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1.0.0 | problem:theoremdb-p4930 | problem | theoremdb-p4930 | Independence number of the circulant graph C(787; 1, 3) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/787\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm3$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4930",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4930",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4930 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4930",
"url": "https://theoremdb.org/statements/P4930",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4930",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:40:16+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4930,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.655Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"00957e83-32df-47c1-bacd-87c6fe650e5c","format_issues":null,"number":5559} |
1.0.0 | problem:theoremdb-p4932 | problem | theoremdb-p4932 | Independence number of the circulant graph C(797; 1, 4) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/797\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm4$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4932",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4932",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4932 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4932",
"url": "https://theoremdb.org/statements/P4932",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4932",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:40:18+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4932,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.659Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"24673c0c-65ec-4882-b77d-3a2be55a05d9","format_issues":null,"number":5560} |
1.0.0 | problem:theoremdb-p4934 | problem | theoremdb-p4934 | Independence number of the circulant graph C(809; 1, 5) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/809\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm5$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4934",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4934",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4934 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4934",
"url": "https://theoremdb.org/statements/P4934",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4934",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:40:40+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4934,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.664Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"529253a1-4494-4ed7-bc5f-3bf944d24f79","format_issues":null,"number":5561} |
1.0.0 | problem:theoremdb-p4936 | problem | theoremdb-p4936 | Independence number of the circulant graph C(811; 1, 6) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/811\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm6$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4936",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4936",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4936 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4936",
"url": "https://theoremdb.org/statements/P4936",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4936",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:40:42+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4936,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.668Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4ee902fa-02ee-4413-ac42-fdea7dd4a8aa","format_issues":null,"number":5562} |
1.0.0 | problem:theoremdb-p4938 | problem | theoremdb-p4938 | Independence number of the circulant graph C(821; 1, 7) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/821\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm7$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4938",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4938",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4938 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4938",
"url": "https://theoremdb.org/statements/P4938",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4938",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:40:51+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4938,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.672Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"afcd10f9-95df-4359-8e68-a0d3f07db0df","format_issues":null,"number":5563} |
1.0.0 | problem:theoremdb-p4940 | problem | theoremdb-p4940 | Independence number of the circulant graph C(823; 1, 8) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/823\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm8$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4940",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4940",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4940 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4940",
"url": "https://theoremdb.org/statements/P4940",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4940",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:41:00+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4940,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.676Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a2f3b582-dd0b-44f5-b781-498434ef34c5","format_issues":null,"number":5564} |
1.0.0 | problem:theoremdb-p4942 | problem | theoremdb-p4942 | Independence number of the circulant graph C(827; 1, 9) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/827\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm9$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4942",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4942",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4942 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4942",
"url": "https://theoremdb.org/statements/P4942",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4942",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:41:07+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4942,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.681Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4f046ada-ab39-42b2-addc-67d34cad6148","format_issues":null,"number":5565} |
1.0.0 | problem:theoremdb-p4944 | problem | theoremdb-p4944 | Independence number of the circulant graph C(829; 1, 10) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/829\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm10$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4944",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4944",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4944 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4944",
"url": "https://theoremdb.org/statements/P4944",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4944",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:41:08+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4944,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.685Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"57ecc468-4d7b-45b7-b81d-3710f1c2717a","format_issues":null,"number":5566} |
1.0.0 | problem:theoremdb-p4946 | problem | theoremdb-p4946 | Independence number of the circulant graph C(839; 1, 11) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/839\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm11$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4946",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4946",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4946 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4946",
"url": "https://theoremdb.org/statements/P4946",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4946",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:41:24+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4946,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.689Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"575432f4-b468-4858-89b7-32b9b24eb7dd","format_issues":null,"number":5567} |
1.0.0 | problem:theoremdb-p4948 | problem | theoremdb-p4948 | Independence number of the circulant graph C(853; 1, 12) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/853\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm12$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4948",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4948",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4948 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4948",
"url": "https://theoremdb.org/statements/P4948",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4948",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:41:43+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4948,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.694Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5768fc9b-f822-42a7-a373-8d990befb8f5","format_issues":null,"number":5568} |
1.0.0 | problem:theoremdb-p4950 | problem | theoremdb-p4950 | Independence number of the circulant graph C(857; 1, 13) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/857\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm13$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4950",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4950",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4950 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4950",
"url": "https://theoremdb.org/statements/P4950",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4950",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:41:50+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4950,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.698Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4d0b76b9-c5a8-4dfd-875f-8aa9b85fe06c","format_issues":null,"number":5569} |
1.0.0 | problem:theoremdb-p4952 | problem | theoremdb-p4952 | Independence number of the circulant graph C(859; 1, 14) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/859\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm14$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4952",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4952",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4952 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4952",
"url": "https://theoremdb.org/statements/P4952",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4952",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:41:53+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4952,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.702Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8c9e0fbe-17e8-4a23-bc38-862a344077b1","format_issues":null,"number":5570} |
1.0.0 | problem:theoremdb-p4954 | problem | theoremdb-p4954 | Independence number of the circulant graph C(863; 1, 15) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/863\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm15$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4954",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4954",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4954 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4954",
