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1.0.0 | problem:theoremdb-p5728 | problem | theoremdb-p5728 | Chromatic number of the circulant graph C(967; 1, 7, 24) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/967\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm24$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5728",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5728",
"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 P5728 · 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 P5728",
"url": "https://theoremdb.org/statements/P5728",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5728",
"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":"2026-08-16T08:50:20+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": "2026-09-08T03:32:51.719Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dd81b6f8-0445-4c72-ae8d-744efcc85ca0","format_issues":null,"number":3699} |
1.0.0 | problem:theoremdb-p5730 | problem | theoremdb-p5730 | Chromatic number of the circulant graph C(971; 1, 8, 25) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/971\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm25$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5730",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5730",
"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 P5730 · 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 P5730",
"url": "https://theoremdb.org/statements/P5730",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5730",
"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":"2026-08-16T08:50:32+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": "2026-09-08T03:32:51.723Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f9b19368-ae93-4e9e-b7e0-b6bcb90f1d6e","format_issues":null,"number":3700} |
1.0.0 | problem:theoremdb-p5732 | problem | theoremdb-p5732 | Chromatic number of the circulant graph C(977; 1, 9, 26) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/977\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm26$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5732",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5732",
"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 P5732 · 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 P5732",
"url": "https://theoremdb.org/statements/P5732",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5732",
"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":"2026-08-16T08:50:47+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": "2026-09-08T03:32:51.727Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"18c88073-468b-4f3c-935f-b3a0abf8b76c","format_issues":null,"number":3701} |
1.0.0 | problem:theoremdb-p5734 | problem | theoremdb-p5734 | Chromatic number of the circulant graph C(983; 1, 10, 27) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/983\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm27$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5734",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5734",
"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 P5734 · 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 P5734",
"url": "https://theoremdb.org/statements/P5734",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5734",
"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":"2026-08-16T08:51:10+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.732Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c1935b62-c98e-4a46-b3a2-831d39f84b21","format_issues":null,"number":3702} |
1.0.0 | problem:theoremdb-p5736 | problem | theoremdb-p5736 | Chromatic number of the circulant graph C(991; 1, 11, 28) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/991\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm28$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5736",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5736",
"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 P5736 · 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 P5736",
"url": "https://theoremdb.org/statements/P5736",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5736",
"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":"2026-08-16T08:51:36+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5736,"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": "2026-09-08T03:32:51.735Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eebbea64-4a48-4e43-b48e-393278267db2","format_issues":null,"number":3703} |
1.0.0 | problem:theoremdb-p5738 | problem | theoremdb-p5738 | Chromatic number of the circulant graph C(997; 1, 12, 29) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/997\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm29$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5738",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5738",
"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 P5738 · 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 P5738",
"url": "https://theoremdb.org/statements/P5738",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5738",
"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":"2026-08-16T08:51:53+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5738,"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": "2026-09-08T03:32:51.740Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2d507a53-acf6-4f64-ad9e-245e797cda53","format_issues":null,"number":3704} |
1.0.0 | problem:theoremdb-p5740 | problem | theoremdb-p5740 | Chromatic number of the circulant graph C(1009; 1, 2, 30) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1009\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm30$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5740",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5740",
"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 P5740 · 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 P5740",
"url": "https://theoremdb.org/statements/P5740",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5740",
"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":"2026-08-16T08:52:11+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5740,"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": "2026-09-08T03:32:51.122Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ea0cdbf8-8198-42e3-8ed8-cb77588667f9","format_issues":null,"number":3565} |
1.0.0 | problem:theoremdb-p5742 | problem | theoremdb-p5742 | Chromatic number of the circulant graph C(1013; 1, 3, 14) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1013\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm14$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5742",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5742",
"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 P5742 · 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 P5742",
"url": "https://theoremdb.org/statements/P5742",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5742",
"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":"2026-08-16T08:52:28+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5742,"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": "2026-09-08T03:32:51.126Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f05dc338-8ada-45ee-ab56-980b839e901c","format_issues":null,"number":3566} |
1.0.0 | problem:theoremdb-p5744 | problem | theoremdb-p5744 | Chromatic number of the circulant graph C(1019; 1, 4, 15) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1019\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm15$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5744",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5744",
"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 P5744 · 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 P5744",
"url": "https://theoremdb.org/statements/P5744",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5744",
"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":"2026-08-16T08:52:40+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5744,"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": "2026-09-08T03:32:51.131Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"078e3086-a7a5-46c5-a9dc-6616871d8084","format_issues":null,"number":3567} |
1.0.0 | problem:theoremdb-p5746 | problem | theoremdb-p5746 | Chromatic number of the circulant graph C(1021; 1, 5, 16) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1021\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm16$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5746",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5746",
"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 P5746 · 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 P5746",
"url": "https://theoremdb.org/statements/P5746",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5746",
"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":"2026-08-16T08:53:02+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5746,"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": "2026-09-08T03:32:51.135Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"df53c343-990d-4d4b-acde-8c0b9575d481","format_issues":null,"number":3568} |
1.0.0 | problem:theoremdb-p5748 | problem | theoremdb-p5748 | Chromatic number of the circulant graph C(1031; 1, 6, 17) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1031\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm17$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5748",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5748",
"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 P5748 · 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 P5748",
"url": "https://theoremdb.org/statements/P5748",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5748",
"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":"2026-08-16T08:53:20+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5748,"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": "2026-09-08T03:32:51.139Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2de9f688-929a-48d6-ae3f-8ff632e76e5c","format_issues":null,"number":3569} |
1.0.0 | problem:theoremdb-p5750 | problem | theoremdb-p5750 | Chromatic number of the circulant graph C(1033; 1, 7, 18) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1033\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm18$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5750",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5750",
