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1.0.0 | problem:theoremdb-p5124 | problem | theoremdb-p5124 | Domination number of the 30 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 $\mathbb{Z}/30\mathbb{Z}\times\mathbb{Z}/33\mathbb{Z}$, 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 · P5124",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5124",
"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 P5124 · 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 P5124",
"url": "https://theoremdb.org/statements/P5124",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5124",
"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":"2026-08-16T08:11:07+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": "2026-09-08T03:32:54.243Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7bf43a2d-5c88-47e7-a377-ab7c01f4702e","format_issues":null,"number":4256} |
1.0.0 | problem:theoremdb-p5126 | problem | theoremdb-p5126 | Domination number of the 30 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 $\mathbb{Z}/30\mathbb{Z}\times\mathbb{Z}/34\mathbb{Z}$, 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 · P5126",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5126",
"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 P5126 · 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 P5126",
"url": "https://theoremdb.org/statements/P5126",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5126",
"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":"2026-08-16T08:11:08+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": "2026-09-08T03:32:54.247Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8f956d01-eb86-4d52-a8ce-f38d45a7e73b","format_issues":null,"number":4257} |
1.0.0 | problem:theoremdb-p5128 | problem | theoremdb-p5128 | Domination number of the 30 by 35 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 $\mathbb{Z}/30\mathbb{Z}\times\mathbb{Z}/35\mathbb{Z}$, 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 · P5128",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5128",
"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 P5128 · 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 P5128",
"url": "https://theoremdb.org/statements/P5128",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5128",
"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":"2026-08-16T08:11:12+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": "2026-09-08T03:32:54.252Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"345ec115-2044-4184-b8b5-3cecf616c162","format_issues":null,"number":4258} |
1.0.0 | problem:theoremdb-p5130 | problem | theoremdb-p5130 | Domination number of the 31 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 $\mathbb{Z}/31\mathbb{Z}\times\mathbb{Z}/32\mathbb{Z}$, 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 · P5130",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5130",
"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 P5130 · 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 P5130",
"url": "https://theoremdb.org/statements/P5130",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5130",
"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":"2026-08-16T08:11:18+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": "2026-09-08T03:32:54.256Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"43d871cf-3856-438a-9b3c-77fb076a1ce5","format_issues":null,"number":4259} |
1.0.0 | problem:theoremdb-p5132 | problem | theoremdb-p5132 | Domination number of the 31 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 $\mathbb{Z}/31\mathbb{Z}\times\mathbb{Z}/33\mathbb{Z}$, 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 · P5132",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5132",
"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 P5132 · 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 P5132",
"url": "https://theoremdb.org/statements/P5132",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5132",
"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":"2026-08-16T08:11:30+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": "2026-09-08T03:32:54.260Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"62651606-b70c-406b-b1cc-fa5e3e28f244","format_issues":null,"number":4260} |
1.0.0 | problem:theoremdb-p5134 | problem | theoremdb-p5134 | Domination number of the 31 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 $\mathbb{Z}/31\mathbb{Z}\times\mathbb{Z}/34\mathbb{Z}$, 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 · P5134",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5134",
"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 P5134 · 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 P5134",
"url": "https://theoremdb.org/statements/P5134",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5134",
"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":"2026-08-16T08:11:36+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": "2026-09-08T03:32:54.264Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"564ede11-0bf2-4913-b811-fc3f05abaea5","format_issues":null,"number":4261} |
1.0.0 | problem:theoremdb-p5136 | problem | theoremdb-p5136 | Domination number of the 31 by 35 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 $\mathbb{Z}/31\mathbb{Z}\times\mathbb{Z}/35\mathbb{Z}$, 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 · P5136",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5136",
"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 P5136 · 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 P5136",
"url": "https://theoremdb.org/statements/P5136",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5136",
"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":"2026-08-16T08:11:43+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": "2026-09-08T03:32:54.268Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dfc4efb0-52cd-4cad-88df-59c60955d8ba","format_issues":null,"number":4262} |
1.0.0 | problem:theoremdb-p5138 | problem | theoremdb-p5138 | Domination number of the 31 by 36 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 $\mathbb{Z}/31\mathbb{Z}\times\mathbb{Z}/36\mathbb{Z}$, 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 · P5138",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5138",
"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 P5138 · 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 P5138",
"url": "https://theoremdb.org/statements/P5138",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5138",
"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":"2026-08-16T08:11:49+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": "2026-09-08T03:32:54.273Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3aae80f3-32e9-4421-93e7-3e941026d8af","format_issues":null,"number":4263} |
1.0.0 | problem:theoremdb-p5140 | problem | theoremdb-p5140 | Domination number of the 32 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 $\mathbb{Z}/32\mathbb{Z}\times\mathbb{Z}/33\mathbb{Z}$, 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 · P5140",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5140",
"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 P5140 · 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 P5140",
"url": "https://theoremdb.org/statements/P5140",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5140",
"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":"2026-08-16T08:11:57+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": "2026-09-08T03:32:54.277Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d49e0780-bda4-4e33-ae41-46a6bba02a6d","format_issues":null,"number":4264} |
1.0.0 | problem:theoremdb-p5142 | problem | theoremdb-p5142 | Domination number of the 32 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 $\mathbb{Z}/32\mathbb{Z}\times\mathbb{Z}/34\mathbb{Z}$, 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",
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"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5142 · 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"
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{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"5131f9f2-c76f-4110-8092-65df9790587c","format_issues":null,"number":4265} |
1.0.0 | problem:theoremdb-p5144 | problem | theoremdb-p5144 | Domination number of the 32 by 35 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 $\mathbb{Z}/32\mathbb{Z}\times\mathbb{Z}/35\mathbb{Z}$, 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 · P5144",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5144",
"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 P5144 · 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 P5144",
"url": "https://theoremdb.org/statements/P5144",
"note": null,
"sort_order": 0
}
] | {
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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":"2026-08-16T08:12:00+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... | [
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.287Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b7b29aa8-96d2-4b33-bfc7-75b962f1a240","format_issues":null,"number":4266} |
1.0.0 | problem:theoremdb-p5146 | problem | theoremdb-p5146 | Domination number of the 32 by 36 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 $\mathbb{Z}/32\mathbb{Z}\times\mathbb{Z}/36\mathbb{Z}$, 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 · P5146",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5146",
"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 P5146 · 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 P5146",
"url": "https://theoremdb.org/statements/P5146",
"note": null,
"sort_order": 0
}
] | {
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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":"2026-08-16T08:12:04+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... | [
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.291Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bd8051e1-0ec8-44e7-a7a8-a462e83af065","format_issues":null,"number":4267} |
1.0.0 | problem:theoremdb-p5148 | problem | theoremdb-p5148 | Domination number of the 32 by 37 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 $\mathbb{Z}/32\mathbb{Z}\times\mathbb{Z}/37\mathbb{Z}$, 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 · P5148",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5148",
"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 P5148 · 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 P5148",
"url": "https://theoremdb.org/statements/P5148",
"note": null,
"sort_order": 0
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] | {
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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":"2026-08-16T08:12:07+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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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.295Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5f1c818d-b801-4cfc-aed8-5aa60c85865c","format_issues":null,"number":4268} |