"url": "https://theoremdb.org/statements/P4954",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4954",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:42:04+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4954,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.706Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"36ddffae-f404-4aab-b99a-796a8cc4c3e6","format_issues":null,"number":5571} |
1.0.0 | problem:theoremdb-p4956 | problem | theoremdb-p4956 | Independence number of the circulant graph C(877; 1, 16) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/877\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm16$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4956",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4956",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4956 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4956",
"url": "https://theoremdb.org/statements/P4956",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4956",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:42:22+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4956,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.710Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"db0ab7cb-7e22-452f-a427-755bc6de8b55","format_issues":null,"number":5572} |
1.0.0 | problem:theoremdb-p4958 | problem | theoremdb-p4958 | Independence number of the circulant graph C(881; 1, 17) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/881\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm17$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4958",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4958",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4958 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4958",
"url": "https://theoremdb.org/statements/P4958",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4958",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:42:39+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4958,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.714Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"255751ac-f7ed-4da0-8c62-cf9386309a4e","format_issues":null,"number":5573} |
1.0.0 | problem:theoremdb-p4960 | problem | theoremdb-p4960 | Independence number of the circulant graph C(883; 1, 18) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/883\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm18$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4960",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4960",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4960 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4960",
"url": "https://theoremdb.org/statements/P4960",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4960",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:42:53+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4960,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.719Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3af9d57d-3b30-41e1-9676-3701f726b528","format_issues":null,"number":5574} |
1.0.0 | problem:theoremdb-p4962 | problem | theoremdb-p4962 | Independence number of the circulant graph C(887; 1, 19) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/887\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm19$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4962",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4962",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4962 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4962",
"url": "https://theoremdb.org/statements/P4962",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4962",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:43:01+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4962,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.723Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1ad947fe-c0ac-4120-a4d7-ed651890f418","format_issues":null,"number":5575} |
1.0.0 | problem:theoremdb-p4964 | problem | theoremdb-p4964 | Independence number of the circulant graph C(907; 1, 20) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/907\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm20$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4964",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4964",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4964 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4964",
"url": "https://theoremdb.org/statements/P4964",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4964",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:43:09+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4964,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.727Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a4302fe5-52e1-4bbb-a85b-7887ff03f908","format_issues":null,"number":5576} |
1.0.0 | problem:theoremdb-p4966 | problem | theoremdb-p4966 | Independence number of the circulant graph C(911; 1, 21) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/911\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm21$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4966",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4966",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4966 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4966",
"url": "https://theoremdb.org/statements/P4966",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4966",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:43:31+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4966,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.732Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3ece96a4-b066-4f37-bb8c-b6f2455103ce","format_issues":null,"number":5577} |
1.0.0 | problem:theoremdb-p4968 | problem | theoremdb-p4968 | Independence number of the circulant graph C(919; 1, 22) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/919\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm22$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4968",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4968",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4968 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4968",
"url": "https://theoremdb.org/statements/P4968",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4968",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:43:47+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4968,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.737Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4b54fc75-156a-4a2c-8615-26576bffe30c","format_issues":null,"number":5578} |
1.0.0 | problem:theoremdb-p4970 | problem | theoremdb-p4970 | Independence number of the circulant graph C(929; 1, 23) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/929\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm23$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4970",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4970",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4970 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4970",
"url": "https://theoremdb.org/statements/P4970",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4970",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:44:03+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4970,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.741Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8387495b-0cf7-4bd6-977a-1f128cab2bc2","format_issues":null,"number":5579} |
1.0.0 | problem:theoremdb-p4972 | problem | theoremdb-p4972 | Independence number of the circulant graph C(937; 1, 24) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/937\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm24$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4972",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4972",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4972 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4972",
"url": "https://theoremdb.org/statements/P4972",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4972",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:44:20+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4972,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.746Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"210a17ef-48bc-4d40-b6cd-370ebf0f531d","format_issues":null,"number":5580} |
1.0.0 | problem:theoremdb-p4974 | problem | theoremdb-p4974 | Independence number of the circulant graph C(941; 1, 25) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/941\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm25$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4974",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4974",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4974 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4974",
"url": "https://theoremdb.org/statements/P4974",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4974",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:44:29+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4974,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.750Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"664a09f6-3ebe-41b1-ac4c-a4f7292dc20e","format_issues":null,"number":5581} |
1.0.0 | problem:theoremdb-p4976 | problem | theoremdb-p4976 | Independence number of the circulant graph C(947; 1, 26) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/947\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm26$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4976",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4976",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4976 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4976",
"url": "https://theoremdb.org/statements/P4976",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4976",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:44:30+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4976,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.754Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9c8777cb-5260-4d82-a6ea-2d82072ea2f4","format_issues":null,"number":5582} |
1.0.0 | problem:theoremdb-p4978 | problem | theoremdb-p4978 | Independence number of the circulant graph C(953; 1, 27) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/953\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm27$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4978",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4978",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4978 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4978",
"url": "https://theoremdb.org/statements/P4978",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4978",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:44:35+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4978,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.758Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fd44ba6d-8d89-4466-82f7-0733245f15d9","format_issues":null,"number":5583} |