"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 P5750 · 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 P5750",
"url": "https://theoremdb.org/statements/P5750",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5750",
"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":"2026-08-16T08:53:43+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5750,"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": "2026-09-08T03:32:51.143Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"16044f8e-78a0-4f65-a444-adae03fa832f","format_issues":null,"number":3570} |
1.0.0 | problem:theoremdb-p5752 | problem | theoremdb-p5752 | Chromatic number of the circulant graph C(1039; 1, 8, 19) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1039\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm19$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5752",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5752",
"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 P5752 · 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 P5752",
"url": "https://theoremdb.org/statements/P5752",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5752",
"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":"2026-08-16T08:54:03+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5752,"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": "2026-09-08T03:32:51.148Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"50688556-5a93-4622-9412-f095a90740ec","format_issues":null,"number":3571} |
1.0.0 | problem:theoremdb-p5754 | problem | theoremdb-p5754 | Chromatic number of the circulant graph C(1049; 1, 9, 20) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1049\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm20$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5754",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5754",
"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 P5754 · 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 P5754",
"url": "https://theoremdb.org/statements/P5754",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5754",
"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":"2026-08-16T08:54:23+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5754,"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": "2026-09-08T03:32:51.152Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"00c65376-c24d-4341-a9d5-af0e2db0e06c","format_issues":null,"number":3572} |
1.0.0 | problem:theoremdb-p5756 | problem | theoremdb-p5756 | Chromatic number of the circulant graph C(1051; 1, 10, 21) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1051\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm21$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5756",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5756",
"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 P5756 · 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 P5756",
"url": "https://theoremdb.org/statements/P5756",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5756",
"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":"2026-08-16T08:54:42+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5756,"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": "2026-09-08T03:32:51.157Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"240f908e-b4b5-469b-8c3e-d327136f6f96","format_issues":null,"number":3573} |
1.0.0 | problem:theoremdb-p5758 | problem | theoremdb-p5758 | Chromatic number of the circulant graph C(1061; 1, 11, 22) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1061\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm22$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5758",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5758",
"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 P5758 · 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 P5758",
"url": "https://theoremdb.org/statements/P5758",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5758",
"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":"2026-08-16T08:55:02+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5758,"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": "2026-09-08T03:32:51.161Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"764436a3-c8e5-4e34-8edf-991acf55b2bf","format_issues":null,"number":3574} |
1.0.0 | problem:theoremdb-p5760 | problem | theoremdb-p5760 | Chromatic number of the circulant graph C(1063; 1, 12, 23) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1063\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm23$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5760",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5760",
"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 P5760 · 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 P5760",
"url": "https://theoremdb.org/statements/P5760",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5760",
"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":"2026-08-16T08:55:24+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5760,"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": "2026-09-08T03:32:51.166Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"80ffd51d-e20a-44d2-9915-76d6b345351f","format_issues":null,"number":3575} |
1.0.0 | problem:theoremdb-p5762 | problem | theoremdb-p5762 | Chromatic number of the circulant graph C(1069; 1, 2, 24) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1069\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm24$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5762",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5762",
"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 P5762 · 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 P5762",
"url": "https://theoremdb.org/statements/P5762",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5762",
"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":"2026-08-16T08:55:48+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5762,"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": "2026-09-08T03:32:51.170Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"67683b6a-bd2b-47b2-85e9-95e2e9182f2b","format_issues":null,"number":3576} |
1.0.0 | problem:theoremdb-p5764 | problem | theoremdb-p5764 | Chromatic number of the circulant graph C(1087; 1, 3, 25) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1087\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm25$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5764",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5764",
"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 P5764 · 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 P5764",
"url": "https://theoremdb.org/statements/P5764",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5764",
"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":"2026-08-16T08:56:07+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5764,"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": "2026-09-08T03:32:51.174Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c54d7dd1-5714-4681-8634-ce01bad9389e","format_issues":null,"number":3577} |
1.0.0 | problem:theoremdb-p5766 | problem | theoremdb-p5766 | Chromatic number of the circulant graph C(1091; 1, 4, 26) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1091\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm26$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5766",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5766",
"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 P5766 · 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 P5766",
"url": "https://theoremdb.org/statements/P5766",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5766",
"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":"2026-08-16T08:56:30+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5766,"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": "2026-09-08T03:32:51.178Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b668ff9f-3bd1-4057-b1d6-47cb3f2dfe49","format_issues":null,"number":3578} |
1.0.0 | problem:theoremdb-p5768 | problem | theoremdb-p5768 | Chromatic number of the circulant graph C(1093; 1, 5, 27) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1093\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm27$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5768",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5768",
"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 P5768 · 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 P5768",
"url": "https://theoremdb.org/statements/P5768",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5768",
"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":"2026-08-16T08:56:57+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5768,"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": "2026-09-08T03:32:51.183Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cb86fbc8-ae05-44cb-ad2b-287127068254","format_issues":null,"number":3579} |
1.0.0 | problem:theoremdb-p5770 | problem | theoremdb-p5770 | Chromatic number of the circulant graph C(1097; 1, 6, 28) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1097\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm28$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5770",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5770",
"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 P5770 · 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 P5770",
"url": "https://theoremdb.org/statements/P5770",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5770",
"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":"2026-08-16T08:57:15+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5770,"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": "2026-09-08T03:32:51.187Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5874f1fb-56cb-4246-bfbc-84ef484f6cf5","format_issues":null,"number":3580} |
1.0.0 | problem:theoremdb-p5772 | problem | theoremdb-p5772 | Chromatic number of the circulant graph C(1103; 1, 7, 29) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1103\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm29$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5772",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5772",