1.0.0 | problem:theoremdb-p5150 | problem | theoremdb-p5150 | Domination number of the 33 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 $\mathbb{Z}/33\mathbb{Z}\times\mathbb{Z}/34\mathbb{Z}$, 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 · P5150",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5150",
"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 P5150 · 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 P5150",
"url": "https://theoremdb.org/statements/P5150",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5150",
"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":"2026-08-16T08:12:08+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": "2026-09-08T03:32:54.302Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"121d7ef5-001a-433f-bb18-7e7a50cab4db","format_issues":null,"number":4269} |
1.0.0 | problem:theoremdb-p5152 | problem | theoremdb-p5152 | Domination number of the 33 by 35 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 $\mathbb{Z}/33\mathbb{Z}\times\mathbb{Z}/35\mathbb{Z}$, 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 · P5152",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5152",
"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 P5152 · 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 P5152",
"url": "https://theoremdb.org/statements/P5152",
"note": null,
"sort_order": 0
}
] | {
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"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":"2026-08-16T08:12:11+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": "2026-09-08T03:32:54.306Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3dbbb46b-9e8f-465d-a855-c3940e944813","format_issues":null,"number":4270} |
1.0.0 | problem:theoremdb-p5154 | problem | theoremdb-p5154 | Domination number of the 33 by 36 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 $\mathbb{Z}/33\mathbb{Z}\times\mathbb{Z}/36\mathbb{Z}$, 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 · P5154",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5154",
"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 P5154 · 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 P5154",
"url": "https://theoremdb.org/statements/P5154",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5154",
"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":"2026-08-16T08:12:20+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": "2026-09-08T03:32:54.311Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"56e2cb48-077e-44d7-8903-de5b989f5373","format_issues":null,"number":4271} |
1.0.0 | problem:theoremdb-p5156 | problem | theoremdb-p5156 | Domination number of the 33 by 37 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 $\mathbb{Z}/33\mathbb{Z}\times\mathbb{Z}/37\mathbb{Z}$, 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 · P5156",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5156",
"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 P5156 · 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 P5156",
"url": "https://theoremdb.org/statements/P5156",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5156",
"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":"2026-08-16T08:12:37+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": "2026-09-08T03:32:54.315Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"00069b16-935f-4cf8-9e56-8225d9df736f","format_issues":null,"number":4272} |
1.0.0 | problem:theoremdb-p5158 | problem | theoremdb-p5158 | Domination number of the 33 by 38 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 $\mathbb{Z}/33\mathbb{Z}\times\mathbb{Z}/38\mathbb{Z}$, 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 · P5158",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5158",
"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 P5158 · 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 P5158",
"url": "https://theoremdb.org/statements/P5158",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5158",
"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":"2026-08-16T08:12:40+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": "2026-09-08T03:32:54.319Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"beaff97b-22ce-42f3-85ed-f73b084b1194","format_issues":null,"number":4273} |
1.0.0 | problem:theoremdb-p5160 | problem | theoremdb-p5160 | Domination number of the 34 by 35 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 $\mathbb{Z}/34\mathbb{Z}\times\mathbb{Z}/35\mathbb{Z}$, 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 · P5160",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5160",
"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 P5160 · 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 P5160",
"url": "https://theoremdb.org/statements/P5160",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5160",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
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"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6a37154e-1db1-4ea5-8841-754b17cef37c","format_issues":null,"number":4274} |
1.0.0 | problem:theoremdb-p5162 | problem | theoremdb-p5162 | Domination number of the 34 by 36 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 $\mathbb{Z}/34\mathbb{Z}\times\mathbb{Z}/36\mathbb{Z}$, 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 · P5162",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5162",
"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 P5162 · 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 P5162",
"url": "https://theoremdb.org/statements/P5162",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5162",
"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":"2026-08-16T08:12:44+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... | [
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.328Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"43c75a99-caba-4577-973b-83b3a4794ea0","format_issues":null,"number":4275} |
1.0.0 | problem:theoremdb-p5164 | problem | theoremdb-p5164 | Domination number of the 34 by 37 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 $\mathbb{Z}/34\mathbb{Z}\times\mathbb{Z}/37\mathbb{Z}$, 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 · P5164",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5164",
"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 P5164 · 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 P5164",
"url": "https://theoremdb.org/statements/P5164",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5164",
"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":"2026-08-16T08:12:48+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... | [
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.334Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9c70b731-e492-4c48-b72e-719fb443948f","format_issues":null,"number":4276} |
1.0.0 | problem:theoremdb-p5166 | problem | theoremdb-p5166 | Domination number of the 34 by 38 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 $\mathbb{Z}/34\mathbb{Z}\times\mathbb{Z}/38\mathbb{Z}$, 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 · P5166",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5166",
"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 P5166 · 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 P5166",
"url": "https://theoremdb.org/statements/P5166",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5166",
"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":"2026-08-16T08:12:50+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": "2026-09-08T03:32:54.338Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d33e4936-b6cd-49a9-9c68-bce051d45b03","format_issues":null,"number":4277} |
1.0.0 | problem:theoremdb-p5168 | problem | theoremdb-p5168 | Domination number of the 34 by 39 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 $\mathbb{Z}/34\mathbb{Z}\times\mathbb{Z}/39\mathbb{Z}$, 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 · P5168",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5168",
"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 P5168 · 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 P5168",
"url": "https://theoremdb.org/statements/P5168",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5168",
"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":"2026-08-16T08:12:51+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": "2026-09-08T03:32:54.342Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"593cd2ec-eaf5-4408-af1f-a1859384de87","format_issues":null,"number":4278} |
1.0.0 | problem:theoremdb-p5170 | problem | theoremdb-p5170 | Domination number of the 35 by 36 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 $\mathbb{Z}/35\mathbb{Z}\times\mathbb{Z}/36\mathbb{Z}$, 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 · P5170",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5170",
"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 P5170 · 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 P5170",
"url": "https://theoremdb.org/statements/P5170",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5170",
"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":"2026-08-16T08:12:57+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": "2026-09-08T03:32:54.346Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9397463a-e9c5-4305-98ec-e1d5015be8c7","format_issues":null,"number":4279} |
1.0.0 | problem:theoremdb-p5172 | problem | theoremdb-p5172 | Domination number of the 35 by 37 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 $\mathbb{Z}/35\mathbb{Z}\times\mathbb{Z}/37\mathbb{Z}$, 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 · P5172",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5172",
"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 P5172 · 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 P5172",
"url": "https://theoremdb.org/statements/P5172",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5172",
"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":"2026-08-16T08:13:01+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": "2026-09-08T03:32:54.350Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6d8d5a85-903e-44af-8310-3586cd31c85a","format_issues":null,"number":4280} |
1.0.0 | problem:theoremdb-p5174 | problem | theoremdb-p5174 | Domination number of the 35 by 38 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 $\mathbb{Z}/35\mathbb{Z}\times\mathbb{Z}/38\mathbb{Z}$, 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 · P5174",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5174",
"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 P5174 · 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 P5174",
"url": "https://theoremdb.org/statements/P5174",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5174",
"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":"2026-08-16T08:13:02+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": "2026-09-08T03:32:54.355Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f8fda981-e3cb-4a44-bf2e-f9ed03fa052d","format_issues":null,"number":4281} |
