuum equations such as the Boltzmann equation be rigorously derived as scaling limits of deterministic many-particle dynamics, in particular for ballistic annihilation with random initial data? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Analysis and Probability in Physics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/06, pp. 281--349](https://doi.org/10.4171/owr/2012/06)
## Literature review (checked 2026... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official contribution presents the continuum-limit question as motivation and then derives the announced Boltzmann scaling result; the e) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11573-002",
"literature-status:open",
"owr-year:2012"
] | The statement is a truncated setup for a Boltzmann-limit problem in ballistic annihilation, not a complete claim that can be marked solved or disproved. | [
{
"url": "https://doi.org/10.4171/owr/2012/06",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/06 | null | null | null | null | Can continuum equations such as the Boltzmann equation be rigorously derived as scaling limits of deterministic many-particle dynamics, in particular for ballistic annihilation with random initial data? | unrecoverable | The official contribution presents the continuum-limit question as motivation and then derives the announced Boltzmann scaling result; the extraction is not a separately retained open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Interplay of Analysis and Probability in Physics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/06, pp. 281--349 |
30,001,981 | OWR-11575-002 | Random Axioms in Computability and Kolmogorov Complexity | Are random axioms useful in computability theory and Kolmogorov complexity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455](https://doi.org/10.4171/owr/2012/08)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,012 | 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-11575-002",
"literature-status:open",
"owr-year:2012"
] | The broad question about the usefulness of random axioms has no precise formal statement in the extraction; it remains unresolved as a research question. | [
{
"url": "https://doi.org/10.4171/owr/2012/08",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/08 | null | null | null | Are random axioms useful in computability theory and Kolmogorov complexity? | Are random axioms useful in computability theory and Kolmogorov complexity? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455 |
30,001,982 | OWR-11575-003 | Random Minimal Pairs and Cupping Below the Halting Problem | For every noncomputable $A<_T\varnothing'$ that is not $K$-trivial, does there exist a Martin-Löf random $R<_T\varnothing'$ such that $A\oplus R\equiv_T\varnothing'$ and every $B\leq_T A,R$ is $K$-trivial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455](https://doi.org/10.4171/owr/2012/08)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,012 | 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-11575-003",
"literature-status:open",
"owr-year:2012"
] | The report explicitly labels this strengthened Martin--Lof random minimal-pair and cupping formulation unknown; the later literature located did not resolve this exact statement. | [
{
"url": "https://doi.org/10.4171/owr/2012/08",
"label": "original Oberwolfach report"
},
{
"url": "https://people.math.wisc.edu/~jsmiller8/Papers/MLcuppable.pdf",
"label": "cupping with random sets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/08 | null | null | null | For every noncomputable $A<_T\varnothing'$ that is not $K$-trivial, does there exist a Martin-Löf random $R<_T\varnothing'$ such that $A\oplus R\equiv_T\varnothing'$ and every $B\leq_T A,R$ is $K$-trivial? | For every noncomputable A <_T \varnothing' that is not K-trivial, does there exist a Martin-Löf random R <_T \varnothing' such that A \oplus R \equiv_T \varnothing' and every B \leq_T A,R is K-trivial? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455 |
30,001,983 | OWR-11575-006 | Complexity of Maximal Chains in Computable Well-Partial-Orders | For a computable well-partial-order $P$, how complicated must any function be that maps $P$ to a maximal chain in $P$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455](https://doi.org/10.4171/owr/2012/08)
## Literature review (checked 2026-08-21)
**Status:** partial... | 3 | partially_solved | null | 2,012 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source)**. A. Marcone (joint with A. Montalbán and R. Shore; OWR 8/2012, p. 420, Question 2) asks how complicated a function taking a computable well partial order to a maximal chain must be. Theorem 8 there answers it: no hyperarithmetic procedure... | [
"owr",
"oberwolfach-reports",
"OWR-11575-006",
"literature-status:partially-solved",
"owr-year:2012"
] | The report proves substantial upper and lower complexity results for maximal chains in computable well partial orders, but the extracted general optimal-complexity question is not fully settled by those results. | [
{
"url": "https://doi.org/10.4171/owr/2012/08",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/08 | null | null | null | For a computable well-partial-order $P$, how complicated must any function be that maps $P$ to a maximal chain in $P$? | For a computable well-partial-order P, how complicated must any function be that maps P to a maximal chain in P? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455 |
30,001,984 | OWR-11575-007 | Complete Sets in D-Maximal Orbits | For the D-maximal c.e. sets and their infinitely many orbits, do all but finitely many of the remaining orbits contain complete sets? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455](https://doi.org/10.4171/owr/2012/08)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,012 | 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-11575-007",
"literature-status:open",
"owr-year:2012"
] | The report states that whether the remaining D-maximal orbits contain complete sets is unknown; the extracted classification therefore remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/08",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/08 | null | null | null | For the D-maximal c.e. sets and their infinitely many orbits, do all but finitely many of the remaining orbits contain complete sets? | For the D-maximal c.e. sets and their infinitely many orbits, do all but finitely many of the remaining orbits contain complete sets? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455 |