"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 P5772 · 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 P5772",
"url": "https://theoremdb.org/statements/P5772",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5772",
"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":"2026-08-16T08:57:36+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5772,"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": "2026-09-08T03:32:51.191Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2832ac62-02ba-4840-83ae-950871045dcf","format_issues":null,"number":3581} |
1.0.0 | problem:theoremdb-p5774 | problem | theoremdb-p5774 | Chromatic number of the circulant graph C(1109; 1, 8, 30) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1109\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm30$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5774",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5774",
"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 P5774 · 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 P5774",
"url": "https://theoremdb.org/statements/P5774",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5774",
"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":"2026-08-16T08:57:55+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5774,"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": "2026-09-08T03:32:51.195Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9166f92a-1644-4e40-8132-f16fa6cf4804","format_issues":null,"number":3582} |
1.0.0 | problem:theoremdb-p5776 | problem | theoremdb-p5776 | Chromatic number of the circulant graph C(1117; 1, 9, 14) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1117\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm14$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5776",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5776",
"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 P5776 · 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 P5776",
"url": "https://theoremdb.org/statements/P5776",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5776",
"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":"2026-08-16T08:58:11+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5776,"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": "2026-09-08T03:32:51.199Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5cc41f7b-9497-4ac1-9efb-9fe0aba1ff5a","format_issues":null,"number":3583} |
1.0.0 | problem:theoremdb-p5778 | problem | theoremdb-p5778 | Chromatic number of the circulant graph C(1123; 1, 10, 15) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1123\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm15$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5778",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5778",
"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 P5778 · 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 P5778",
"url": "https://theoremdb.org/statements/P5778",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5778",
"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":"2026-08-16T08:58:26+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5778,"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": "2026-09-08T03:32:51.203Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8ec64d2f-c303-44a9-9970-525236b5a64e","format_issues":null,"number":3584} |
1.0.0 | problem:theoremdb-p5780 | problem | theoremdb-p5780 | Chromatic number of the circulant graph C(1129; 1, 11, 16) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1129\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm16$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5780",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5780",
"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 P5780 · 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 P5780",
"url": "https://theoremdb.org/statements/P5780",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5780",
"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":"2026-08-16T08:58:36+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5780,"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": "2026-09-08T03:32:51.208Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"38b49f43-7c48-4bee-8a90-ee6983365324","format_issues":null,"number":3585} |
1.0.0 | problem:theoremdb-p5782 | problem | theoremdb-p5782 | Chromatic number of the circulant graph C(1151; 1, 12, 17) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1151\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm17$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5782",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5782",
"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 P5782 · 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 P5782",
"url": "https://theoremdb.org/statements/P5782",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5782",
"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":"2026-08-16T08:58:54+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5782,"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": "2026-09-08T03:32:51.215Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cdd85f8f-dedf-492a-914d-db5f197da223","format_issues":null,"number":3586} |
1.0.0 | problem:theoremdb-p5784 | problem | theoremdb-p5784 | Chromatic number of the circulant graph C(1153; 1, 2, 18) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1153\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm18$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5784",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5784",
"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 P5784 · 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 P5784",
"url": "https://theoremdb.org/statements/P5784",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5784",
"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":"2026-08-16T08:59:00+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5784,"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": "2026-09-08T03:32:51.219Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ad8ee3a9-499b-4485-9f1d-1944b50a0ec3","format_issues":null,"number":3587} |
1.0.0 | problem:theoremdb-p5786 | problem | theoremdb-p5786 | Chromatic number of the circulant graph C(1163; 1, 3, 19) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1163\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm19$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5786",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5786",
"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 P5786 · 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 P5786",
"url": "https://theoremdb.org/statements/P5786",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5786",
"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":"2026-08-16T08:59:25+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5786,"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": "2026-09-08T03:32:51.224Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"37fc2bef-52e9-4fb7-9359-05a5e9c096ad","format_issues":null,"number":3588} |
1.0.0 | problem:theoremdb-p5788 | problem | theoremdb-p5788 | Chromatic number of the circulant graph C(1171; 1, 4, 20) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1171\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm20$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5788",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5788",
"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 P5788 · 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 P5788",
"url": "https://theoremdb.org/statements/P5788",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5788",
"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":"2026-08-16T08:59:30+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5788,"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": "2026-09-08T03:32:51.228Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"28fd5029-01e8-4d73-a01c-1e7e8d5527a6","format_issues":null,"number":3589} |
1.0.0 | problem:theoremdb-p5790 | problem | theoremdb-p5790 | Chromatic number of the circulant graph C(1181; 1, 5, 21) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1181\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm21$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5790",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5790",
"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 P5790 · 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 P5790",
"url": "https://theoremdb.org/statements/P5790",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5790",
"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":"2026-08-16T08:59:31+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5790,"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": "2026-09-08T03:32:51.232Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6b36073f-d7c8-483e-9572-30dcbc979f45","format_issues":null,"number":3590} |
1.0.0 | problem:theoremdb-p5792 | problem | theoremdb-p5792 | Chromatic number of the circulant graph C(1187; 1, 6, 22) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1187\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm22$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5792",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5792",
"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 P5792 · 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 P5792",
"url": "https://theoremdb.org/statements/P5792",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5792",
"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":"2026-08-16T08:59:44+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5792,"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": "2026-09-08T03:32:51.237Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e7a261f1-1e43-4fe4-9b33-ce4c2d910661","format_issues":null,"number":3591} |
1.0.0 | problem:theoremdb-p5794 | problem | theoremdb-p5794 | Chromatic number of the circulant graph C(1193; 1, 7, 23) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1193\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm23$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5794",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5794",