1.0.0 | problem:theoremdb-p5176 | problem | theoremdb-p5176 | Domination number of the 35 by 39 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 $\mathbb{Z}/35\mathbb{Z}\times\mathbb{Z}/39\mathbb{Z}$, 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 · P5176",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5176",
"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 P5176 · 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 P5176",
"url": "https://theoremdb.org/statements/P5176",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5176",
"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":"2026-08-16T08:13:03+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": "2026-09-08T03:32:54.359Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"752d6490-5dc5-420e-b62b-ea7db23b2eff","format_issues":null,"number":4282} |
1.0.0 | problem:theoremdb-p5178 | problem | theoremdb-p5178 | Domination number of the 35 by 40 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 $\mathbb{Z}/35\mathbb{Z}\times\mathbb{Z}/40\mathbb{Z}$, 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 · P5178",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5178",
"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 P5178 · 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 P5178",
"url": "https://theoremdb.org/statements/P5178",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5178",
"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":"2026-08-16T08:13:07+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": "2026-09-08T03:32:54.364Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8830e705-a654-40da-be33-9be5fb6dd538","format_issues":null,"number":4283} |
1.0.0 | problem:theoremdb-p5180 | problem | theoremdb-p5180 | Domination number of the 36 by 37 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 $\mathbb{Z}/36\mathbb{Z}\times\mathbb{Z}/37\mathbb{Z}$, 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",
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"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5180 · 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 | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"4d41f7c5-603d-4a4d-baa3-f58e8daa5cab","format_issues":null,"number":4284} |
1.0.0 | problem:theoremdb-p5182 | problem | theoremdb-p5182 | Domination number of the 36 by 38 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 $\mathbb{Z}/36\mathbb{Z}\times\mathbb{Z}/38\mathbb{Z}$, 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 · P5182",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5182",
"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 P5182 · 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 P5182",
"url": "https://theoremdb.org/statements/P5182",
"note": null,
"sort_order": 0
}
] | {
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"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":"2026-08-16T08:13:13+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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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.372Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2a86baf8-3e0f-46eb-95b6-7844b552164b","format_issues":null,"number":4285} |
1.0.0 | problem:theoremdb-p5184 | problem | theoremdb-p5184 | Domination number of the 36 by 39 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 $\mathbb{Z}/36\mathbb{Z}\times\mathbb{Z}/39\mathbb{Z}$, 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 · P5184",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5184",
"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 P5184 · 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 P5184",
"url": "https://theoremdb.org/statements/P5184",
"note": null,
"sort_order": 0
}
] | {
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"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":"2026-08-16T08:13:16+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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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.376Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5650fd4d-f714-4ecf-a849-49e0f09ee35c","format_issues":null,"number":4286} |
1.0.0 | problem:theoremdb-p5186 | problem | theoremdb-p5186 | Domination number of the 36 by 40 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 $\mathbb{Z}/36\mathbb{Z}\times\mathbb{Z}/40\mathbb{Z}$, 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 · P5186",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5186",
"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 P5186 · 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 P5186",
"url": "https://theoremdb.org/statements/P5186",
"note": null,
"sort_order": 0
}
] | {
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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":"2026-08-16T08:13:18+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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] | [] | {
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.380Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"472cf23f-aa82-4ebb-b4b6-63eba1507f2d","format_issues":null,"number":4287} |
1.0.0 | problem:theoremdb-p5188 | problem | theoremdb-p5188 | Domination number of the 36 by 41 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 $\mathbb{Z}/36\mathbb{Z}\times\mathbb{Z}/41\mathbb{Z}$, 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 · P5188",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5188",
"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 P5188 · 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 P5188",
"url": "https://theoremdb.org/statements/P5188",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5188",
"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":"2026-08-16T08:13:19+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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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.385Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4519f005-4fb0-45ad-a245-2027069f28eb","format_issues":null,"number":4288} |
1.0.0 | problem:theoremdb-p5190 | problem | theoremdb-p5190 | Domination number of the 37 by 38 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 $\mathbb{Z}/37\mathbb{Z}\times\mathbb{Z}/38\mathbb{Z}$, 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 · P5190",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5190",
"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 P5190 · 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 P5190",
"url": "https://theoremdb.org/statements/P5190",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5190",
"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":"2026-08-16T08:13:21+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": "2026-09-08T03:32:54.389Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"27ddfd2b-0d65-4e14-ad0b-33ceae8c116f","format_issues":null,"number":4289} |
1.0.0 | problem:theoremdb-p5192 | problem | theoremdb-p5192 | Domination number of the 37 by 39 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 $\mathbb{Z}/37\mathbb{Z}\times\mathbb{Z}/39\mathbb{Z}$, 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 · P5192",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5192",
"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 P5192 · 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 P5192",
"url": "https://theoremdb.org/statements/P5192",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5192",
"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":"2026-08-16T08:13:27+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": "2026-09-08T03:32:54.393Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ad60af6e-545e-4518-b1ae-cae4a642cb0d","format_issues":null,"number":4290} |
1.0.0 | problem:theoremdb-p5194 | problem | theoremdb-p5194 | Domination number of the 37 by 40 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 $\mathbb{Z}/37\mathbb{Z}\times\mathbb{Z}/40\mathbb{Z}$, 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 · P5194",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5194",
"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 P5194 · 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 P5194",
"url": "https://theoremdb.org/statements/P5194",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5194",
"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":"2026-08-16T08:13:29+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": "2026-09-08T03:32:54.397Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b7050496-5df5-46a7-ba3f-c2030b644a1a","format_issues":null,"number":4291} |
1.0.0 | problem:theoremdb-p5196 | problem | theoremdb-p5196 | Domination number of the 37 by 41 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 $\mathbb{Z}/37\mathbb{Z}\times\mathbb{Z}/41\mathbb{Z}$, 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 · P5196",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5196",
"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 P5196 · 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 P5196",
"url": "https://theoremdb.org/statements/P5196",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5196",
"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":"2026-08-16T08:13:30+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": "2026-09-08T03:32:54.402Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"aedcd00c-5935-4343-bd77-e719f3132e5b","format_issues":null,"number":4292} |
1.0.0 | problem:theoremdb-p5198 | problem | theoremdb-p5198 | Domination number of the 37 by 42 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 $\mathbb{Z}/37\mathbb{Z}\times\mathbb{Z}/42\mathbb{Z}$, 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 · P5198",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5198",
"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 P5198 · 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 P5198",
"url": "https://theoremdb.org/statements/P5198",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5198",
"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":"2026-08-16T08:13:33+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": "2026-09-08T03:32:54.407Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bb3510cd-ee9a-487e-bd38-af699a9fb5d0","format_issues":null,"number":4293} |
1.0.0 | problem:theoremdb-p52 | problem | theoremdb-p52 | Hadwiger-Nelson problem | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Determine the chromatic number $\chi(\mathbb{R}^2)$ of the unit-distance graph on the Euclidean plane, whose vertices are points of $\mathbb{R}^2$ and whose edges join pairs at distance $1$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P52",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P52",
"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 P52 · discrete geometry | 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 P52",