30,001,985 | OWR-11575-009 | Recursive Spectra of Strongly Minimal Theories | If $T$ is a strongly minimal theory in a finite language satisfying Zilber's conjecture, is the collection of recursively presentable models of $T$ equal to $\varnothing$, all countable models of $T$, or the prime model of $T$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455](https://doi.org/10.4171/owr/2012/08)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,012 | 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-11575-009",
"literature-status:open",
"owr-year:2012"
] | The extraction records a conjecture about recursive spectra of strongly minimal theories; no primary source located through the current search resolves this general conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2012/08",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/08 | null | null | null | If $T$ is a strongly minimal theory in a finite language satisfying Zilber's conjecture, is the collection of recursively presentable models of $T$ equal to $\varnothing$, all countable models of $T$, or the prime model of $T$? | If T is a strongly minimal theory in a finite language satisfying Zilber's conjecture, is the collection of recursively presentable models of T equal to \varnothing, all countable models of T, or the prime model of T? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455 |
30,001,986 | OWR-11575-013 | Turing Degree of Finite-Set Cardinality Indices | In computability theory and algorithmic randomness, let $(K_e)_{e \in \omega}$ be a standard effective listing of the finite $K$-trivial classes (sets of reals $A$ with prefix-free Kolmogorov complexity $K(A \upharpoonright n) \leq K(n) + e$ for all $n$). Does the cardinality function $e \mapsto |K_e|$ compute the Turi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455](https://doi.org/10.4171/owr/2012/08)
## Literature review (checked 2026-08-21)
**Status:** partial... | 3 | partially_solved | null | 2,012 | 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-11575-013",
"literature-status:partially-solved",
"owr-year:2012"
] | The counting function is proved Delta-three and not Delta-two, but the stronger question whether it computes the first or second halting jump is not resolved by the located literature. | [
{
"url": "https://doi.org/10.4171/owr/2012/08",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.tcs.2011.09.020",
"label": "K-trivial counting theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/08 | null | null | null | In computability theory and algorithmic randomness, let $(K_e)_{e \in \omega}$ be a standard effective listing of the finite $K$-trivial classes (sets of reals $A$ with prefix-free Kolmogorov complexity $K(A \upharpoonright n) \leq K(n) + e$ for all $n$). Does the cardinality function $e \mapsto |K_e|$ compute the Turi... | Does the function e \mapsto |K_e| compute \varnothing' or even \varnothing''? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455 |
30,001,987 | OWR-11575-014 | Turing Degrees of Differential-Field Embedding Images | For Harrington's computable differential-field embedding $g$, what is the Turing degree of the image $g(K)$, and what is the appropriate differential analogue of the splitting set? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455](https://doi.org/10.4171/owr/2012/08)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | partially_solved | null | 2,012 | 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://doi.org/10.1016/j.jalgebra.2014.02.032",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved** (answered in part in the source). R. Miller (joint with A. Ovchinnikov and D. Trushin; OWR 8/2012, pp. 440–441) asks what the Turing degree of the image g(K) of Harrington's embedding of a computable differential field is, and what the differential anal... | [
"owr",
"oberwolfach-reports",
"OWR-11575-014",
"literature-status:open",
"owr-year:2012"
] | The extraction is a historical fragment about reducibility of polynomial representations and does not state a complete decidable theorem; the underlying question remains unresolved as extracted. | [
{
"url": "https://doi.org/10.4171/owr/2012/08",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/08 | null | null | null | For Harrington's computable differential-field embedding $g$, what is the Turing degree of the image $g(K)$, and what is the appropriate differential analogue of the splitting set? | For Harrington's computable differential-field embedding g, what is the Turing degree of the image g(K), and what is the appropriate differential analogue of the splitting set? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455 |
30,001,988 | OWR-11575-015 | Splitting Sets Under Differential-Transcendental Extensions | If $K$ is a computable differential field and $z$ is differentially transcendental over $K$ in a larger computable differential field, is $T_{K\langle z\rangle}$ Turing-computable from $T_K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455](https://doi.org/10.4171/owr/2012/08)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,012 | 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-11575-015",
"literature-status:open",
"owr-year:2012"
] | The report presents this differential-field computability statement as a conjecture and explicitly says that the relevant proof remains to be checked; it is therefore unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2012/08",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/08 | null | null | null | If $K$ is a computable differential field and $z$ is differentially transcendental over $K$ in a larger computable differential field, is $T_{K\langle z\rangle}$ Turing-computable from $T_K$? | If K is a computable differential field and z is differentially transcendental over K in a larger computable differential field, is T_{K\langle z\rangle} Turing-computable from T_K? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455 |
30,001,989 | OWR-11575-016 | Finite Lattices in Computably Enumerable Turing Degrees | Which finite lattices can be embedded into the computably enumerable Turing degrees while preserving joins and meets? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455](https://doi.org/10.4171/owr/2012/08)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,012 | 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-11575-016",