"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 P5794 · 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 P5794",
"url": "https://theoremdb.org/statements/P5794",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5794",
"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":"2026-08-16T08:59:48+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5794,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.242Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"041e295a-22be-43f5-98a8-e0094f66a295","format_issues":null,"number":3592} |
1.0.0 | problem:theoremdb-p5796 | problem | theoremdb-p5796 | Chromatic number of the circulant graph C(1201; 1, 8, 24) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1201\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm24$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5796",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5796",
"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 P5796 · 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 P5796",
"url": "https://theoremdb.org/statements/P5796",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5796",
"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":"2026-08-16T08:59:58+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5796,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.246Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"17b1bf65-e711-47ba-afd0-9dd1a9d62a0e","format_issues":null,"number":3593} |
1.0.0 | problem:theoremdb-p5798 | problem | theoremdb-p5798 | Chromatic number of the circulant graph C(1213; 1, 9, 25) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1213\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm25$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5798",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5798",
"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 P5798 · 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 P5798",
"url": "https://theoremdb.org/statements/P5798",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5798",
"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":"2026-08-16T09:00:06+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5798,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.250Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ebae9d2a-1271-4fcc-a216-a268c11afea0","format_issues":null,"number":3594} |
1.0.0 | problem:theoremdb-p5800 | problem | theoremdb-p5800 | Chromatic number of the circulant graph C(1217; 1, 10, 26) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1217\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm26$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5800",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5800",
"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 P5800 · 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 P5800",
"url": "https://theoremdb.org/statements/P5800",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5800",
"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":"2026-08-16T09:00:10+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5800,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.254Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4ed89f24-a368-4f7c-b2f6-5d2fdfc56621","format_issues":null,"number":3595} |
1.0.0 | problem:theoremdb-p5802 | problem | theoremdb-p5802 | Chromatic number of the circulant graph C(1223; 1, 11, 27) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1223\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm27$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5802",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5802",
"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 P5802 · 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 P5802",
"url": "https://theoremdb.org/statements/P5802",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5802",
"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":"2026-08-16T09:00:20+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5802,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.259Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"87bdcd71-e8b2-45dd-9b4f-ff94e2d71c16","format_issues":null,"number":3596} |
1.0.0 | problem:theoremdb-p5804 | problem | theoremdb-p5804 | Chromatic number of the circulant graph C(1229; 1, 12, 28) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1229\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm28$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5804",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5804",
"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 P5804 · 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 P5804",
"url": "https://theoremdb.org/statements/P5804",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5804",
"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":"2026-08-16T09:00:22+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5804,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.263Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f7f60906-854f-40e4-8d95-7fcd4876df16","format_issues":null,"number":3597} |
1.0.0 | problem:theoremdb-p5806 | problem | theoremdb-p5806 | Chromatic number of the circulant graph C(1231; 1, 2, 29) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1231\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm29$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5806",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5806",
"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 P5806 · 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 P5806",
"url": "https://theoremdb.org/statements/P5806",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5806",
"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":"2026-08-16T09:00:33+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5806,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.268Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8bff884a-7c1c-40f7-a647-e65978fd49b8","format_issues":null,"number":3598} |
1.0.0 | problem:theoremdb-p5808 | problem | theoremdb-p5808 | Chromatic number of the circulant graph C(1237; 1, 3, 30) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1237\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm30$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5808",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5808",
"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 P5808 · 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 P5808",
"url": "https://theoremdb.org/statements/P5808",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5808",
"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":"2026-08-16T09:00:48+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5808,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.272Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d5c1f92d-68a4-46ae-bcf5-08f0a68f17e0","format_issues":null,"number":3599} |
1.0.0 | problem:theoremdb-p5810 | problem | theoremdb-p5810 | Chromatic number of the circulant graph C(1249; 1, 4, 14) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1249\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm14$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5810",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5810",
"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 P5810 · 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 P5810",
"url": "https://theoremdb.org/statements/P5810",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5810",
"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":"2026-08-16T09:00:54+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5810,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.277Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"95ebf152-034e-4303-a826-d962134a5463","format_issues":null,"number":3600} |
1.0.0 | problem:theoremdb-p5812 | problem | theoremdb-p5812 | Chromatic number of the circulant graph C(1259; 1, 5, 15) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1259\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm15$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5812",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5812",
"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 P5812 · 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 P5812",
"url": "https://theoremdb.org/statements/P5812",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5812",
"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":"2026-08-16T09:01:07+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5812,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.281Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6f17e116-0c1d-41c4-8819-7c0da56cc2a8","format_issues":null,"number":3601} |
1.0.0 | problem:theoremdb-p5814 | problem | theoremdb-p5814 | Chromatic number of the circulant graph C(1277; 1, 6, 16) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1277\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm16$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5814",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5814",
"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 P5814 · 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 P5814",
"url": "https://theoremdb.org/statements/P5814",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5814",
"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":"2026-08-16T09:01:22+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5814,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reas... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.285Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"49f186e6-8407-4c6e-a298-d176a5a8e8cd","format_issues":null,"number":3602} |
1.0.0 | problem:theoremdb-p5816 | problem | theoremdb-p5816 | Chromatic number of the circulant graph C(1279; 1, 7, 17) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1279\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm17$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5816",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5816",
"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 P5816 · 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 P5816",
"url": "https://theoremdb.org/statements/P5816",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5816",