1.0.0 | problem:theoremdb-p4980 | problem | theoremdb-p4980 | Independence number of the circulant graph C(967; 1, 28) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/967\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm28$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4980",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4980",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4980 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4980",
"url": "https://theoremdb.org/statements/P4980",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4980",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:44:40+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4980,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.762Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8865fec7-6920-49c2-89f2-f8ad2cd14796","format_issues":null,"number":5584} |
1.0.0 | problem:theoremdb-p4982 | problem | theoremdb-p4982 | Independence number of the circulant graph C(971; 1, 29) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/971\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm29$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4982",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4982",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4982 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4982",
"url": "https://theoremdb.org/statements/P4982",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4982",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:44:43+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4982,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.766Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"579d356b-18d3-43a7-928a-fc8457ae28a2","format_issues":null,"number":5585} |
1.0.0 | problem:theoremdb-p4984 | problem | theoremdb-p4984 | Independence number of the circulant graph C(977; 1, 30) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/977\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm30$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4984",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4984",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4984 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4984",
"url": "https://theoremdb.org/statements/P4984",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4984",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:44:48+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4984,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.772Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"df944f19-fd73-4352-aa36-260530545bf6","format_issues":null,"number":5586} |
1.0.0 | problem:theoremdb-p4986 | problem | theoremdb-p4986 | Independence number of the circulant graph C(983; 1, 31) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/983\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm31$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4986",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4986",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4986 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4986",
"url": "https://theoremdb.org/statements/P4986",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4986",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:48:48+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4986,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.776Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5a8db058-b3b4-491a-8151-cc79ffccfcea","format_issues":null,"number":5587} |
1.0.0 | problem:theoremdb-p4988 | problem | theoremdb-p4988 | Independence number of the circulant graph C(991; 1, 2) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/991\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm2$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4988",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4988",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4988 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. Not Lean-verified | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4988",
"url": "https://theoremdb.org/statements/P4988",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4988",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:48:58+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4988,"public_status":{"evidence":{"hasFormalization":true,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"Not Lean... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.780Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"19f64874-6b8d-4b8e-84fe-a8f990266aff","format_issues":null,"number":5588} |
1.0.0 | problem:theoremdb-p4990 | problem | theoremdb-p4990 | Independence number of the circulant graph C(997; 1, 3) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/997\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm3$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4990",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4990",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4990 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4990",
"url": "https://theoremdb.org/statements/P4990",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4990",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:49:04+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4990,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.784Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e60a73fb-2bc5-4cb7-99fd-00512ca848f1","format_issues":null,"number":5589} |
1.0.0 | problem:theoremdb-p4992 | problem | theoremdb-p4992 | Independence number of the circulant graph C(1009; 1, 4) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1009\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm4$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4992",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4992",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4992 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4992",
"url": "https://theoremdb.org/statements/P4992",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4992",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:49:13+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4992,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.695Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"efaeeddf-5c3b-4514-aa6d-102278b494cb","format_issues":null,"number":5450} |
1.0.0 | problem:theoremdb-p4994 | problem | theoremdb-p4994 | Independence number of the circulant graph C(1013; 1, 5) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1013\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm5$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4994",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4994",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4994 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4994",
"url": "https://theoremdb.org/statements/P4994",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4994",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:49:26+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4994,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.700Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f18157df-8084-4cf2-a100-b9d15ecc0e4a","format_issues":null,"number":5451} |
1.0.0 | problem:theoremdb-p4996 | problem | theoremdb-p4996 | Independence number of the circulant graph C(1019; 1, 6) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1019\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm6$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4996",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4996",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4996 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4996",
"url": "https://theoremdb.org/statements/P4996",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4996",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:49:35+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4996,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.704Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6dc5cfae-7e42-466c-b742-455cf3e2688b","format_issues":null,"number":5452} |
1.0.0 | problem:theoremdb-p4998 | problem | theoremdb-p4998 | Independence number of the circulant graph C(1021; 1, 7) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1021\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm7$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4998",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4998",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4998 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P4998",
"url": "https://theoremdb.org/statements/P4998",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4998",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:49:37+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4998,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.709Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"28504b0e-3152-4077-8eb6-1f732dda02e0","format_issues":null,"number":5453} |
1.0.0 | problem:theoremdb-p5 | problem | theoremdb-p5 | Erdős-Straus conjecture | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | For every integer $n\ge 2$, there exist positive integers $x,y,z$ such that $\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem packe... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5 · number theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5",
"url": "https://theoremdb.org/statements/P5",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "Xiaoping Xu, arXiv:2605.23601, introduction and abstract",
"url": "https://arxiv.org/abs/2605.23601",
"note": null... | {
"source_record": "P5",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been perf... | {"created_at":"2026-07-22T21:49:47+00:00","display_standard":{"editorial_review":"source_backed","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernel... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:56.651Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eb563169-c342-40d8-9a10-60c9a2b389fa","format_issues":null,"number":4786} |
1.0.0 | problem:theoremdb-p50 | problem | theoremdb-p50 | Kaplansky zero-divisor conjecture | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | If $K$ is a field and $G$ is a torsion-free group, then the group algebra $K[G]$ has no nonzero zero divisors. | open | {
"key": "theoremdb",
"name": "TheoremDB · P50",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P50",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem pac... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P50 · algebra | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P50",
"url": "https://theoremdb.org/statements/P50",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "Sam P. Fisher and Pablo Sánchez-Peralta, Journal of Combinatorial Algebra 10 (2026), introduction",
"url": "https://... | {
"source_record": "P50",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been per... | {"created_at":"2026-07-22T21:49:48+00:00","display_standard":{"editorial_review":"source_backed","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":50,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kerne... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:02.166Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d0d99dd3-2388-4e6c-97b8-4f1e5cc5f724","format_issues":null,"number":5818} |