"url": "https://theoremdb.org/statements/P52",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "Aubrey de Grey, arXiv:1804.02385, abstract and construction",
"url": "https://arxiv.org/abs/1804.02385",
"note":... | {
"source_record": "P52",
"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":52,"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": "2026-09-08T03:32:59.549Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3149ef99-2447-4d9a-a681-b91951ddb6f2","format_issues":null,"number":5419} |
1.0.0 | problem:theoremdb-p5200 | problem | theoremdb-p5200 | Domination number of the 38 by 39 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 $\mathbb{Z}/38\mathbb{Z}\times\mathbb{Z}/39\mathbb{Z}$, 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 · P5200",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5200",
"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 P5200 · 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 P5200",
"url": "https://theoremdb.org/statements/P5200",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5200",
"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":"2026-08-16T08:13:36+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": "2026-09-08T03:32:54.411Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2486e357-17f3-4927-b98c-9b8b3d5a7c41","format_issues":null,"number":4294} |
1.0.0 | problem:theoremdb-p5202 | problem | theoremdb-p5202 | Domination number of the 38 by 40 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 $\mathbb{Z}/38\mathbb{Z}\times\mathbb{Z}/40\mathbb{Z}$, 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 · P5202",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5202",
"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 P5202 · 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 P5202",
"url": "https://theoremdb.org/statements/P5202",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5202",
"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":"2026-08-16T08:13:38+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": "2026-09-08T03:32:54.416Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"13a16b22-ad39-4448-b5a8-2b2a8ca17b0c","format_issues":null,"number":4295} |
1.0.0 | problem:theoremdb-p5204 | problem | theoremdb-p5204 | Domination number of the 38 by 41 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 $\mathbb{Z}/38\mathbb{Z}\times\mathbb{Z}/41\mathbb{Z}$, 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 · P5204",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5204",
"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 P5204 · 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 P5204",
"url": "https://theoremdb.org/statements/P5204",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5204",
"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":"2026-08-16T08:13:38+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": "2026-09-08T03:32:54.422Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4a82d8eb-f923-4b40-b205-4afdee40d681","format_issues":null,"number":4296} |
1.0.0 | problem:theoremdb-p5206 | problem | theoremdb-p5206 | Domination number of the 38 by 42 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 $\mathbb{Z}/38\mathbb{Z}\times\mathbb{Z}/42\mathbb{Z}$, 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 · P5206",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5206",
"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 P5206 · 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 P5206",
"url": "https://theoremdb.org/statements/P5206",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5206",
"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":"2026-08-16T08:13:46+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... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.427Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2d3ace12-5ec3-44f4-8128-ad5c984ef812","format_issues":null,"number":4297} |
1.0.0 | problem:theoremdb-p5208 | problem | theoremdb-p5208 | Domination number of the 38 by 43 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 $\mathbb{Z}/38\mathbb{Z}\times\mathbb{Z}/43\mathbb{Z}$, 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 · P5208",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5208",
"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 P5208 · 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 P5208",
"url": "https://theoremdb.org/statements/P5208",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5208",
"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":"2026-08-16T08:13:54+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": "2026-09-08T03:32:54.431Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"46d602e1-7fdf-4d12-93d5-6c926295f3ea","format_issues":null,"number":4298} |
1.0.0 | problem:theoremdb-p5210 | problem | theoremdb-p5210 | Domination number of the 39 by 40 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 $\mathbb{Z}/39\mathbb{Z}\times\mathbb{Z}/40\mathbb{Z}$, 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 · P5210",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5210",
"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 P5210 · 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 P5210",
"url": "https://theoremdb.org/statements/P5210",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5210",
"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":"2026-08-16T08:13:55+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": "2026-09-08T03:32:54.435Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dddca39c-9a2d-4a37-83d0-e0c404108b3a","format_issues":null,"number":4299} |
1.0.0 | problem:theoremdb-p5212 | problem | theoremdb-p5212 | Domination number of the 39 by 41 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 $\mathbb{Z}/39\mathbb{Z}\times\mathbb{Z}/41\mathbb{Z}$, 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 · P5212",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5212",
"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 P5212 · 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 P5212",
"url": "https://theoremdb.org/statements/P5212",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5212",
"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":"2026-08-16T08:13:56+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": "2026-09-08T03:32:54.440Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"656a5dbd-35c8-4f61-b2d1-e9ef29230bb6","format_issues":null,"number":4300} |
1.0.0 | problem:theoremdb-p5214 | problem | theoremdb-p5214 | Domination number of the 39 by 42 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 $\mathbb{Z}/39\mathbb{Z}\times\mathbb{Z}/42\mathbb{Z}$, 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 · P5214",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5214",
"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 P5214 · 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 P5214",
"url": "https://theoremdb.org/statements/P5214",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5214",
"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":"2026-08-16T08:13:57+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": "2026-09-08T03:32:54.444Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f174b6eb-b517-4dc0-aa19-13ff64faf1bc","format_issues":null,"number":4301} |
1.0.0 | problem:theoremdb-p5216 | problem | theoremdb-p5216 | Domination number of the 39 by 43 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 $\mathbb{Z}/39\mathbb{Z}\times\mathbb{Z}/43\mathbb{Z}$, 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 · P5216",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5216",
"citation": null,
"doi": null,
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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 P5216 · 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 P5216",
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] | {
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"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":"2026-08-16T08:13:58+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5216,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.449Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2e8e0a49-467a-49f2-8890-93d6cdb39467","format_issues":null,"number":4302} |
1.0.0 | problem:theoremdb-p5218 | problem | theoremdb-p5218 | Domination number of the 39 by 44 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 $\mathbb{Z}/39\mathbb{Z}\times\mathbb{Z}/44\mathbb{Z}$, 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 · P5218",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5218",
"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 P5218 · 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 P5218",
"url": "https://theoremdb.org/statements/P5218",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5218",
"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":"2026-08-16T08:13:59+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5218,"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": "2026-09-08T03:32:54.453Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"10749d1f-0673-4291-9840-05e7fcbfdd72","format_issues":null,"number":4303} |
1.0.0 | problem:theoremdb-p5220 | problem | theoremdb-p5220 | Domination number of the 40 by 41 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 $\mathbb{Z}/40\mathbb{Z}\times\mathbb{Z}/41\mathbb{Z}$, 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 · P5220",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5220",
"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 P5220 · 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 P5220",
"url": "https://theoremdb.org/statements/P5220",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5220",
"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":"2026-08-16T08:13:59+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5220,"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": "2026-09-08T03:32:54.457Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8403ed37-78ba-4bc4-874a-8850176a640a","format_issues":null,"number":4304} |
1.0.0 | problem:theoremdb-p5222 | problem | theoremdb-p5222 | Domination number of the 40 by 42 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 $\mathbb{Z}/40\mathbb{Z}\times\mathbb{Z}/42\mathbb{Z}$, 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 · P5222",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5222",
"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 P5222 · 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 P5222",
"url": "https://theoremdb.org/statements/P5222",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5222",
"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":"2026-08-16T08:14:01+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5222,"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": "2026-09-08T03:32:54.462Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ec4fc4b9-f5c7-4a74-a533-94674ae2c335","format_issues":null,"number":4305} |