"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":"2026-08-16T09:01:38+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": "2026-09-08T03:32:51.289Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b418dbe6-7c3d-416e-9d21-1187d4dcbd1c","format_issues":null,"number":3603} |
1.0.0 | problem:theoremdb-p5818 | problem | theoremdb-p5818 | Chromatic number of the circulant graph C(1283; 1, 8, 18) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1283\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm18$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5818",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5818",
"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 P5818 · 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 P5818",
"url": "https://theoremdb.org/statements/P5818",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5818",
"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":"2026-08-16T09:01:47+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": "2026-09-08T03:32:51.293Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"62a9c3ff-93b4-4c48-b9dc-a3987b854064","format_issues":null,"number":3604} |
1.0.0 | problem:theoremdb-p5820 | problem | theoremdb-p5820 | Chromatic number of the circulant graph C(1289; 1, 9, 19) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1289\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm19$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5820",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5820",
"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 P5820 · 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 P5820",
"url": "https://theoremdb.org/statements/P5820",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5820",
"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":"2026-08-16T09:01:57+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": "2026-09-08T03:32:51.298Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0258a0f1-7e4b-4cbd-9a43-b256a3078152","format_issues":null,"number":3605} |
1.0.0 | problem:theoremdb-p5822 | problem | theoremdb-p5822 | Chromatic number of the circulant graph C(1291; 1, 10, 20) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1291\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm20$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5822",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5822",
"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 P5822 · 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 P5822",
"url": "https://theoremdb.org/statements/P5822",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5822",
"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":"2026-08-16T09:02:05+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": "2026-09-08T03:32:51.302Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f312e6fa-8d3a-42e9-b4a7-ea944cfa1b1e","format_issues":null,"number":3606} |
1.0.0 | problem:theoremdb-p5824 | problem | theoremdb-p5824 | Chromatic number of the circulant graph C(1297; 1, 11, 21) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1297\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm21$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5824",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5824",
"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 P5824 · 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 P5824",
"url": "https://theoremdb.org/statements/P5824",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5824",
"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":"2026-08-16T09:02:17+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": "2026-09-08T03:32:51.306Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"88d61470-5291-416f-b39b-109e647e3af3","format_issues":null,"number":3607} |
1.0.0 | problem:theoremdb-p5826 | problem | theoremdb-p5826 | Chromatic number of the circulant graph C(1301; 1, 12, 22) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1301\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm22$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5826",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5826",
"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 P5826 · 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 P5826",
"url": "https://theoremdb.org/statements/P5826",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5826",
"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":"2026-08-16T09:02:20+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": "2026-09-08T03:32:51.310Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e0d54e10-2e1f-4149-a95a-4a1fa09ac3b9","format_issues":null,"number":3608} |
1.0.0 | problem:theoremdb-p5828 | problem | theoremdb-p5828 | Chromatic number of the circulant graph C(1303; 1, 2, 23) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1303\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm23$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5828",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5828",
"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 P5828 · 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 P5828",
"url": "https://theoremdb.org/statements/P5828",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5828",
"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":"2026-08-16T09:02:32+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": "2026-09-08T03:32:51.315Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b42493d6-04b1-4fcd-b71c-06bd08f35e88","format_issues":null,"number":3609} |
1.0.0 | problem:theoremdb-p5830 | problem | theoremdb-p5830 | Chromatic number of the circulant graph C(1307; 1, 3, 24) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1307\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm24$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5830",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5830",
"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 P5830 · 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 P5830",
"url": "https://theoremdb.org/statements/P5830",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5830",
"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":"2026-08-16T09:02:38+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": "2026-09-08T03:32:51.319Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b52ed6ba-abd0-49e2-92e2-b92e30dc334d","format_issues":null,"number":3610} |
1.0.0 | problem:theoremdb-p5832 | problem | theoremdb-p5832 | Chromatic number of the circulant graph C(1319; 1, 4, 25) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1319\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm25$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5832",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5832",
"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 P5832 · 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 P5832",
"url": "https://theoremdb.org/statements/P5832",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5832",
"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":"2026-08-16T09:02:42+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": "2026-09-08T03:32:51.323Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fac43ee1-f430-4b0d-a47d-681a80d27409","format_issues":null,"number":3611} |
1.0.0 | problem:theoremdb-p5834 | problem | theoremdb-p5834 | Chromatic number of the circulant graph C(1321; 1, 5, 26) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1321\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm26$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5834",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5834",
"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 P5834 · 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 P5834",
"url": "https://theoremdb.org/statements/P5834",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5834",
"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":"2026-08-16T09:02:46+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": "2026-09-08T03:32:51.327Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f416c27c-22ca-450a-b3e2-f4b628765440","format_issues":null,"number":3612} |
1.0.0 | problem:theoremdb-p5836 | problem | theoremdb-p5836 | Chromatic number of the circulant graph C(1327; 1, 6, 27) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1327\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm27$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5836",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5836",
"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 P5836 · 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 P5836",
"url": "https://theoremdb.org/statements/P5836",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5836",
"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":"2026-08-16T09:02:51+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": "2026-09-08T03:32:51.334Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1db52b03-874b-42a7-9f6a-734118f2a5e8","format_issues":null,"number":3613} |
1.0.0 | problem:theoremdb-p5838 | problem | theoremdb-p5838 | Chromatic number of the circulant graph C(1361; 1, 7, 28) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1361\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm28$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5838",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5838",
"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 P5838 · 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 P5838",
"url": "https://theoremdb.org/statements/P5838",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5838",
"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":"2026-08-16T09:02:58+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.338Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ab801c00-2940-4f4e-9d59-759f351f6edc","format_issues":null,"number":3614} |
1.0.0 | problem:theoremdb-p5840 | problem | theoremdb-p5840 | Chromatic number of the circulant graph C(1367; 1, 8, 29) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1367\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm29$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5840",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5840",
"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 P5840 · 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 P5840",