"literature-status:open",
"owr-year:2012"
] | A current status survey still describes the characterization of finite lattices embeddable in the computably enumerable degrees as a longstanding open problem, with only substantial subclasses classified. | [
{
"url": "https://doi.org/10.4171/owr/2012/08",
"label": "original Oberwolfach report"
},
{
"url": "https://people.math.wisc.edu/~slempp/papers/muenster.pdf",
"label": "finite-lattice status survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/08 | null | null | null | Which finite lattices can be embedded into the computably enumerable Turing degrees while preserving joins and meets? | Which finite lattices can be embedded into the computably enumerable Turing degrees while preserving joins and meets? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455 |
30,001,990 | OWR-11575-017 | Finite-Lattice Obstructions in Enumerable Reducibility Degrees | Does there exist a finite lattice that cannot be embedded into the recursively enumerable cl-degrees or ibT-degrees? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455](https://doi.org/10.4171/owr/2012/08)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,012 | 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-11575-017",
"literature-status:open",
"owr-year:2012"
] | The report asks whether a finite lattice fails to embed into the computably enumerable computable-Lipschitz or identity-bounded degrees; no complete answer to this exact question was located. | [
{
"url": "https://doi.org/10.4171/owr/2012/08",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/08 | null | null | null | Does there exist a finite lattice that cannot be embedded into the recursively enumerable cl-degrees or ibT-degrees? | Does there exist a finite lattice that cannot be embedded into the recursively enumerable cl-degrees or ibT-degrees? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Computability Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/08, pp. 397--455 |
30,001,991 | OWR-11576-001 | Stability of Finite-Element Methods for Incompressible Elasticity | For two benchmark problems in two-dimensional incompressible finite elasticity, what are the stability properties of the continuum solutions and of their displacement, mixed, and mixed-enhanced finite-element discretizations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Advanced Computational Engineering (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/09, pp. 457--553](https://doi.org/10.4171/owr/2012/09)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,012 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11576-001",
"literature-status:open",
"owr-year:2012"
] | This is an incomplete extraction of a finite-element stability benchmark labelled Problem 1; it supplies neither a complete mathematical statement nor a resolution. | [
{
"url": "https://doi.org/10.4171/owr/2012/09",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/09 | null | null | null | For two benchmark problems in two-dimensional incompressible finite elasticity, what are the stability properties of the continuum solutions and of their displacement, mixed, and mixed-enhanced finite-element discretizations? | For the two two-dimensional incompressible finite-elasticity benchmark problems, what are the stability properties of the continuum solutions and their displacement, mixed, and mixed-enhanced finite-element discretizations? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Advanced Computational Engineering (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/09, pp. 457--553 |
30,001,992 | OWR-11576-002 | Constraint Functions in $Q_2$–$P_1$ Incompressible Elasticity | For a $Q_2$–$P_1$ discretization of incompressible finite elasticity, how does the choice of constraint function $\Theta$ affect stability and the numerical solution as the mesh is refined? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Advanced Computational Engineering (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/09, pp. 457--553](https://doi.org/10.4171/owr/2012/09)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,012 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11576-002",
"literature-status:open",
"owr-year:2012"
] | The extracted finite-element stability question reports numerical dependence on the penalty function but does not establish a general theorem; the research problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/09",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/09 | null | null | null | For a $Q_2$–$P_1$ discretization of incompressible finite elasticity, how does the choice of constraint function $\Theta$ affect stability and the numerical solution as the mesh is refined? | For incompressible finite-elasticity Problem 2, how does the choice of the constraint function \Theta affect the stability and numerical solution of the Q2-P1 discretization as the mesh is refined? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Advanced Computational Engineering (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/09, pp. 457--553 |
30,001,993 | OWR-11576-003 | Competitiveness of High-Order Hybridizable DG Wave Methods | Are high-order and hybridizable discontinuous Galerkin methods competitive for demanding wave-propagation computations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Advanced Computational Engineering (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/09, pp. 457--553](https://doi.org/10.4171/owr/2012/09)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,012 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11576-003",
"literature-status:open",
"owr-year:2012"
] | The competitiveness question is a broad computational-method comparison without a fixed model, metric, or theorem, so the extracted problem remains open rather than solved or disproved. | [
{
"url": "https://doi.org/10.4171/owr/2012/09",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/09 | null | null | null | Are high-order and hybridizable discontinuous Galerkin methods competitive for demanding wave-propagation computations? | Are high-order and hybridizable discontinuous Galerkin methods competitive for demanding wave-propagation computations? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Advanced Computational Engineering (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/09, pp. 457--553 |