1.0.0 | problem:theoremdb-p5224 | problem | theoremdb-p5224 | Domination number of the 40 by 43 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 $\mathbb{Z}/40\mathbb{Z}\times\mathbb{Z}/43\mathbb{Z}$, 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 · P5224",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5224",
"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 P5224 · 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 P5224",
"url": "https://theoremdb.org/statements/P5224",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5224",
"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":"2026-08-16T08:14:03+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5224,"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": "2026-09-08T03:32:54.467Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e958ccf2-85d5-4a73-a05d-c9e5438abb96","format_issues":null,"number":4306} |
1.0.0 | problem:theoremdb-p5226 | problem | theoremdb-p5226 | Domination number of the 40 by 44 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 $\mathbb{Z}/40\mathbb{Z}\times\mathbb{Z}/44\mathbb{Z}$, 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 · P5226",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5226",
"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 P5226 · 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 P5226",
"url": "https://theoremdb.org/statements/P5226",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5226",
"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":"2026-08-16T08:14:11+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5226,"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": "2026-09-08T03:32:54.470Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"60d107fe-9612-47e2-b6b1-3c77bd54e3a0","format_issues":null,"number":4307} |
1.0.0 | problem:theoremdb-p5228 | problem | theoremdb-p5228 | Domination number of the 40 by 45 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 $\mathbb{Z}/40\mathbb{Z}\times\mathbb{Z}/45\mathbb{Z}$, 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 · P5228",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5228",
"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 P5228 · 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 P5228",
"url": "https://theoremdb.org/statements/P5228",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5228",
"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":"2026-08-16T08:14:14+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5228,"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": "2026-09-08T03:32:54.474Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"29649ba0-84a8-4a37-a57c-bdc7763fc856","format_issues":null,"number":4308} |
1.0.0 | problem:theoremdb-p5230 | problem | theoremdb-p5230 | Domination number of the 41 by 42 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 $\mathbb{Z}/41\mathbb{Z}\times\mathbb{Z}/42\mathbb{Z}$, 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 · P5230",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5230",
"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 P5230 · 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 P5230",
"url": "https://theoremdb.org/statements/P5230",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5230",
"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":"2026-08-16T08:14:15+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5230,"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": "2026-09-08T03:32:54.479Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fd89de2d-beba-48db-a80d-d8dd79d25766","format_issues":null,"number":4309} |
1.0.0 | problem:theoremdb-p5232 | problem | theoremdb-p5232 | Domination number of the 41 by 43 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 $\mathbb{Z}/41\mathbb{Z}\times\mathbb{Z}/43\mathbb{Z}$, 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 · P5232",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5232",
"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 P5232 · 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 P5232",
"url": "https://theoremdb.org/statements/P5232",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5232",
"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":"2026-08-16T08:14:16+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5232,"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": "2026-09-08T03:32:54.483Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"78079d53-d20a-4b30-b656-e1f614e4dbaa","format_issues":null,"number":4310} |
1.0.0 | problem:theoremdb-p5234 | problem | theoremdb-p5234 | Domination number of the 41 by 44 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 $\mathbb{Z}/41\mathbb{Z}\times\mathbb{Z}/44\mathbb{Z}$, 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 · P5234",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5234",
"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 P5234 · 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 P5234",
"url": "https://theoremdb.org/statements/P5234",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5234",
"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":"2026-08-16T08:14:22+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5234,"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": "2026-09-08T03:32:54.487Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e2a221e1-58e4-4a5b-a369-170bb4d71c10","format_issues":null,"number":4311} |
1.0.0 | problem:theoremdb-p5236 | problem | theoremdb-p5236 | Domination number of the 41 by 45 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 $\mathbb{Z}/41\mathbb{Z}\times\mathbb{Z}/45\mathbb{Z}$, 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 · P5236",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5236",
"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 P5236 · 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 P5236",
"url": "https://theoremdb.org/statements/P5236",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5236",
"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":"2026-08-16T08:14:28+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5236,"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": "2026-09-08T03:32:54.492Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ef239d3a-0510-4626-8a03-870268d1d57e","format_issues":null,"number":4312} |
1.0.0 | problem:theoremdb-p5238 | problem | theoremdb-p5238 | Domination number of the 41 by 46 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 $\mathbb{Z}/41\mathbb{Z}\times\mathbb{Z}/46\mathbb{Z}$, 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 · P5238",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5238",
"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 P5238 · 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 P5238",
"url": "https://theoremdb.org/statements/P5238",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5238",
"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":"2026-08-16T08:14:31+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5238,"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": "2026-09-08T03:32:54.497Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dd10cf44-75e5-447f-b57c-5be45460216c","format_issues":null,"number":4313} |
1.0.0 | problem:theoremdb-p5240 | problem | theoremdb-p5240 | Domination number of the 42 by 43 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 $\mathbb{Z}/42\mathbb{Z}\times\mathbb{Z}/43\mathbb{Z}$, 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 · P5240",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5240",
"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 P5240 · 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 P5240",
"url": "https://theoremdb.org/statements/P5240",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5240",
"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":"2026-08-16T08:14:34+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5240,"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": "2026-09-08T03:32:54.501Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a92529de-a829-4526-a114-e1cf76617a76","format_issues":null,"number":4314} |
1.0.0 | problem:theoremdb-p5242 | problem | theoremdb-p5242 | Domination number of the 42 by 44 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 $\mathbb{Z}/42\mathbb{Z}\times\mathbb{Z}/44\mathbb{Z}$, 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 · P5242",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5242",
"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 P5242 · 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 P5242",
"url": "https://theoremdb.org/statements/P5242",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5242",
"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":"2026-08-16T08:14:38+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5242,"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": "2026-09-08T03:32:54.505Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d216dd26-983a-4167-ac95-33203c7ef11a","format_issues":null,"number":4315} |
1.0.0 | problem:theoremdb-p5244 | problem | theoremdb-p5244 | Domination number of the 42 by 45 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 $\mathbb{Z}/42\mathbb{Z}\times\mathbb{Z}/45\mathbb{Z}$, 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 · P5244",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5244",
"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 P5244 · 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 P5244",
"url": "https://theoremdb.org/statements/P5244",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5244",
"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":"2026-08-16T08:14:40+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5244,"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": "2026-09-08T03:32:54.509Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7695d925-89ac-4e24-8515-1a2206b644d3","format_issues":null,"number":4316} |
1.0.0 | problem:theoremdb-p5246 | problem | theoremdb-p5246 | Domination number of the 42 by 46 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 $\mathbb{Z}/42\mathbb{Z}\times\mathbb{Z}/46\mathbb{Z}$, 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 · P5246",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5246",
"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 P5246 · 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 P5246",
"url": "https://theoremdb.org/statements/P5246",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5246",
"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":"2026-08-16T08:14:48+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5246,"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": "2026-09-08T03:32:54.513Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"37fc5b8e-c69e-4421-99c1-43efe745adc5","format_issues":null,"number":4317} |
1.0.0 | problem:theoremdb-p5248 | problem | theoremdb-p5248 | Domination number of the 42 by 47 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 $\mathbb{Z}/42\mathbb{Z}\times\mathbb{Z}/47\mathbb{Z}$, 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 · P5248",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5248",