1.0.0 | problem:theoremdb-p5000 | problem | theoremdb-p5000 | Independence number of the circulant graph C(1031; 1, 8) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1031\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm8$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5000",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5000",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5000 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5000",
"url": "https://theoremdb.org/statements/P5000",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5000",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:49:40+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5000,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.713Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6ace74cd-88f4-4111-8dd8-a837c63beca3","format_issues":null,"number":5454} |
1.0.0 | problem:theoremdb-p5002 | problem | theoremdb-p5002 | Independence number of the circulant graph C(1033; 1, 9) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1033\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm9$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5002",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5002",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5002 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5002",
"url": "https://theoremdb.org/statements/P5002",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5002",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:49:50+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5002,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.718Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c1a747d2-d0fd-48b1-8951-c08387b70d34","format_issues":null,"number":5455} |
1.0.0 | problem:theoremdb-p5004 | problem | theoremdb-p5004 | Independence number of the circulant graph C(1039; 1, 10) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1039\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm10$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5004",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5004",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5004 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5004",
"url": "https://theoremdb.org/statements/P5004",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5004",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:50:01+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5004,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.722Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eefc1525-e49b-485a-aebc-e08d74c4c170","format_issues":null,"number":5456} |
1.0.0 | problem:theoremdb-p5006 | problem | theoremdb-p5006 | Independence number of the circulant graph C(1049; 1, 11) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1049\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm11$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5006",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5006",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5006 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5006",
"url": "https://theoremdb.org/statements/P5006",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5006",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:50:03+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5006,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.726Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fd8bf494-fc05-44d4-8e55-076293170d2d","format_issues":null,"number":5457} |
1.0.0 | problem:theoremdb-p5008 | problem | theoremdb-p5008 | Independence number of the circulant graph C(1051; 1, 12) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1051\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm12$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5008",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5008",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5008 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5008",
"url": "https://theoremdb.org/statements/P5008",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5008",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:50:20+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5008,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.730Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fc0ba46d-9c6e-4173-913d-99a23e3a4e1c","format_issues":null,"number":5458} |
1.0.0 | problem:theoremdb-p5010 | problem | theoremdb-p5010 | Exact value of A(64, 6, 4) for binary constant-weight codes | {
"main": "math",
"sub": "control and information",
"slug": "control-and-information",
"name": "Control and information theory",
"original_discipline": "mathematics"
} | [] | [] | Determine $A_2(64,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{64}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5010",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5010",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5010 · coding theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5010",
"url": "https://theoremdb.org/statements/P5010",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5010",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:58:32+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5010,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:58.075Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cf702af3-84b8-4a87-af46-757a518283f0","format_issues":null,"number":5104} |
1.0.0 | problem:theoremdb-p5012 | problem | theoremdb-p5012 | Exact value of A(65, 6, 4) for binary constant-weight codes | {
"main": "math",
"sub": "control and information",
"slug": "control-and-information",
"name": "Control and information theory",
"original_discipline": "mathematics"
} | [] | [] | Determine $A_2(65,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{65}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5012",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5012",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5012 · coding theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5012",
"url": "https://theoremdb.org/statements/P5012",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5012",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:59:21+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5012,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:58.079Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b9dff0e3-5540-4ec3-ab4f-0584ce830352","format_issues":null,"number":5105} |
1.0.0 | problem:theoremdb-p5014 | problem | theoremdb-p5014 | Exact value of A(66, 6, 4) for binary constant-weight codes | {
"main": "math",
"sub": "control and information",
"slug": "control-and-information",
"name": "Control and information theory",
"original_discipline": "mathematics"
} | [] | [] | Determine $A_2(66,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{66}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5014",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5014",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5014 · coding theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5014",
"url": "https://theoremdb.org/statements/P5014",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5014",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:59:47+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5014,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:58.083Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dd0110cc-9c86-43d0-9641-974c0b360838","format_issues":null,"number":5106} |
1.0.0 | problem:theoremdb-p5016 | problem | theoremdb-p5016 | Independence number of the circulant graph C(1061; 1, 13) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1061\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm13$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5016",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5016",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5016 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5016",
"url": "https://theoremdb.org/statements/P5016",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5016",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:59:58+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5016,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.735Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f417fa78-47fd-442f-a412-cdb6e01d39ee","format_issues":null,"number":5459} |
1.0.0 | problem:theoremdb-p5018 | problem | theoremdb-p5018 | Exact value of A(67, 6, 4) for binary constant-weight codes | {
"main": "math",
"sub": "control and information",
"slug": "control-and-information",
"name": "Control and information theory",
"original_discipline": "mathematics"
} | [] | [] | Determine $A_2(67,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{67}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5018",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5018",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5018 · coding theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5018",
"url": "https://theoremdb.org/statements/P5018",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5018",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:00:11+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5018,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:58.088Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"36898751-8954-4b91-8244-1a80498d8cd3","format_issues":null,"number":5107} |
1.0.0 | problem:theoremdb-p5020 | problem | theoremdb-p5020 | Exact value of A(68, 6, 4) for binary constant-weight codes | {
"main": "math",
"sub": "control and information",
"slug": "control-and-information",
"name": "Control and information theory",
"original_discipline": "mathematics"
} | [] | [] | Determine $A_2(68,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{68}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5020",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5020",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5020 · coding theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5020",
"url": "https://theoremdb.org/statements/P5020",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5020",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:00:17+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5020,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:58.092Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eaf0d430-d1d4-4124-951a-6328e1659dd0","format_issues":null,"number":5108} |
1.0.0 | problem:theoremdb-p5022 | problem | theoremdb-p5022 | Exact value of A(69, 6, 4) for binary constant-weight codes | {
"main": "math",
"sub": "control and information",
"slug": "control-and-information",
"name": "Control and information theory",
"original_discipline": "mathematics"
} | [] | [] | Determine $A_2(69,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{69}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5022",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5022",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5022 · coding theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5022",