30,001,994 | OWR-11578-001 | Variational Eddy Currents with Degenerate Conductivity | For general nonnegative $\sigma\in L^\infty(\mathbb R^3)$, can the mapping $A\mapsto\phi_A$ be defined in the variational formulation of the eddy-current equation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Inverse Problems for Partial Differential Equations (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/11, pp. 611--659](https://doi.org/10.4171/owr/2012/11)
## Literature review (checked 2... | 3 | open | null | 2,012 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23049211",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] OWR-11578-001: a counterexample to Harrach's general potential-map question is now public. (https://zenodo.org/records/23049211) | [
"owr",
"oberwolfach-reports",
"OWR-11578-001",
"literature-status:open",
"owr-year:2012"
] | The report explicitly leaves the extension to arbitrary nonnegative bounded conductivity open; no general well posed definition of the map was found by the checked date. | [
{
"url": "https://doi.org/10.4171/owr/2012/11",
"label": "Oberwolfach Report 11 2012"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/11 | null | null | null | For general nonnegative $\sigma\in L^\infty(\mathbb R^3)$, can the mapping $A\mapsto\phi_A$ be defined in the variational formulation of the eddy-current equation? | For general nonnegative \sigma \in L^\infty(\mathbb{R}^3), can the mapping A \mapsto \phi_A be defined in the variational formulation of the eddy-current equation? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Inverse Problems for Partial Differential Equations (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/11, pp. 611--659 |
30,001,995 | OWR-11578-002 | Vanishing-Regularization Convergence for Nonlinear Iterations | In iterative regularization for nonlinear inverse PDE problems $R(u) = g$, let $B$ be a nonlinear forward/reconstruction operator with local approximations $B_k$, and let $S_n = N_{\rho, \alpha_n} \circ R$ be the regularized inverse step using Tikhonov regularization with parameter $\alpha_n \to 0$. Can the convergence... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Inverse Problems for Partial Differential Equations (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/11, pp. 611--659](https://doi.org/10.4171/owr/2012/11)
## Literature review (checked 2... | 3 | open | null | 2,012 | 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-11578-002",
"literature-status:open",
"owr-year:2012"
] | The requested convergence theory for Tikhonov regularization with vanishing parameters is still stated as an open extension, and no primary paper establishing it in this setting was located. | [
{
"url": "https://doi.org/10.4171/owr/2012/11",
"label": "Oberwolfach Report 11 2012"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/11 | null | null | null | In iterative regularization for nonlinear inverse PDE problems $R(u) = g$, let $B$ be a nonlinear forward/reconstruction operator with local approximations $B_k$, and let $S_n = N_{\rho, \alpha_n} \circ R$ be the regularized inverse step using Tikhonov regularization with parameter $\alpha_n \to 0$. Can the convergence... | Can the convergence analysis of the iteration g_{n+1}=g_k+B(S(g_n))-B_k(S(g_n)) be extended when S is replaced by S_n=N_{\rho,\alpha_n}\circ R with Tikhonov regularization and \alpha_n\to0? | corrected_verified | The official report confirms the displayed iteration and the vanishing-regularization question, but the short report excerpt does not define all operators sufficiently for a fully self-contained promotion. | null | null | null | null | null | Inverse Problems for Partial Differential Equations (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/11, pp. 611--659 |
30,001,996 | OWR-11579-001 | Ensemble Controllability from Individual Controllability | If every individual system in a parameterized ensemble is controllable, under what additional conditions is the ensemble jointly controllable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: Mathematical Perspectives on Complex Networked Systems (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/12, pp. 661--732](https://doi.org/10.4171/owr/2012/12)
## Literatur... | 3 | partially_solved | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11579-001",
"literature-status:partially-solved",
"owr-year:2012"
] | General smooth ensembles remain broader than the known theory, but the individual-to-ensemble implication is proved for important bilinear ensembles on semisimple Lie groups and related special classes. | [
{
"url": "https://doi.org/10.4171/owr/2012/12",
"label": "Oberwolfach Report 12 2012"
},
{
"url": "https://arxiv.org/abs/2008.03243",
"label": "Ensemble Control on Lie Groups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/12 | null | null | null | If every individual system in a parameterized ensemble is controllable, under what additional conditions is the ensemble jointly controllable? | What can be said about controllability of the joint system when every individual system in the ensemble is controllable? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Control Theory: Mathematical Perspectives on Complex Networked Systems (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/12, pp. 661--732 |
30,001,997 | OWR-11579-002 | Joint Event-Trigger and Control Optimization | In event-triggered stochastic linear-quadratic control with an average communication budget $\bar m$, what are the optimal control policy $f^*$ and event-triggering policy $\gamma^*$ minimizing $\mathbb E[J_C]$ subject to $\mathbb E[J_E]\leq\bar m$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Theory: Mathematical Perspectives on Complex Networked Systems (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/12, pp. 661--732](https://doi.org/10.4171/owr/2012/12)
## Literatur... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11579-002",
"literature-status:open",
"owr-year:2012"
] | Certainty equivalence is available as a structural preliminary result, but the constrained joint optimization over event and control policies remains difficult and no general optimal policy characterization was found. | [
{
"url": "https://doi.org/10.4171/owr/2012/12",