"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 P5248 · 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 P5248",
"url": "https://theoremdb.org/statements/P5248",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5248",
"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":"2026-08-16T08:14:52+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5248,"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": "2026-09-08T03:32:54.518Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4d7e85ad-7125-44ef-a656-97ac905c02af","format_issues":null,"number":4318} |
1.0.0 | problem:theoremdb-p5250 | problem | theoremdb-p5250 | Domination number of the 43 by 44 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 $\mathbb{Z}/43\mathbb{Z}\times\mathbb{Z}/44\mathbb{Z}$, 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 · P5250",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5250",
"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 P5250 · 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 P5250",
"url": "https://theoremdb.org/statements/P5250",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5250",
"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":"2026-08-16T08:14:56+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5250,"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": "2026-09-08T03:32:54.522Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"de8f77be-5739-4af2-ae8b-da0601e19004","format_issues":null,"number":4319} |
1.0.0 | problem:theoremdb-p5252 | problem | theoremdb-p5252 | Domination number of the 43 by 45 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 $\mathbb{Z}/43\mathbb{Z}\times\mathbb{Z}/45\mathbb{Z}$, 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 · P5252",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5252",
"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 P5252 · 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 P5252",
"url": "https://theoremdb.org/statements/P5252",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5252",
"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":"2026-08-16T08:15:01+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5252,"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": "2026-09-08T03:32:54.526Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"843a6fdf-c1ba-45d2-9580-02040bdf6f63","format_issues":null,"number":4320} |
1.0.0 | problem:theoremdb-p5254 | problem | theoremdb-p5254 | Domination number of the 43 by 46 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 $\mathbb{Z}/43\mathbb{Z}\times\mathbb{Z}/46\mathbb{Z}$, 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 · P5254",
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"url": "https://theoremdb.org/statements/P5254",
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"doi": null,
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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 P5254 · 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 | [
{
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"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f4d00819-7800-4045-817c-047e0cd5d6cb","format_issues":null,"number":4321} |
1.0.0 | problem:theoremdb-p5256 | problem | theoremdb-p5256 | Domination number of the 43 by 47 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 $\mathbb{Z}/43\mathbb{Z}\times\mathbb{Z}/47\mathbb{Z}$, 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 · P5256",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5256",
"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 P5256 · 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 P5256",
"url": "https://theoremdb.org/statements/P5256",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5256",
"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":"2026-08-16T08:15:14+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5256,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:54.535Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"356cf09b-d66c-4ed9-9dce-63f9fd3d8b41","format_issues":null,"number":4322} |
1.0.0 | problem:theoremdb-p5258 | problem | theoremdb-p5258 | Domination number of the 43 by 48 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 $\mathbb{Z}/43\mathbb{Z}\times\mathbb{Z}/48\mathbb{Z}$, 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 · P5258",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5258",
"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 P5258 · 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 P5258",
"url": "https://theoremdb.org/statements/P5258",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5258",
"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":"2026-08-16T08:15:23+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5258,"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": "2026-09-08T03:32:54.538Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"631ce64d-7ddc-4af2-b6dd-4c7469185502","format_issues":null,"number":4323} |
1.0.0 | problem:theoremdb-p5260 | problem | theoremdb-p5260 | Domination number of the 44 by 45 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 $\mathbb{Z}/44\mathbb{Z}\times\mathbb{Z}/45\mathbb{Z}$, 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 · P5260",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5260",
"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 P5260 · 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 P5260",
"url": "https://theoremdb.org/statements/P5260",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5260",
"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":"2026-08-16T08:15:39+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5260,"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": "2026-09-08T03:32:54.546Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ce915c07-879e-4f98-b6c6-42d7fe124410","format_issues":null,"number":4324} |
1.0.0 | problem:theoremdb-p5264 | problem | theoremdb-p5264 | Domination number of the 44 by 46 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 $\mathbb{Z}/44\mathbb{Z}\times\mathbb{Z}/46\mathbb{Z}$, 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 · P5264",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5264",
"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 P5264 · 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 P5264",
"url": "https://theoremdb.org/statements/P5264",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5264",
"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":"2026-08-16T08:19:09+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5264,"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": "2026-09-08T03:32:54.551Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3d1d7435-a3e9-43e8-aa65-e2a1ebf3b9bf","format_issues":null,"number":4325} |
1.0.0 | problem:theoremdb-p5266 | problem | theoremdb-p5266 | Domination number of the 44 by 47 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 $\mathbb{Z}/44\mathbb{Z}\times\mathbb{Z}/47\mathbb{Z}$, 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 · P5266",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5266",
"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 P5266 · 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 P5266",
"url": "https://theoremdb.org/statements/P5266",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5266",
"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":"2026-08-16T08:19:21+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5266,"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": "2026-09-08T03:32:54.556Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f76e8e32-fef2-4291-ae41-7da8f572ba8d","format_issues":null,"number":4326} |
1.0.0 | problem:theoremdb-p5268 | problem | theoremdb-p5268 | Domination number of the 44 by 48 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 $\mathbb{Z}/44\mathbb{Z}\times\mathbb{Z}/48\mathbb{Z}$, 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 · P5268",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5268",
"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 P5268 · 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 P5268",
"url": "https://theoremdb.org/statements/P5268",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5268",
"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":"2026-08-16T08:19:35+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5268,"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": "2026-09-08T03:32:54.560Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b031d791-e432-4b46-b3a2-5257c0a84fcd","format_issues":null,"number":4327} |
1.0.0 | problem:theoremdb-p5270 | problem | theoremdb-p5270 | Domination number of the 44 by 49 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 $\mathbb{Z}/44\mathbb{Z}\times\mathbb{Z}/49\mathbb{Z}$, 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 · P5270",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5270",
"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 P5270 · 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 P5270",
"url": "https://theoremdb.org/statements/P5270",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5270",
"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":"2026-08-16T08:19:39+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5270,"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": "2026-09-08T03:32:54.564Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f4b74c0d-2b17-4c85-b80b-7ba07881b53d","format_issues":null,"number":4328} |
1.0.0 | problem:theoremdb-p5272 | problem | theoremdb-p5272 | Domination number of the 45 by 46 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 $\mathbb{Z}/45\mathbb{Z}\times\mathbb{Z}/46\mathbb{Z}$, 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 · P5272",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5272",
"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 P5272 · 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 P5272",
"url": "https://theoremdb.org/statements/P5272",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5272",
"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":"2026-08-16T08:19:41+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5272,"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": "2026-09-08T03:32:54.569Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"74cf422b-414a-4fb0-a40b-27f0e0b899ec","format_issues":null,"number":4329} |
1.0.0 | problem:theoremdb-p5274 | problem | theoremdb-p5274 | Domination number of the 45 by 47 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 $\mathbb{Z}/45\mathbb{Z}\times\mathbb{Z}/47\mathbb{Z}$, 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 · P5274",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5274",
"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 P5274 · 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 P5274",
"url": "https://theoremdb.org/statements/P5274",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5274",