"url": "https://theoremdb.org/statements/P5022",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5022",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:00:18+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5022,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:58.097Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e550fda8-e060-448b-bc37-74b9bf2f53cb","format_issues":null,"number":5109} |
1.0.0 | problem:theoremdb-p5024 | problem | theoremdb-p5024 | Independence number of the circulant graph C(1063; 1, 14) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1063\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm14$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5024",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5024",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5024 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5024",
"url": "https://theoremdb.org/statements/P5024",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5024",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:02:48+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5024,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.739Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bb5d959a-e88c-4596-83fc-3a56666ecf4b","format_issues":null,"number":5460} |
1.0.0 | problem:theoremdb-p5026 | problem | theoremdb-p5026 | Independence number of the circulant graph C(1069; 1, 15) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1069\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm15$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5026",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5026",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5026 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5026",
"url": "https://theoremdb.org/statements/P5026",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5026",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:02:56+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5026,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.743Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a38f33e3-5c50-4c13-ae90-742736e2cdce","format_issues":null,"number":5461} |
1.0.0 | problem:theoremdb-p5028 | problem | theoremdb-p5028 | Independence number of the circulant graph C(1087; 1, 16) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1087\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm16$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5028",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5028",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5028 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5028",
"url": "https://theoremdb.org/statements/P5028",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5028",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:05+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5028,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.747Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9f389835-bf20-4df8-8be3-2de2846f8c76","format_issues":null,"number":5462} |
1.0.0 | problem:theoremdb-p5030 | problem | theoremdb-p5030 | Independence number of the circulant graph C(1091; 1, 17) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1091\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm17$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5030",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5030",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5030 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5030",
"url": "https://theoremdb.org/statements/P5030",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5030",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:10+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5030,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.751Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fb65b9dc-26d2-4a7b-9ac0-52fef0435e18","format_issues":null,"number":5463} |
1.0.0 | problem:theoremdb-p5032 | problem | theoremdb-p5032 | Independence number of the circulant graph C(1093; 1, 18) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1093\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm18$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5032",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5032",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5032 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5032",
"url": "https://theoremdb.org/statements/P5032",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5032",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:14+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5032,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.756Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d5952119-992f-434e-9d73-6f9056251689","format_issues":null,"number":5464} |
1.0.0 | problem:theoremdb-p5034 | problem | theoremdb-p5034 | Independence number of the circulant graph C(1097; 1, 19) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1097\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm19$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5034",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5034",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5034 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5034",
"url": "https://theoremdb.org/statements/P5034",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5034",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:19+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5034,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.760Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7920d6f4-a520-4f52-9ae3-42429b35c805","format_issues":null,"number":5465} |
1.0.0 | problem:theoremdb-p5036 | problem | theoremdb-p5036 | Independence number of the circulant graph C(1103; 1, 20) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1103\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm20$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5036",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5036",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5036 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5036",
"url": "https://theoremdb.org/statements/P5036",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5036",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:25+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5036,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.766Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"37793544-e665-439b-84bf-25bd4a2dc2a3","format_issues":null,"number":5466} |
1.0.0 | problem:theoremdb-p5038 | problem | theoremdb-p5038 | Independence number of the circulant graph C(1109; 1, 21) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1109\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm21$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5038",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5038",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5038 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5038",
"url": "https://theoremdb.org/statements/P5038",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5038",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:28+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5038,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.770Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"70b0a3ee-67be-4493-b139-e24908854b27","format_issues":null,"number":5467} |
1.0.0 | problem:theoremdb-p5040 | problem | theoremdb-p5040 | Independence number of the circulant graph C(1117; 1, 22) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1117\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm22$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5040",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5040",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5040 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5040",
"url": "https://theoremdb.org/statements/P5040",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5040",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:30+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5040,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.775Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4e184ce8-89a9-4456-ad04-6b18b21bba16","format_issues":null,"number":5468} |
1.0.0 | problem:theoremdb-p5042 | problem | theoremdb-p5042 | Independence number of the circulant graph C(1123; 1, 23) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1123\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm23$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5042",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5042",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5042 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5042",
"url": "https://theoremdb.org/statements/P5042",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5042",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:36+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5042,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.779Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"83175ad6-7593-40c8-b302-179d3ce8eabc","format_issues":null,"number":5469} |
1.0.0 | problem:theoremdb-p5044 | problem | theoremdb-p5044 | Independence number of the circulant graph C(1129; 1, 24) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1129\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm24$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5044",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5044",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5044 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5044",
"url": "https://theoremdb.org/statements/P5044",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5044",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:38+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5044,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.784Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9b1a63ce-a46e-4e83-85e2-7009251c4514","format_issues":null,"number":5470} |
1.0.0 | problem:theoremdb-p5046 | problem | theoremdb-p5046 | Independence number of the circulant graph C(1151; 1, 25) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1151\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm25$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5046",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5046",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5046 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5046",
"url": "https://theoremdb.org/statements/P5046",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5046",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:42+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5046,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.788Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"831b69a1-4440-4f3d-8b69-965832587ae2","format_issues":null,"number":5471} |