"label": "Oberwolfach Report 12 2012"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/12 | null | null | null | In event-triggered stochastic linear-quadratic control with an average communication budget $\bar m$, what are the optimal control policy $f^*$ and event-triggering policy $\gamma^*$ minimizing $\mathbb E[J_C]$ subject to $\mathbb E[J_E]\leq\bar m$? | In event-triggered stochastic linear-quadratic control with an average communication budget \bar m, what are the optimal control policy f^* and event-triggering policy \gamma^* minimizing E[J_C] subject to E[J_E]\leq\bar m? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Control Theory: Mathematical Perspectives on Complex Networked Systems (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/12, pp. 661--732 |
30,001,998 | OWR-11580-002 | Cohomology and Classification of Group Schemes over DVRs | Describe the coherent cohomology ring of group schemes over a discrete valuation ring, and classify anti-affine group schemes over a discrete valuation ring. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | open | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-002",
"literature-status:open",
"owr-year:2012"
] | The coherent cohomology ring over a discrete valuation ring and the structure of anti-affine group schemes remain unresolved in the generality stated. | [
{
"url": "https://doi.org/10.4171/owr/2012/13",
"label": "Oberwolfach Report 13 2012"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | Describe the coherent cohomology ring of group schemes over a discrete valuation ring, and classify anti-affine group schemes over a discrete valuation ring. | Describe the coherent cohomology ring of group schemes over a discrete valuation ring, and classify anti-affine group schemes in this setting. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,001,999 | OWR-11580-003 | Feigin–Frenkel–Lusztig Character Formula | Prove the Feigin–Frenkel–Lusztig character formula expressing the character of a critical-level simple module $L(\lambda)$ in terms of periodic polynomials. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | open | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-003",
"literature-status:open",
"owr-year:2012"
] | The extracted item is an unfinished conjectural program linking sheaves on the affine flag setting to positive-level category O; the available literature does not establish the stated general critical-representation consequences. | [
{
"url": "https://doi.org/10.4171/owr/2012/13",
"label": "Oberwolfach Report 13 2012"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | Prove the Feigin–Frenkel–Lusztig character formula expressing the character of a critical-level simple module $L(\lambda)$ in terms of periodic polynomials. | Prove the Feigin--Frenkel--Lusztig character formula expressing the character of a critical-level simple module L(\lambda) in terms of periodic polynomials. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,000 | OWR-11580-004 | $q$-Whittaker Eigenfunctions of Lattice Quantum Toda Operators | For a semisimple simply connected group $G$, prove existence and uniqueness of the $q$-Whittaker polynomials $\Psi_{\check{\lambda}}(q,z)$ satisfying vanishing outside dominant weights, $\Psi_0=1$, and $M_f^{\mathrm{lat}}(\Psi(q,z))=f(z)\Psi(q,z)$ for every Weyl-invariant $f$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | open | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-004",
"literature-status:open",
"owr-year:2012"
] | The original lattice quantum Toda joint-eigenfunction conjecture is explicitly presented as unproved; later work proves modified or related formulations, not this exact Mlat statement in full generality. | [
{
"url": "https://doi.org/10.4171/owr/2012/13",
"label": "Oberwolfach Report 13 2012"
},
{
"url": "https://arxiv.org/abs/1203.1583",
"label": "Weyl Modules and q-Whittaker Functions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | For a semisimple simply connected group $G$, prove existence and uniqueness of the $q$-Whittaker polynomials $\Psi_{\check{\lambda}}(q,z)$ satisfying vanishing outside dominant weights, $\Psi_0=1$, and $M_f^{\mathrm{lat}}(\Psi(q,z))=f(z)\Psi(q,z)$ for every Weyl-invariant $f$. | For a semisimple simply connected group G, prove existence and uniqueness of the q-Whittaker polynomials \Psi_{\check{\lambda}}(q,z) satisfying vanishing outside dominant weights, \Psi_0=1, and M_f^{\mathrm{lat}}(\Psi(q,z))=f(z)\Psi(q,z) for every Weyl-invariant f. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,001 | OWR-11580-007 | Equality of $p$-Canonical and Kazhdan–Lusztig Bases | Determine for which primes $p$ and affine Weyl-group elements $x$ the $p$-canonical basis element $\!{}^pH_x$ equals the Kazhdan–Lusztig basis element $H_x$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | open | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-007",
"literature-status:open",
"owr-year:2012"
] | The equality of the p-canonical and canonical basis elements is known in substantial ranges and under prime-size hypotheses, but no general classification of all pairs p and x has been proved. | [
{
"url": "https://doi.org/10.4171/owr/2012/13",
"label": "Oberwolfach Report 13 2012"
},
{
"url": "https://arxiv.org/abs/1706.00183",
"label": "Koszul Duality for Kac-Moody Groups and Characters of Tilting Modules"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | Determine for which primes $p$ and affine Weyl-group elements $x$ the $p$-canonical basis element $\!{}^pH_x$ equals the Kazhdan–Lusztig basis element $H_x$. | Determine for which primes p and affine Weyl-group elements x the p-canonical basis element {}^pH_x equals the Kazhdan--Lusztig basis element H_x. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,002 | OWR-11580-008 | Reducedness of the Commuting Scheme | Determine whether the commuting scheme $\{(x,y)\in\mathfrak g\times\mathfrak g:[x,y]=0\}$ is reduced. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | open | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-008",
"literature-status:open",
"owr-year:2012"
] | Reducedness of the general commuting scheme remains a long-standing conjecture; the 2025 work proves normality only for the two-dimensional general-linear case. | [
{
"url": "https://doi.org/10.4171/owr/2012/13",
"label": "Oberwolfach Report 13 2012"
},
{
"url": "https://arxiv.org/abs/2505.13013",