"url": "https://theoremdb.org/statements/P5840",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5840",
"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":"2026-08-16T09:03:01+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": "2026-09-08T03:32:51.343Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bb420ed5-0d29-40a2-a0fc-41696082ec83","format_issues":null,"number":3615} |
1.0.0 | problem:theoremdb-p5842 | problem | theoremdb-p5842 | Chromatic number of the circulant graph C(1373; 1, 9, 30) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1373\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm30$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5842",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5842",
"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 P5842 · 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 P5842",
"url": "https://theoremdb.org/statements/P5842",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5842",
"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":"2026-08-16T09:03:08+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": "2026-09-08T03:32:51.347Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"326b3551-db24-434a-9801-a14d297baafa","format_issues":null,"number":3616} |
1.0.0 | problem:theoremdb-p5844 | problem | theoremdb-p5844 | Chromatic number of the circulant graph C(1381; 1, 10, 14) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1381\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm14$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5844",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5844",
"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 P5844 · 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 P5844",
"url": "https://theoremdb.org/statements/P5844",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5844",
"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":"2026-08-16T09:03:16+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... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.351Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"253a3611-ea54-4a6a-b94b-0a86322bf491","format_issues":null,"number":3617} |
1.0.0 | problem:theoremdb-p5846 | problem | theoremdb-p5846 | Chromatic number of the circulant graph C(1399; 1, 11, 15) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1399\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm15$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5846",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5846",
"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 P5846 · 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 P5846",
"url": "https://theoremdb.org/statements/P5846",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5846",
"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":"2026-08-16T09:03:22+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": "2026-09-08T03:32:51.356Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"27999cc3-4d1b-4c42-8cd5-3a3de2fa4c29","format_issues":null,"number":3618} |
1.0.0 | problem:theoremdb-p5848 | problem | theoremdb-p5848 | Chromatic number of the circulant graph C(1409; 1, 12, 16) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1409\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm16$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5848",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5848",
"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 P5848 · 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 P5848",
"url": "https://theoremdb.org/statements/P5848",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5848",
"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":"2026-08-16T09:03:33+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": "2026-09-08T03:32:51.360Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"50ab9f67-56ef-4962-b86e-bcb3d32be8de","format_issues":null,"number":3619} |
1.0.0 | problem:theoremdb-p5850 | problem | theoremdb-p5850 | Chromatic number of the circulant graph C(1423; 1, 2, 17) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1423\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm17$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5850",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5850",
"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 P5850 · 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 P5850",
"url": "https://theoremdb.org/statements/P5850",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5850",
"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":"2026-08-16T09:03:40+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": "2026-09-08T03:32:51.364Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4dee4ada-25c2-45d6-bd83-de0d037e94c7","format_issues":null,"number":3620} |
1.0.0 | problem:theoremdb-p5852 | problem | theoremdb-p5852 | Chromatic number of the circulant graph C(1427; 1, 3, 18) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1427\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm18$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5852",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5852",
"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 P5852 · 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 P5852",
"url": "https://theoremdb.org/statements/P5852",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5852",
"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":"2026-08-16T09:03:46+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": "2026-09-08T03:32:51.369Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"946336e1-9566-4dfb-8be2-592821db4682","format_issues":null,"number":3621} |
1.0.0 | problem:theoremdb-p5854 | problem | theoremdb-p5854 | Chromatic number of the circulant graph C(1429; 1, 4, 19) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1429\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm19$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5854",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5854",
"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 P5854 · 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 P5854",
"url": "https://theoremdb.org/statements/P5854",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5854",
"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":"2026-08-16T09:03:51+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": "2026-09-08T03:32:51.373Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"873f74bb-a903-4920-84bc-e9347c08c2db","format_issues":null,"number":3622} |
1.0.0 | problem:theoremdb-p5856 | problem | theoremdb-p5856 | Chromatic number of the circulant graph C(1433; 1, 5, 20) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1433\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm20$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5856",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5856",
"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 P5856 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. Not Lean-verified | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5856",
"url": "https://theoremdb.org/statements/P5856",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5856",
"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":"2026-08-16T09:03:58+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.378Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9c63d73e-c09f-4872-884f-7ad37f95f3f2","format_issues":null,"number":3623} |
1.0.0 | problem:theoremdb-p5858 | problem | theoremdb-p5858 | Chromatic number of the circulant graph C(1439; 1, 6, 21) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1439\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm21$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5858",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5858",
"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 P5858 · 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 P5858",
"url": "https://theoremdb.org/statements/P5858",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5858",
"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":"2026-08-16T09:04:10+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.382Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9f620e5a-ae03-42d6-a2a9-0dc934e88632","format_issues":null,"number":3624} |
1.0.0 | problem:theoremdb-p5860 | problem | theoremdb-p5860 | Chromatic number of the circulant graph C(1447; 1, 7, 22) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1447\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm22$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5860",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5860",
"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 P5860 · 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 P5860",
"url": "https://theoremdb.org/statements/P5860",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5860",
"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":"2026-08-16T09:04:22+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": "2026-09-08T03:32:51.387Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4cf5b84b-a0d5-4d0e-ac3f-91b67b0b9ed7","format_issues":null,"number":3625} |
1.0.0 | problem:theoremdb-p5862 | problem | theoremdb-p5862 | Chromatic number of the circulant graph C(1451; 1, 8, 23) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1451\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm23$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5862",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5862",
"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 P5862 · 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 P5862",
"url": "https://theoremdb.org/statements/P5862",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5862",
"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":"2026-08-16T09:04:39+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": "2026-09-08T03:32:51.391Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"360cf7f9-b388-4b22-8151-063d4feb2b46","format_issues":null,"number":3626} |
1.0.0 | problem:theoremdb-p5864 | problem | theoremdb-p5864 | Chromatic number of the circulant graph C(1453; 1, 9, 24) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1453\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm24$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5864",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5864",