1.0.0 | problem:theoremdb-p5048 | problem | theoremdb-p5048 | Independence number of the circulant graph C(1153; 1, 26) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1153\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm26$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5048",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5048",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5048 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5048",
"url": "https://theoremdb.org/statements/P5048",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5048",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:44+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5048,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.793Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9a84b038-c6d3-4c56-8496-62fc75fa0408","format_issues":null,"number":5472} |
1.0.0 | problem:theoremdb-p5050 | problem | theoremdb-p5050 | Independence number of the circulant graph C(1163; 1, 27) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1163\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm27$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5050",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5050",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5050 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5050",
"url": "https://theoremdb.org/statements/P5050",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5050",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:47+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5050,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.796Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"495896ab-d624-43a4-af01-062320eb1c65","format_issues":null,"number":5473} |
1.0.0 | problem:theoremdb-p5052 | problem | theoremdb-p5052 | Independence number of the circulant graph C(1171; 1, 28) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1171\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm28$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5052",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5052",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5052 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5052",
"url": "https://theoremdb.org/statements/P5052",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5052",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:50+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5052,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.801Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c45212d9-be15-418e-a69d-9e19475d0a01","format_issues":null,"number":5474} |
1.0.0 | problem:theoremdb-p5054 | problem | theoremdb-p5054 | Independence number of the circulant graph C(1181; 1, 29) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1181\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm29$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5054",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5054",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5054 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5054",
"url": "https://theoremdb.org/statements/P5054",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5054",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:53+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5054,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.805Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"04976ebe-cc81-485f-96ba-e064469ebaea","format_issues":null,"number":5475} |
1.0.0 | problem:theoremdb-p5056 | problem | theoremdb-p5056 | Independence number of the circulant graph C(1187; 1, 30) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1187\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm30$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5056",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5056",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5056 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5056",
"url": "https://theoremdb.org/statements/P5056",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5056",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:54+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5056,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.809Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bff98079-0d6c-47f5-acec-33ee3d5d5d8e","format_issues":null,"number":5476} |
1.0.0 | problem:theoremdb-p5058 | problem | theoremdb-p5058 | Independence number of the circulant graph C(1193; 1, 31) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1193\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm31$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5058",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5058",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5058 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5058",
"url": "https://theoremdb.org/statements/P5058",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5058",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:03:58+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5058,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.814Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7e648b7a-4693-48f3-a6f9-d0d405421d47","format_issues":null,"number":5477} |
1.0.0 | problem:theoremdb-p5060 | problem | theoremdb-p5060 | Independence number of the circulant graph C(1201; 1, 2) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1201\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm2$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5060",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5060",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5060 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5060",
"url": "https://theoremdb.org/statements/P5060",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5060",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:04+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5060,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.818Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"66452b54-db2d-464f-aa18-0ba1af809f51","format_issues":null,"number":5478} |
1.0.0 | problem:theoremdb-p5062 | problem | theoremdb-p5062 | Independence number of the circulant graph C(1213; 1, 3) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1213\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm3$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5062",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5062",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5062 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5062",
"url": "https://theoremdb.org/statements/P5062",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5062",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:10+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5062,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.822Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"da3bb850-8d2e-4acd-8893-bcb7d3b72867","format_issues":null,"number":5479} |
1.0.0 | problem:theoremdb-p5064 | problem | theoremdb-p5064 | Independence number of the circulant graph C(1217; 1, 4) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1217\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm4$. Determine the independence number $\alpha(G)$. | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P5064",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5064",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5064 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Solution submitted. Not Lean-verified | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5064",
"url": "https://theoremdb.org/statements/P5064",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5064",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: candidate_resolution. Source verification claims are attributed only; no local Lean verific... | {"created_at":"2026-08-16T08:04:17+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5064,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":true,"hasRecordedWork":true,"solutionRecord":{"id":null,"pr... | [
"upstream-reports-proof-text-not-collected",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.827Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6b7604ea-4681-414d-8709-6d6c7053fcc0","format_issues":null,"number":5480} |
1.0.0 | problem:theoremdb-p5066 | problem | theoremdb-p5066 | Independence number of the circulant graph C(1223; 1, 5) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1223\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm5$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5066",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5066",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5066 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5066",
"url": "https://theoremdb.org/statements/P5066",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5066",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:25+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5066,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.831Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ee2952f5-06d7-48a8-ae7d-37944ea275a1","format_issues":null,"number":5481} |
1.0.0 | problem:theoremdb-p5068 | problem | theoremdb-p5068 | Independence number of the circulant graph C(1229; 1, 6) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1229\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm6$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5068",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5068",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5068 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5068",
"url": "https://theoremdb.org/statements/P5068",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5068",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:31+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5068,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.836Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"adb6f3d2-6810-46b6-88c5-89bcd3d10ee9","format_issues":null,"number":5482} |
1.0.0 | problem:theoremdb-p5070 | problem | theoremdb-p5070 | Independence number of the circulant graph C(1231; 1, 7) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1231\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm7$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5070",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5070",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5070 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5070",
"url": "https://theoremdb.org/statements/P5070",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5070",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:37+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5070,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.840Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"38a2a2aa-8f6d-4a0b-8690-54765285087a","format_issues":null,"number":5483} |