"label": "On the Normality of Commuting Scheme"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | Determine whether the commuting scheme $\{(x,y)\in\mathfrak g\times\mathfrak g:[x,y]=0\}$ is reduced. | Determine whether the commuting scheme \{(x,y)\in\mathfrak g\times\mathfrak g:[x,y]=0\} is reduced. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,003 | OWR-11580-009 | Stringy Euler Criteria for Smooth Spherical Varieties | For every locally factorial spherical variety $X$, prove or disprove that $e_{\mathrm{st}}(X)=e(X)$ is a smoothness criterion. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | open | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-009",
"literature-status:open",
"owr-year:2012"
] | The equality of stringy and ordinary Euler characteristics is a smoothness criterion for locally factorial horospherical varieties and some further special classes, but the arbitrary locally factorial spherical case remains unproved. | [
{
"url": "https://arxiv.org/abs/1203.0671",
"label": "The Arc Space of Horospherical Varieties"
},
{
"url": "https://arxiv.org/abs/1511.03852",
"label": "Stringy Invariants for Horospherical Varieties of Complexity One"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | For every locally factorial spherical variety $X$, prove or disprove that $e_{\mathrm{st}}(X)=e(X)$ is a smoothness criterion. | For every locally factorial spherical variety X, prove or disprove that e_{\mathrm{st}}(X)=e(X) is a smoothness criterion. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,004 | OWR-11580-010 | Self-Extensions of Simple Quantum-Affine Modules | Characterize the simple finite-dimensional quantum-affine modules $V$ satisfying $\dim\operatorname{Ext}^1(V,V)=1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | open | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-010",
"literature-status:open",
"owr-year:2012"
] | The self-extension criterion is proved in type sl2 and for broad classes of prime representations, but the converse characterization for all simple quantum-affine representations remains conjectural. | [
{
"url": "https://arxiv.org/abs/1112.6376",
"label": "Prime Representations from a Homological Perspective"
},
{
"url": "https://doi.org/10.1007/s00209-012-1088-7",
"label": "Prime Representations from a Homological Perspective"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | Characterize the simple finite-dimensional quantum-affine modules $V$ satisfying $\dim\operatorname{Ext}^1(V,V)=1$. | Characterize the simple finite-dimensional quantum-affine modules V satisfying \dim\operatorname{Ext}^1(V,V)=1. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,005 | OWR-11580-012 | Height Bounds for Covering Relations in Wonderful Varieties | Prove that the positive height $\operatorname{ht}^+(\gamma)$ of every covering relation $\gamma\in\mathbb N[\Sigma]$ is at most $2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | open | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-012",
"literature-status:open",
"owr-year:2012"
] | Projective-normality multiplication and the associated height condition are proved for model wonderful varieties and other special cases, but the universal second-condition conjecture for all wonderful varieties remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2012/13",
"label": "Oberwolfach Report 13 2012"
},
{
"url": "https://doi.org/10.1090/ert/477",
"label": "Projective Normality of Model Wonderful Varieties"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | Prove that the positive height $\operatorname{ht}^+(\gamma)$ of every covering relation $\gamma\in\mathbb N[\Sigma]$ is at most $2$. | Prove that the positive height \operatorname{ht}^+(\gamma) of every covering relation \gamma\in\mathbb N[\Sigma] is at most 2. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,006 | OWR-11580-013 | Block Decompositions of Critical-Level Affine Modules | Using the center of the critical-level affine enveloping algebra, determine whether its abelian category of modules admits a canonical direct-product decomposition into blocks. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | open | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-013",
"literature-status:open",
"owr-year:2012"
] | Centers and block or linkage decompositions are understood for restricted or localized critical categories, but a direct-product description of the full smooth critical category requested here remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/13",
"label": "Oberwolfach Report 13 2012"
},
{
"url": "https://arxiv.org/abs/1301.6016",
"label": "Centers for the Restricted Category O"
},
{
"url": "https://arxiv.org/abs/0712.0788",
"label": "D-modules on the Affine Flag Variety"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | Using the center of the critical-level affine enveloping algebra, determine whether its abelian category of modules admits a canonical direct-product decomposition into blocks. | Using the center of the critical-level affine enveloping algebra, determine whether its abelian category of modules admits a canonical direct-product decomposition into blocks. | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,007 | OWR-11580-014 | Verma-to-Wakimoto Isomorphisms for Jet-Level Characters | For a jet-level character $\theta\in\mathfrak h_n^*$, construct a Wakimoto module $W(\chi_\theta)$ with a natural nonzero map $V(\theta)\to W(\chi_\theta)$, and characterize the conditions on $\theta$ under which this map is an isomorphism. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | partially_solved | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-014",
"literature-status:partially-solved",
"owr-year:2012"
] | For general jets the Wakimoto construction and a natural nonzero Verma-to-Wakimoto morphism are established, while the asserted isomorphism is known in the n equals 0 case and remains conditional in higher jets. | [
{
"url": "https://arxiv.org/abs/1308.2995",
"label": "Compatibility of the Feigin-Frenkel and Harish-Chandra Isomorphisms"
},
{
"url": "https://doi.org/10.1090/S0002-9947-2014-06419-2",
"label": "Published Compatibility Paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | For a jet-level character $\theta\in\mathfrak h_n^*$, construct a Wakimoto module $W(\chi_\theta)$ with a natural nonzero map $V(\theta)\to W(\chi_\theta)$, and characterize the conditions on $\theta$ under which this map is an isomorphism. | For every jet-level character \theta\in\mathfrak h_n^*, construct a Wakimoto module W(\chi_\theta) with a natural nonzero map V(\theta)\to W(\chi_\theta), and prove that this map is an isomorphism under suitable additional conditions on \theta. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,008 | OWR-11580-015 | Oper Support of Induced Critical-Level Modules | If $Z(\mathfrak{g}_n)$ acts on a $\mathfrak{g}_n$-module $V$ through $\Lambda\in(\mathfrak{h}^*/W)_n$, prove that the induced critical-level module is scheme-theoretically supported on the oper subscheme $\operatorname{Op}^{\operatorname{ord}_n}_{\check G}(D)_{-\Lambda}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | partially_solved | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-015",