"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 P5864 · 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 P5864",
"url": "https://theoremdb.org/statements/P5864",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5864",
"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":"2026-08-16T09:04:56+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": "2026-09-08T03:32:51.396Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ae8e1a62-6641-4c69-afb5-7a04cbc36c00","format_issues":null,"number":3627} |
1.0.0 | problem:theoremdb-p5866 | problem | theoremdb-p5866 | Chromatic number of the circulant graph C(1459; 1, 10, 25) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1459\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm25$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5866",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5866",
"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 P5866 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. Not Lean-verified | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5866",
"url": "https://theoremdb.org/statements/P5866",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5866",
"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":"2026-08-16T09:05:00+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.400Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"075bcc24-80f7-49ae-a02e-4035422a1489","format_issues":null,"number":3628} |
1.0.0 | problem:theoremdb-p5868 | problem | theoremdb-p5868 | Chromatic number of the circulant graph C(1471; 1, 11, 26) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1471\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm26$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5868",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5868",
"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 P5868 · 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 P5868",
"url": "https://theoremdb.org/statements/P5868",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5868",
"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":"2026-08-16T09:05:05+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": "2026-09-08T03:32:51.404Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"63bbe3e5-00cd-4785-a14b-5ca448c5416b","format_issues":null,"number":3629} |
1.0.0 | problem:theoremdb-p5870 | problem | theoremdb-p5870 | Chromatic number of the circulant graph C(1481; 1, 12, 27) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1481\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm27$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5870",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5870",
"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 P5870 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. Not Lean-verified | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5870",
"url": "https://theoremdb.org/statements/P5870",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5870",
"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":"2026-08-16T09:05:27+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": "2026-09-08T03:32:51.408Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"88057049-9d0a-4530-98a5-b97bbefcbbd3","format_issues":null,"number":3630} |
1.0.0 | problem:theoremdb-p5872 | problem | theoremdb-p5872 | Chromatic number of the circulant graph C(1483; 1, 2, 28) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/1483\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm28$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5872",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5872",
"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 P5872 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. Not Lean-verified | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5872",
"url": "https://theoremdb.org/statements/P5872",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5872",
"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":"2026-08-16T09:05:35+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": "2026-09-08T03:32:51.412Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"acfe5668-1b2d-450e-948c-8fd94b9dabe1","format_issues":null,"number":3631} |
1.0.0 | problem:theoremdb-p6 | problem | theoremdb-p6 | Erdős-Moser conjecture | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | The equation $1^k+2^k+\cdots+(m-1)^k=m^k$ has no solution in integers $k>1$ and $m>1$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P6",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem packe... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P6 · number theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P6",
"url": "https://theoremdb.org/statements/P6",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "Guillaume Lambard, arXiv:2411.13146, abstract and introduction",
"url": "https://arxiv.org/abs/2411.13146",
"note"... | {
"source_record": "P6",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been perf... | {"created_at":"2026-07-22T21:49:47+00:00","display_standard":{"editorial_review":"source_backed","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":6,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernel... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:56.646Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"df190cf8-0bff-4af1-aaf7-4bd1da03e367","format_issues":null,"number":4785} |
1.0.0 | problem:theoremdb-p7 | problem | theoremdb-p7 | Hodge conjecture | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Let $X$ be a smooth projective complex variety and let $p\ge 0$. Every class in $H^{2p}(X,\mathbb{Q})\cap H^{p,p}(X)$ is a rational linear combination of cohomology classes of algebraic cycles of codimension $p$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P7",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem packe... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P7 · algebraic 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 P7",
"url": "https://theoremdb.org/statements/P7",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "Official Problem Description by Pierre Deligne; listed under Unsolved Millennium Prize Problems",
"url": "https://www.... | {
"source_record": "P7",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been perf... | {"created_at":"2026-07-22T21:49:47+00:00","display_standard":{"editorial_review":"source_backed","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":7,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernel... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.622Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6dc17592-38db-47fd-b0d5-48b9591c35d9","format_issues":null,"number":5435} |
1.0.0 | problem:theoremdb-p8 | problem | theoremdb-p8 | Fermat-Catalan conjecture | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | There are only finitely many primitive solutions $(a,b,c,m,n,k)\in\mathbb{Z}_{>0}^6$ to $a^m+b^n=c^k$ with $m,n,k\ge2$ and $1/m+1/n+1/k<1$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P8",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem packe... | /-
Copyright 2025 The Formal Conjectures Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
https://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in ... | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "/-\nCopyright 2025 The Formal Conjectures Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n https://www.apache.org/licenses/LICENSE-2... | [] | TheoremDB P8 · number theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. Not Lean-verified | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8",
"url": "https://theoremdb.org/statements/P8",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "Adam S. Sikora, arXiv:2410.21552, introduction and motivating conjectures",
"url": "https://arxiv.org/abs/2410.21552",... | {
"source_record": "P8",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been perf... | {"created_at":"2026-07-22T21:49:47+00:00","display_standard":{"editorial_review":"source_backed","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":8,"public_status":{"evidence":{"hasFormalization":true,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kernelA... | [
"lean-statement-from-linked-source-file",
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:58.957Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ac07f56e-8e18-4d18-bbe4-65bb98359ba7","format_issues":null,"number":5291} |
1.0.0 | problem:theoremdb-p8078 | problem | theoremdb-p8078 | Representation of perfect squares as ratios of consecutive integer products | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | For integers $N \geq 2$, let $N$ be called a represented square if $N$ is a perfect square and there exist integers $k \geq 2$, $n \geq 0$, and $m \geq n + k$ such that
$$
N = \frac{\prod_{i=1}^{k} (m+i)}{\prod_{i=1}^{k} (n+i)}.
$$
Is every perfect square $N \geq 2$ a represented square? | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8078",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8078",
"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... | theorem erdos_686.variants.square :
answer(sorry) ↔ ∀ N ≥ (2 : ℕ), (IsSquare N) → ∃ᵉ (k ≥ 2) (n : ℕ) (m ≥ n + k),
(N : ℚ) = (∏ i ∈ Finset.Icc 1 k, (m + i)) / (∏ i ∈ Finset.Icc 1 k, (n + i)) | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_686.variants.square :\n answer(sorry) ↔ ∀ N ≥ (2 : ℕ), (IsSquare N) → ∃ᵉ (k ≥ 2) (n : ℕ) (m ≥ n + k),\n (N : ℚ) = (∏ i ∈ Finset.Icc 1 k, (m + i)) / (∏ i ∈ Finset.Icc 1 k, (n + i))",
"target": null,
"source_url": "https://theoremdb.org/statement... | [] | TheoremDB P8078 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8078",
"url": "https://theoremdb.org/statements/P8078",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8078",
"not... | {
"source_record": "P8078",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:33+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8078,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:05.632Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"acf97f61-0b48-484a-8680-102a3a694e77","format_issues":null,"number":6569} |