1.0.0 | problem:theoremdb-p5072 | problem | theoremdb-p5072 | Independence number of the circulant graph C(1237; 1, 8) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1237\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm8$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5072",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5072",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5072 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5072",
"url": "https://theoremdb.org/statements/P5072",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5072",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:38+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5072,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.845Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e90b388c-13e3-43c8-bbd9-cf905ef6b4a0","format_issues":null,"number":5484} |
1.0.0 | problem:theoremdb-p5074 | problem | theoremdb-p5074 | Independence number of the circulant graph C(1249; 1, 9) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1249\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm9$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5074",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5074",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5074 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5074",
"url": "https://theoremdb.org/statements/P5074",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5074",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:39+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5074,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.848Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"df58f625-e30d-487a-984b-64d72e5e630e","format_issues":null,"number":5485} |
1.0.0 | problem:theoremdb-p5076 | problem | theoremdb-p5076 | Independence number of the circulant graph C(1259; 1, 10) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1259\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm10$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5076",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5076",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5076 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5076",
"url": "https://theoremdb.org/statements/P5076",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5076",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:41+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5076,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.853Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1b1bf038-7f02-45b3-9348-abc3bc91dbce","format_issues":null,"number":5486} |
1.0.0 | problem:theoremdb-p5078 | problem | theoremdb-p5078 | Independence number of the circulant graph C(1277; 1, 11) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/1277\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm11$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5078",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5078",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5078 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5078",
"url": "https://theoremdb.org/statements/P5078",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5078",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:47+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5078,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.857Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"88936ba7-7512-4fa3-a3be-0a71d4a426a2","format_issues":null,"number":5487} |
1.0.0 | problem:theoremdb-p5080 | problem | theoremdb-p5080 | Domination number of the 26 by 27 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/26\mathbb{Z}\times\mathbb{Z}/27\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5080",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5080",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5080 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5080",
"url": "https://theoremdb.org/statements/P5080",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5080",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:53+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.146Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6280261d-6180-4381-88fc-01272607f665","format_issues":null,"number":4234} |
1.0.0 | problem:theoremdb-p5082 | problem | theoremdb-p5082 | Domination number of the 26 by 28 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/26\mathbb{Z}\times\mathbb{Z}/28\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5082",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5082",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5082 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5082",
"url": "https://theoremdb.org/statements/P5082",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5082",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:04:58+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.150Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2c0a7f72-0881-4183-9800-14b07604b2f7","format_issues":null,"number":4235} |
1.0.0 | problem:theoremdb-p5084 | problem | theoremdb-p5084 | Domination number of the 26 by 29 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/26\mathbb{Z}\times\mathbb{Z}/29\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5084",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5084",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5084 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5084",
"url": "https://theoremdb.org/statements/P5084",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5084",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:05:00+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.154Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a547713b-0968-47f2-b391-7664561c57ca","format_issues":null,"number":4236} |
1.0.0 | problem:theoremdb-p5086 | problem | theoremdb-p5086 | Domination number of the 26 by 30 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/26\mathbb{Z}\times\mathbb{Z}/30\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5086",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5086",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5086 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5086",
"url": "https://theoremdb.org/statements/P5086",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5086",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:05:12+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.159Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fec5e3b2-0395-4732-be5a-b5454e442bc0","format_issues":null,"number":4237} |
1.0.0 | problem:theoremdb-p5088 | problem | theoremdb-p5088 | Domination number of the 26 by 31 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/26\mathbb{Z}\times\mathbb{Z}/31\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5088",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5088",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5088 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5088",
"url": "https://theoremdb.org/statements/P5088",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5088",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:05:28+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.163Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"40b44fb2-331d-41e8-8452-407c3df336e1","format_issues":null,"number":4238} |
1.0.0 | problem:theoremdb-p5090 | problem | theoremdb-p5090 | Domination number of the 27 by 28 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/27\mathbb{Z}\times\mathbb{Z}/28\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5090",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5090",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5090 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5090",
"url": "https://theoremdb.org/statements/P5090",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5090",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:05:44+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.167Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a7a0b6f8-c7b8-4f64-8dcf-f494724a17cc","format_issues":null,"number":4239} |
1.0.0 | problem:theoremdb-p5092 | problem | theoremdb-p5092 | Domination number of the 27 by 29 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/27\mathbb{Z}\times\mathbb{Z}/29\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5092",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5092",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5092 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5092",
"url": "https://theoremdb.org/statements/P5092",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5092",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:06:04+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.172Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"87dd4e2e-e8a5-422e-bcd9-d9dd5dbda3d1","format_issues":null,"number":4240} |
1.0.0 | problem:theoremdb-p5094 | problem | theoremdb-p5094 | Domination number of the 27 by 30 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/27\mathbb{Z}\times\mathbb{Z}/30\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5094",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5094",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5094 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5094",
"url": "https://theoremdb.org/statements/P5094",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5094",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:06:25+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.176Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"467b8431-d86b-41b7-be1a-b52378ea2679","format_issues":null,"number":4241} |
1.0.0 | problem:theoremdb-p5096 | problem | theoremdb-p5096 | Domination number of the 27 by 31 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/27\mathbb{Z}\times\mathbb{Z}/31\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5096",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5096",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5096 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5096",
"url": "https://theoremdb.org/statements/P5096",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5096",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:08:37+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.183Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f69d79e4-fc4d-4d0d-99e0-a26e39a51c0b","format_issues":null,"number":4242} |
1.0.0 | problem:theoremdb-p5098 | problem | theoremdb-p5098 | Domination number of the 27 by 32 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/27\mathbb{Z}\times\mathbb{Z}/32\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5098",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5098",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5098 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5098",
"url": "https://theoremdb.org/statements/P5098",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5098",
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"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:08:46+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