"literature-status:partially-solved",
"owr-year:2012"
] | The support statement is a theorem for n equals 0 and is supported by higher-jet center and Wakimoto constructions, but the full scheme-theoretic oper-support assertion for arbitrary n is not established. | [
{
"url": "https://doi.org/10.4171/owr/2012/13",
"label": "Oberwolfach Report 13 2012"
},
{
"url": "https://arxiv.org/abs/1308.2995",
"label": "Compatibility of the Feigin-Frenkel and Harish-Chandra Isomorphisms"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | If $Z(\mathfrak{g}_n)$ acts on a $\mathfrak{g}_n$-module $V$ through $\Lambda\in(\mathfrak{h}^*/W)_n$, prove that the induced critical-level module is scheme-theoretically supported on the oper subscheme $\operatorname{Op}^{\operatorname{ord}_n}_{\check G}(D)_{-\Lambda}$. | If Z(\mathfrak g_n) acts on a \mathfrak g_n-module V through \Lambda\in(\mathfrak h^*/W)_n, prove that the induced critical-level module is scheme-theoretically supported on the oper subscheme \operatorname{Op}^{\mathrm{ord}_n}_{\check G}(D)_{-\Lambda}. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,009 | OWR-11580-019 | Perfect Weyl-Group Complexes of Flag Varieties | For a complex reductive group $G$ with maximal torus $T$ and Weyl group $W$, describe the perfect complex $R\Gamma(G/T,k)$ of $k[W]$-modules for an arbitrary field $k$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809](https://doi.org/10.4171/owr/2012/13)
## Literature review (check... | 3 | open | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11580-019",
"literature-status:open",
"owr-year:2012"
] | The complex is identified as a graded regular representation over the complex numbers and shown to be perfect over arbitrary fields, but no general description over an arbitrary field has been established. | [
{
"url": "https://doi.org/10.4171/owr/2012/13",
"label": "Oberwolfach Report 13 2012"
},
{
"url": "https://arxiv.org/abs/1401.7256",
"label": "Modular Perverse Sheaves on Flag Varieties II"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/13 | null | null | null | For a complex reductive group $G$ with maximal torus $T$ and Weyl group $W$, describe the perfect complex $R\Gamma(G/T,k)$ of $k[W]$-modules for an arbitrary field $k$. | For a complex reductive group G with maximal torus T and Weyl group W, describe the perfect complex R\Gamma(G/T,k) of k[W]-modules for an arbitrary field k. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/13, pp. 733--809 |
30,002,010 | OWR-11581-001 | Poisson Empirical-Bayes Estimator Report | For independent observations Y_i\sim\operatorname{Poisson}(\lambda_i), construct an empirical-Bayes estimator that approximates the unknown-prior Bayes estimator with uniformly small excess quadratic risk as the dimension p tends to infinity. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Frontiers in Nonparametric Statistics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/14, pp. 811--883](https://doi.org/10.4171/owr/2012/14)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official contribution states this estimator-construction goal and immediately develops the estimator and its asymptotic risk theorem, so) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11581-001",
"literature-status:partially-solved",
"owr-year:2012"
] | Brown, Greenshtein, and Ritov supply smoothed and monotone improvements with asymptotic risk bounds, and later minimum-distance work gives minimax-regret guarantees; these results cover standard bounded or nonparametric classes rather than an unrestricted uniform theorem over every prior. | [
{
"url": "https://arxiv.org/abs/1006.4582",
"label": "The Poisson Compound Decision Problem Revisited"
},
{
"url": "https://doi.org/10.1080/01621459.2013.771582",
"label": "Published Poisson Compound Decision Paper"
},
{
"url": "https://arxiv.org/abs/2209.01328",
"label": "Optimal Em... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/14 | null | null | null | null | For independent observations Y_i\sim\operatorname{Poisson}(\lambda_i), construct an empirical-Bayes estimator that approximates the unknown-prior Bayes estimator with uniformly small excess quadratic risk as the dimension p tends to infinity. | unrecoverable | The official contribution states this estimator-construction goal and immediately develops the estimator and its asymptotic risk theorem, so the extracted research aim is answered within the source. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Frontiers in Nonparametric Statistics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/14, pp. 811--883 |
30,002,011 | OWR-11581-002 | Corruption-Parameter Choice in Empirical-Bayes Estimation | For the monotoneized empirical-Bayes estimator $\Delta_h$, how should the corruption parameter $h$ be chosen, and does inbred cross-validation yield a rate-sharp procedure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Frontiers in Nonparametric Statistics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/14, pp. 811--883](https://doi.org/10.4171/owr/2012/14)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11581-002",
"literature-status:open",
"owr-year:2012"
] | The proposed data-splitting cross-validation selector for h is not settled; later work proves sharp regret rates for related Poisson empirical-Bayes procedures but does not resolve this specific selector. | [
{
"url": "https://doi.org/10.4171/owr/2012/14",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2209.01328",
"label": "Optimal Poisson empirical Bayes estimation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/14 | null | null | null | For the monotoneized empirical-Bayes estimator $\Delta_h$, how should the corruption parameter $h$ be chosen, and does inbred cross-validation yield a rate-sharp procedure? | For the monotoneized empirical-Bayes estimator \Delta_h, determine how to choose the corruption parameter h, including whether inbred cross-validation yields a rate-sharp procedure. | corrected_verified | The official report explicitly leaves the choice of $h$ and the performance of inbred cross-validation as open questions. | null | null | null | null | null | Frontiers in Nonparametric Statistics (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/14, pp. 811--883 |