"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":"2026-08-16T08:19:49+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5274,"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": "2026-09-08T03:32:54.574Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dbf58adb-ce70-48dd-8e58-f7ea8582f025","format_issues":null,"number":4330} |
1.0.0 | problem:theoremdb-p5276 | problem | theoremdb-p5276 | Domination number of the 45 by 48 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 $\mathbb{Z}/45\mathbb{Z}\times\mathbb{Z}/48\mathbb{Z}$, 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 · P5276",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5276",
"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 P5276 · 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 P5276",
"url": "https://theoremdb.org/statements/P5276",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5276",
"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":"2026-08-16T08:19:54+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5276,"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": "2026-09-08T03:32:54.578Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"20aac930-75b3-4582-acab-a63bfdade137","format_issues":null,"number":4331} |
1.0.0 | problem:theoremdb-p5278 | problem | theoremdb-p5278 | Domination number of the 45 by 49 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 $\mathbb{Z}/45\mathbb{Z}\times\mathbb{Z}/49\mathbb{Z}$, 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 · P5278",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5278",
"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 P5278 · 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 P5278",
"url": "https://theoremdb.org/statements/P5278",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5278",
"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":"2026-08-16T08:20:00+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5278,"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": "2026-09-08T03:32:54.582Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"39c4256f-3387-40de-a571-c86dfc705e21","format_issues":null,"number":4332} |
1.0.0 | problem:theoremdb-p5280 | problem | theoremdb-p5280 | Domination number of the 45 by 50 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 $\mathbb{Z}/45\mathbb{Z}\times\mathbb{Z}/50\mathbb{Z}$, 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 · P5280",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5280",
"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 P5280 · 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 P5280",
"url": "https://theoremdb.org/statements/P5280",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5280",
"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":"2026-08-16T08:20:01+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5280,"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": "2026-09-08T03:32:54.586Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c9d0b1b6-afd1-49b3-9634-d0381e3a9d27","format_issues":null,"number":4333} |
1.0.0 | problem:theoremdb-p5282 | problem | theoremdb-p5282 | Exact value of A(70, 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 $A_2(70,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{70}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5282",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5282",
"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 P5282 · 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 P5282",
"url": "https://theoremdb.org/statements/P5282",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5282",
"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":"2026-08-16T08:20:09+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5282,"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": "2026-09-08T03:32:58.101Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bdd173d6-5c85-4ef7-9c8f-551efd53f57e","format_issues":null,"number":5110} |
1.0.0 | problem:theoremdb-p5284 | problem | theoremdb-p5284 | Exact value of A(71, 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 $A_2(71,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{71}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5284",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5284",
"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 P5284 · 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 P5284",
"url": "https://theoremdb.org/statements/P5284",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5284",
"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":"2026-08-16T08:20:11+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5284,"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": "2026-09-08T03:32:58.105Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"393e419e-2521-464b-91a1-f0365f1f8672","format_issues":null,"number":5111} |
1.0.0 | problem:theoremdb-p5286 | problem | theoremdb-p5286 | Exact value of A(72, 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 $A_2(72,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{72}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5286",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5286",
"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 P5286 · 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 P5286",
"url": "https://theoremdb.org/statements/P5286",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5286",
"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":"2026-08-16T08:20:18+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5286,"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": "2026-09-08T03:32:58.109Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c74e969b-fa72-4774-b715-cd48d1d32ad4","format_issues":null,"number":5112} |
1.0.0 | problem:theoremdb-p5288 | problem | theoremdb-p5288 | Exact value of A(73, 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 $A_2(73,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{73}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5288",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5288",
"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 P5288 · 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 P5288",
"url": "https://theoremdb.org/statements/P5288",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5288",
"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":"2026-08-16T08:20:25+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5288,"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": "2026-09-08T03:32:58.114Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1d9ec55b-ab29-4172-9bc1-a2ccbc9ca653","format_issues":null,"number":5113} |
1.0.0 | problem:theoremdb-p5290 | problem | theoremdb-p5290 | Exact value of A(74, 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 $A_2(74,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{74}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5290",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5290",
"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 P5290 · 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 P5290",
"url": "https://theoremdb.org/statements/P5290",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5290",
"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":"2026-08-16T08:20:34+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5290,"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": "2026-09-08T03:32:58.118Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"96aee1d5-0e38-46ce-b90b-2c9d8cd3f043","format_issues":null,"number":5114} |
1.0.0 | problem:theoremdb-p5292 | problem | theoremdb-p5292 | Exact value of A(75, 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 $A_2(75,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{75}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5292",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5292",
"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 P5292 · 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 P5292",
"url": "https://theoremdb.org/statements/P5292",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5292",
"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":"2026-08-16T08:20:40+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5292,"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": "2026-09-08T03:32:58.125Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a086587a-e66e-44fa-9910-a6714e46ad43","format_issues":null,"number":5115} |
1.0.0 | problem:theoremdb-p5294 | problem | theoremdb-p5294 | Exact value of A(76, 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 $A_2(76,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{76}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5294",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5294",
"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 P5294 · 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 P5294",
"url": "https://theoremdb.org/statements/P5294",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5294",
"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":"2026-08-16T08:20:43+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5294,"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": "2026-09-08T03:32:58.129Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1a91e69b-4eb9-4919-9bb2-2c69a0779287","format_issues":null,"number":5116} |
1.0.0 | problem:theoremdb-p5296 | problem | theoremdb-p5296 | Exact value of A(77, 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 $A_2(77,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{77}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5296",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5296",
"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 P5296 · 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 P5296",
"url": "https://theoremdb.org/statements/P5296",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5296",
"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":"2026-08-16T08:20:47+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5296,"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": "2026-09-08T03:32:58.134Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e9f87960-05b0-46e0-a9ad-55a9ec75ab2d","format_issues":null,"number":5117} |
1.0.0 | problem:theoremdb-p5298 | problem | theoremdb-p5298 | Exact value of A(78, 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 $A_2(78,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{78}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5298",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5298",
"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 P5298 · 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 P5298",
"url": "https://theoremdb.org/statements/P5298",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5298",
"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":"2026-08-16T08:20:54+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5298,"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": "2026-09-08T03:32:58.143Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"10379a38-4206-4e99-b000-8deaca03d5c3","format_issues":null,"number":5119} |