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"published_at": "2026-09-08T03:32:54.188Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fb702849-3a5c-4e9e-8a67-62c1b66578ed","format_issues":null,"number":4243} |
1.0.0 | problem:theoremdb-p51 | problem | theoremdb-p51 | Novikov conjecture | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For every discrete group $\Gamma$, the higher signatures associated with classes in $H^*(B\Gamma;\mathbb{Q})$ are invariant under oriented homotopy equivalences of closed manifolds. | open | {
"key": "theoremdb",
"name": "TheoremDB · P51",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P51",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem pac... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P51 · topology | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P51",
"url": "https://theoremdb.org/statements/P51",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "Jonathan Rosenberg, arXiv:1506.05408, abstract and survey formulations",
"url": "https://arxiv.org/abs/1506.05408",
... | {
"source_record": "P51",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been per... | {"created_at":"2026-07-22T21:49:48+00:00","display_standard":{"editorial_review":"source_backed","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":51,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kerne... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:04.535Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"01a80b33-a7ba-45d5-bfa4-4a12042bca8a","format_issues":null,"number":6331} |
1.0.0 | problem:theoremdb-p5100 | problem | theoremdb-p5100 | Domination number of the 28 by 29 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/28\mathbb{Z}\times\mathbb{Z}/29\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5100",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5100",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5100 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5100",
"url": "https://theoremdb.org/statements/P5100",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5100",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:08:48+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.192Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b3095d45-b46c-4b6e-bf81-f7c357a19de3","format_issues":null,"number":4244} |
1.0.0 | problem:theoremdb-p5102 | problem | theoremdb-p5102 | Domination number of the 28 by 30 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/28\mathbb{Z}\times\mathbb{Z}/30\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5102",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5102",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5102 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5102",
"url": "https://theoremdb.org/statements/P5102",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5102",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:08:49+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.196Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"530294bd-3b61-44ad-bf0a-6a83d91849f3","format_issues":null,"number":4245} |
1.0.0 | problem:theoremdb-p5104 | problem | theoremdb-p5104 | Domination number of the 28 by 31 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/28\mathbb{Z}\times\mathbb{Z}/31\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5104",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5104",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5104 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5104",
"url": "https://theoremdb.org/statements/P5104",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5104",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:08:58+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.201Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"029ffd76-58d4-4cd7-b159-a621917444c8","format_issues":null,"number":4246} |
1.0.0 | problem:theoremdb-p5106 | problem | theoremdb-p5106 | Domination number of the 28 by 32 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/28\mathbb{Z}\times\mathbb{Z}/32\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5106",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5106",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5106 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5106",
"url": "https://theoremdb.org/statements/P5106",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5106",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:09:15+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.205Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9b58b26b-5ba4-4685-b327-1a568e0e1962","format_issues":null,"number":4247} |
1.0.0 | problem:theoremdb-p5108 | problem | theoremdb-p5108 | Domination number of the 28 by 33 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/28\mathbb{Z}\times\mathbb{Z}/33\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5108",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5108",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5108 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5108",
"url": "https://theoremdb.org/statements/P5108",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5108",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:09:30+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.209Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"03e2b947-708a-414f-a5a8-b91df51b9bfe","format_issues":null,"number":4248} |
1.0.0 | problem:theoremdb-p5110 | problem | theoremdb-p5110 | Domination number of the 29 by 30 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/29\mathbb{Z}\times\mathbb{Z}/30\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5110",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5110",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5110 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5110",
"url": "https://theoremdb.org/statements/P5110",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5110",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:09:40+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.213Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"42c45491-be4b-409c-99dd-ad2f207a31fb","format_issues":null,"number":4249} |
1.0.0 | problem:theoremdb-p5112 | problem | theoremdb-p5112 | Domination number of the 29 by 31 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/29\mathbb{Z}\times\mathbb{Z}/31\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5112",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5112",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5112 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5112",
"url": "https://theoremdb.org/statements/P5112",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5112",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:09:55+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.218Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fdb2f67b-529b-48d9-9469-273efd469e74","format_issues":null,"number":4250} |
1.0.0 | problem:theoremdb-p5114 | problem | theoremdb-p5114 | Domination number of the 29 by 32 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/29\mathbb{Z}\times\mathbb{Z}/32\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5114",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5114",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5114 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5114",
"url": "https://theoremdb.org/statements/P5114",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5114",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:10:10+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.222Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f1a1de07-20e6-49fd-9aa5-8d9e48e1a7db","format_issues":null,"number":4251} |
1.0.0 | problem:theoremdb-p5116 | problem | theoremdb-p5116 | Domination number of the 29 by 33 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/29\mathbb{Z}\times\mathbb{Z}/33\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
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"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5116 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
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"created_at": "2026-09-08T03:32:15.935Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"9f27c49e-8ca1-4da2-89fb-3f3738964047","format_issues":null,"number":4252} |
1.0.0 | problem:theoremdb-p5118 | problem | theoremdb-p5118 | Domination number of the 29 by 34 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/29\mathbb{Z}\times\mathbb{Z}/34\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5118",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5118",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5118 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5118",
"url": "https://theoremdb.org/statements/P5118",
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"sort_order": 0
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] | {
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"imported_at": "2026-09-08",
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"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:10:27+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.230Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e12c9dc4-6178-483a-bf5b-e6f2353d9770","format_issues":null,"number":4253} |
1.0.0 | problem:theoremdb-p5120 | problem | theoremdb-p5120 | Domination number of the 30 by 31 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/30\mathbb{Z}\times\mathbb{Z}/31\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5120",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5120",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5120 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5120",
"url": "https://theoremdb.org/statements/P5120",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5120",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:10:40+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.235Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4f57ad36-8bb0-4dfc-b61e-253823d2a53d","format_issues":null,"number":4254} |
1.0.0 | problem:theoremdb-p5122 | problem | theoremdb-p5122 | Domination number of the 30 by 32 toroidal knight graph | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | On $\mathbb{Z}/30\mathbb{Z}\times\mathbb{Z}/32\mathbb{Z}$, join two cells when their coordinate difference is one of $(\pm1,\pm2)$ or $(\pm2,\pm1)$. Determine the domination number of this toroidal knight graph. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5122",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5122",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5122 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5122",
"url": "https://theoremdb.org/statements/P5122",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5122",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:10:50+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.239Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6c8c3d5b-5359-460f-aee2-85da6b8b330b","format_issues":null,"number":4255} |
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