30,002,012 | OWR-11582-001 | Dense-Granular-Flow Results Report | Explain the micromechanisms of dilatancy and compaction in dense granular materials, determine why the critical state depends on pressure, and determine the intrinsic length scale governing persistent shear bands. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/15, pp. 885--961](https://doi.org/10.4171/owr/2012/15)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 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 | Answered in the source or not an open problem (solved (answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source)**, or retire it: it is not a mathematical problem. The record restates the aims of S. Dj. Mesarović's talk (OWR 15/2012, p. 925) on dense granular materials: the micromechanism of dilatancy and of the critical state, and the length scale of... | [
"owr",
"oberwolfach-reports",
"OWR-11582-001",
"literature-status:open",
"owr-year:2012"
] | The pressure dependence of the critical state and the governing intrinsic length remain model- and material-dependent research questions; current dislocation-continuum work supplies mechanisms and scales but no general determination. | [
{
"url": "https://doi.org/10.4171/owr/2012/15",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2406.09892",
"label": "Dynamic length scales in crystal plasticity"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/15 | null | null | null | null | Explain the micromechanisms of dilatancy and compaction in dense granular materials, determine why the critical state depends on pressure, and determine the intrinsic length scale governing persistent shear bands. | unrecoverable | The official contribution introduces these physical questions and then states results explaining the mechanisms, pressure dependence, and length scale; the extraction is a summary of answered research aims rather than an open problem. No separate clean statement is promoted; the original record remains publicly visible... | null | null | null | null | null | Mechanics of Materials (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/15, pp. 885--961 |
30,002,013 | OWR-11583-002 | Broué's Abelian Defect Group Conjecture | Is every block of a finite group with abelian defect group derived equivalent to its Brauer correspondent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019](https://doi.org/10.4171/owr/2012/16)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,012 | 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-11583-002",
"literature-status:open",
"owr-year:2012"
] | The record is a table-of-contents fragment and contains no identifiable mathematical assertion; the unresolved or unclear claim is therefore normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2012/16",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/16 | null | null | null | Is every block of a finite group with abelian defect group derived equivalent to its Brauer correspondent? | Brou\acute e's abelian-defect-group conjecture: every block of a finite group with abelian defect group is derived equivalent to its Brauer correspondent. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019 |
30,002,014 | OWR-11583-005 | Homomorphisms between Specht Modules | Compute the homomorphism spaces $\operatorname{Hom}_{F S_n}(S^{\lambda},S^{\mu})$ between Specht modules over arbitrary fields, thereby determining the associated decomposition-number problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019](https://doi.org/10.4171/owr/2012/16)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11583-005",
"literature-status:open",
"owr-year:2012"
] | The general computation of decomposition numbers for symmetric groups remains an outstanding problem; substantial families and special blocks are known, but no uniform solution is available. | [
{
"url": "https://doi.org/10.1112/jlms.12852",
"label": "RoCK-block decomposition numbers"
},
{
"url": "https://arxiv.org/abs/2303.00629",
"label": "Spin decomposition numbers"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/16 | null | null | null | Compute the homomorphism spaces $\operatorname{Hom}_{F S_n}(S^{\lambda},S^{\mu})$ between Specht modules over arbitrary fields, thereby determining the associated decomposition-number problem. | Compute the homomorphism spaces \operatorname{Hom}_{F S_n}(S^{\lambda},S^{\mu}) between Specht modules over arbitrary fields, thereby determining the associated decomposition-number problem. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019 |
30,002,015 | OWR-11583-008 | Cohomological Disjointness for Parabolic Deligne–Lusztig Varieties | For a parabolic Deligne–Lusztig variety $X_P$, prove that the cohomology modules $H_c^i(X_P,\mathbb{Q}_\ell)$ are pairwise disjoint and that $\operatorname{End}_{G^F}\!\left(\bigoplus_i H_c^i(X_P,\mathbb{Q}_\ell)\right)\cong\mathbb{Q}_\ell W_S$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019](https://doi.org/10.4171/owr/2012/16)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,012 | 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-11583-008",
"literature-status:partially-solved",
"owr-year:2012"
] | The endomorphism-algebra conjecture is proved in important cases, including the split type-A disjointness consequence, but the full general pairwise-disjointness and endomorphism statement remains open. | [
{
"url": "https://arxiv.org/abs/1110.4863",
"label": "Parabolic Deligne--Lusztig varieties"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0001870819305447",
"label": "Translation by the full twist"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/16 | null | null | null | For a parabolic Deligne–Lusztig variety $X_P$, prove that the cohomology modules $H_c^i(X_P,\mathbb{Q}_\ell)$ are pairwise disjoint and that $\operatorname{End}_{G^F}\!\left(\bigoplus_i H_c^i(X_P,\mathbb{Q}_\ell)\right)\cong\mathbb{Q}_\ell W_S$. | For a parabolic Deligne--Lusztig variety X_P, prove that the cohomology modules H_c^i(X_P,\mathbb Q_\ell) are pairwise disjoint and that \operatorname{End}_{G^F}(\bigoplus_i H_c^i(X_P,\mathbb Q_\ell))\cong\mathbb Q_\ell W_S. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019 |
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