1.0.0 | problem:theoremdb-p5300 | problem | theoremdb-p5300 | Exact value of A(79, 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 $A_2(79,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{79}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5300",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5300",
"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 P5300 · 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 P5300",
"url": "https://theoremdb.org/statements/P5300",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5300",
"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":"2026-08-16T08:21:01+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5300,"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": "2026-09-08T03:32:58.151Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8cfbbb57-802b-4fd3-be77-5466850b2bac","format_issues":null,"number":5121} |
1.0.0 | problem:theoremdb-p5302 | problem | theoremdb-p5302 | Exact value of A(80, 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 $A_2(80,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{80}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5302",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5302",
"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 P5302 · 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 P5302",
"url": "https://theoremdb.org/statements/P5302",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5302",
"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":"2026-08-16T08:21:03+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5302,"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": "2026-09-08T03:32:58.160Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6ed3a388-84fb-422d-bc7b-c5159e5cae2c","format_issues":null,"number":5123} |
1.0.0 | problem:theoremdb-p5304 | problem | theoremdb-p5304 | Exact value of A(81, 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 $A_2(81,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{81}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5304",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5304",
"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 P5304 · 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 P5304",
"url": "https://theoremdb.org/statements/P5304",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5304",
"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":"2026-08-16T08:21:08+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5304,"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": "2026-09-08T03:32:58.169Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"af0d8791-5818-4882-ad52-b8a6a35b454e","format_issues":null,"number":5125} |
1.0.0 | problem:theoremdb-p5306 | problem | theoremdb-p5306 | Exact value of A(82, 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 $A_2(82,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{82}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5306",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5306",
"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 P5306 · 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 P5306",
"url": "https://theoremdb.org/statements/P5306",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5306",
"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":"2026-08-16T08:21:10+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5306,"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": "2026-09-08T03:32:58.177Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b7910ab2-80e1-4c82-a6ab-ba60f404164e","format_issues":null,"number":5127} |
1.0.0 | problem:theoremdb-p5308 | problem | theoremdb-p5308 | Exact value of A(83, 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 $A_2(83,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{83}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5308",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5308",
"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 P5308 · 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 P5308",
"url": "https://theoremdb.org/statements/P5308",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5308",
"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":"2026-08-16T08:21:10+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5308,"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": "2026-09-08T03:32:58.185Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"655d2df4-5994-43a5-a023-6f4a4a74325b","format_issues":null,"number":5129} |
1.0.0 | problem:theoremdb-p5310 | problem | theoremdb-p5310 | Exact value of A(84, 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 $A_2(84,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{84}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5310",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5310",
"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 P5310 · 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 P5310",
"url": "https://theoremdb.org/statements/P5310",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5310",
"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":"2026-08-16T08:21:14+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5310,"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": "2026-09-08T03:32:58.194Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fe970767-f018-458c-b618-581600d198e7","format_issues":null,"number":5131} |
1.0.0 | problem:theoremdb-p5312 | problem | theoremdb-p5312 | Exact value of A(85, 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 $A_2(85,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{85}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5312",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5312",
"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 P5312 · 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 P5312",
"url": "https://theoremdb.org/statements/P5312",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5312",
"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":"2026-08-16T08:21:17+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5312,"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": "2026-09-08T03:32:58.202Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0be32aa5-7057-4747-9c4b-6432b9920c51","format_issues":null,"number":5133} |
1.0.0 | problem:theoremdb-p5314 | problem | theoremdb-p5314 | Exact value of A(86, 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 $A_2(86,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{86}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5314",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5314",
"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 P5314 · 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 P5314",
"url": "https://theoremdb.org/statements/P5314",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5314",
"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":"2026-08-16T08:21:22+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5314,"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": "2026-09-08T03:32:58.210Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3751db55-869d-4649-b993-c6487f0dbf80","format_issues":null,"number":5135} |
1.0.0 | problem:theoremdb-p5316 | problem | theoremdb-p5316 | Exact value of A(87, 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 $A_2(87,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{87}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5316",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5316",
"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 P5316 · 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 P5316",
"url": "https://theoremdb.org/statements/P5316",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5316",
"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":"2026-08-16T08:21:24+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5316,"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": "2026-09-08T03:32:58.219Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"288da66f-5395-4b7a-a208-37e94d01649f","format_issues":null,"number":5137} |
1.0.0 | problem:theoremdb-p5318 | problem | theoremdb-p5318 | Exact value of A(88, 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 $A_2(88,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{88}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5318",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5318",
"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 P5318 · 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 P5318",
"url": "https://theoremdb.org/statements/P5318",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5318",
"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":"2026-08-16T08:21:26+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5318,"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": "2026-09-08T03:32:58.227Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4efd71ce-ceb6-4ef6-86e5-765310e80993","format_issues":null,"number":5139} |
1.0.0 | problem:theoremdb-p5320 | problem | theoremdb-p5320 | Exact value of A(89, 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 $A_2(89,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{89}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5320",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5320",
"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 P5320 · 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 P5320",
"url": "https://theoremdb.org/statements/P5320",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5320",
"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":"2026-08-16T08:21:32+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5320,"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": "2026-09-08T03:32:58.236Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1ec8d279-80c1-42da-8480-50a05c7b5f64","format_issues":null,"number":5141} |
1.0.0 | problem:theoremdb-p5322 | problem | theoremdb-p5322 | Exact value of A(90, 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 $A_2(90,6,4)$, the largest cardinality of a family $C\subseteq\{0,1\}^{90}$ in which every word has Hamming weight $4$ and every two distinct words have Hamming distance at least $6$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5322",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5322",
"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 P5322 · 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 P5322",
"url": "https://theoremdb.org/statements/P5322",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5322",
"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":"2026-08-16T08:21:35+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5322,"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": "2026-09-08T03:32:58.249Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2730c03c-3447-47e9-8925-a7ea3c462688","format_issues":null,"number":5143} |
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