1.0.0 | problem:theoremdb-p8080 | problem | theoremdb-p8080 | Erdős's Problem on Affine Copies of Infinite Sets in Sets of Positive Measure | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "community-map",
"evidence": "Inferred from community field: combinatorics"
}
] | For a set $A \subseteq \mathbb{R}$, say that a set $E \subseteq \mathbb{R}$ avoids affine copies of $A$ if there do not exist $a, b \in \mathbb{R}$ with $a \neq 0$ such that $\{a \cdot x + b : x \in A\} \subseteq E$. Let $A \subseteq \mathbb{R}$ be an infinite set. Must there exist a measurable set $E \subseteq \mathbb... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8080",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8080",
"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... | theorem erdos_120 : answer(sorry) ↔ ∀ A : Set ℝ, A.Infinite → Erdos120For A | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_120 : answer(sorry) ↔ ∀ A : Set ℝ, A.Infinite → Erdos120For A",
"target": null,
"source_url": "https://theoremdb.org/statements/P8080",
"format": "declaration-or-fragment",
"sha256": "26348af1f18a809d6278df7ee50e1254a3249bcfd45d4bb0cd58042df22e0... | [] | TheoremDB P8080 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8080",
"url": "https://theoremdb.org/statements/P8080",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8080",
"not... | {
"source_record": "P8080",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:35+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8080,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:56.437Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"edc2d36a-4c89-424a-8efd-95598ac48145","format_issues":null,"number":4740} |
1.0.0 | problem:theoremdb-p8082 | problem | theoremdb-p8082 | Semi-Magic Square of Cubes | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "community-map",
"evidence": "Inferred from community field: combinatorics"
}
] | A $3 \times 3$ matrix $M = (a_{ij})$ with entries in $\mathbb{N}$ is called a semi-magic square with magic constant $t$ if all row sums and all column sums equal $t$, that is, $\sum_{j=1}^{3} a_{ij} = t$ for each row $i$ and $\sum_{i=1}^{3} a_{ij} = t$ for each column $j$. Does there exist a $3 \times 3$ semi-magic squ... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8082",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8082",
"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... | theorem exists_semi_magic_square_cubes :
answer(sorry) ↔ ∃ m : Fin 3 → Fin 3 → ℕ, ∃ t : ℕ,
m.Injective2 ∧
(∀ i j, ∃ n : ℕ, 0 < n ∧ m i j = n ^ 3) ∧
(∀ i, ∑ j, m i j = t) ∧
(∀ j, ∑ i, m i j = t) | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem exists_semi_magic_square_cubes :\n answer(sorry) ↔ ∃ m : Fin 3 → Fin 3 → ℕ, ∃ t : ℕ,\n m.Injective2 ∧\n (∀ i j, ∃ n : ℕ, 0 < n ∧ m i j = n ^ 3) ∧\n (∀ i, ∑ j, m i j = t) ∧\n (∀ j, ∑ i, m i j = t)",
"target": null,
"source_url": "htt... | [] | TheoremDB P8082 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8082",
"url": "https://theoremdb.org/statements/P8082",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8082",
"not... | {
"source_record": "P8082",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:35+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8082,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:05.774Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8cc39a64-d1c6-4ce5-a2d0-b704ff316051","format_issues":null,"number":6600} |
1.0.0 | problem:theoremdb-p8084 | problem | theoremdb-p8084 | Transcendence of $\pi^\pi$ | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | Let $\pi$ denote the ratio of the circumference of a circle to its diameter. A real number $\alpha$ is said to be transcendental over the rational numbers $\mathbb{Q}$ if there does not exist a nonzero polynomial $P$ with coefficients in $\mathbb{Q}$ such that $P(\alpha) = 0$. Prove that $\pi^\pi$ is transcendental ove... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8084",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8084",
"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... | theorem pi_pow_pi_transcendental : Transcendental ℚ (π ^ π) | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem pi_pow_pi_transcendental : Transcendental ℚ (π ^ π)",
"target": null,
"source_url": "https://theoremdb.org/statements/P8084",
"format": "declaration-or-fragment",
"sha256": "1ca5d82eeff3fd1eac5665d7f48f1d11fe56ba966e64b16e71a44d107571e2d5",
"licen... | [] | TheoremDB P8084 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8084",
"url": "https://theoremdb.org/statements/P8084",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8084",
"not... | {
"source_record": "P8084",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:36+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8084,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:06.954Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"02f4cbc3-b18b-4979-8c0c-3a85cd8bf9f2","format_issues":null,"number":6854} |
1.0.0 | problem:theoremdb-p8086 | problem | theoremdb-p8086 | Magic Square of Squares | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | A $3 \times 3$ magic square is a matrix whose entries are arranged so that the sums of the numbers in each row, each column, and both main diagonals are all equal to the same value, called the magic constant. A magic square of squares is a magic square in which every entry is a perfect square. Does there exist a $3 \ti... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8086",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8086",
"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... | theorem exists_magic_square_squares :
answer(sorry) ↔ ∃ m : Fin 3 → Fin 3 → ℕ, ∃ t : ℕ,
m.Injective2 ∧
(∀ i j, 0 < (m i j) ∧ IsSquare (m i j)) ∧
(∀ i, ∑ j, m i j = t) ∧
(∀ j, ∑ i, m i j = t) ∧
m 0 0 + m 1 1 + m 2 2 = t ∧
m 0 2 + m 1 1 + m 2 0 = t | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem exists_magic_square_squares :\n answer(sorry) ↔ ∃ m : Fin 3 → Fin 3 → ℕ, ∃ t : ℕ,\n m.Injective2 ∧\n (∀ i j, 0 < (m i j) ∧ IsSquare (m i j)) ∧\n (∀ i, ∑ j, m i j = t) ∧\n (∀ j, ∑ i, m i j = t) ∧\n m 0 0 + m 1 1 + m 2 2 = t ∧\n m... | [] | TheoremDB P8086 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8086",
"url": "https://theoremdb.org/statements/P8086",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8086",
"not... | {
"source_record": "P8086",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:36+00:00","display_standard":{"formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8086,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reaso... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:03.595Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f4a32626-7e27-4629-84ab-b1fd9aafb184","format_issues":null,"number":6128} |
1.0.0 | problem:theoremdb-p8088 | problem | theoremdb-p8088 | Infinitely Many Solutions to the Egyptian Fraction Equation with Distinct Prime Denominators | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | Let a pair $(m, P)$ be called a solution if $m$ is an integer with $m \geq 2$, and $P$ is a nonempty finite set of distinct prime numbers, such that
$$
\sum_{p \in P} \frac{1}{p} = 1 - \frac{1}{m}.
$$
Does there exist infinitely many such solutions $(m, P)$? | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8088",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8088",
"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... | theorem erdos_313 : answer(sorry) ↔ erdos313Solutions.Infinite | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_313 : answer(sorry) ↔ erdos313Solutions.Infinite",
"target": null,
"source_url": "https://theoremdb.org/statements/P8088",
"format": "declaration-or-fragment",
"sha256": "54fa7ed4562bd3dd75e7ee3d25c2af7d1582271a16ecf791315fbee81836d4ac",
"li... | [] | TheoremDB P8088 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8088",
"url": "https://theoremdb.org/statements/P8088",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8088",
"not... | {
"source_record": "P8088",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:37+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8088,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:01.054Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cd352988-f2cd-4457-b9bc-672f89f63881","format_issues":null,"number":5647} |
1.0.0 | problem:theoremdb-p8090 | problem | theoremdb-p8090 | Erdős's Additive Representation Density Problem | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | Let $\mathbb{N}$ denote the set of positive integers. For a subset $A \subseteq \mathbb{N}$ and a positive integer $n$, define the additive representation function $r_A(n)$ to be the number of ordered pairs $(a, b) \in A \times A$ such that $a + b = n$. Does there exist a subset $A \subseteq \mathbb{N}$ and a nonzero r... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8090",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8090",
"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... | theorem erdos_66 : answer(sorry) ↔ ∃ (A : Set ℕ) (c : ℝ), c ≠ 0 ∧
Tendsto (fun n ↦ (sumRep A n : ℝ) / Real.log n) atTop (𝓝 c) | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_66 : answer(sorry) ↔ ∃ (A : Set ℕ) (c : ℝ), c ≠ 0 ∧\n Tendsto (fun n ↦ (sumRep A n : ℝ) / Real.log n) atTop (𝓝 c)",
"target": null,
"source_url": "https://theoremdb.org/statements/P8090",
"format": "declaration-or-fragment",
"sha256": "17c06... | [] | TheoremDB P8090 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8090",
"url": "https://theoremdb.org/statements/P8090",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8090",
"not... | {
"source_record": "P8090",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:38+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8090,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:56.306Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1a0aac13-b577-41a8-9de5-7a18097ec542","format_issues":null,"number":4712} |
1.0.0 | problem:theoremdb-p8092 | problem | theoremdb-p8092 | Asymptotic Lower Bound on Distinct Distances from Points in the Plane | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "community-map",
"evidence": "Inferred from community field: combinatorics"
}
] | Let $n$ be a positive integer and let $x_1, \ldots, x_n$ be $n$ distinct points in $\mathbb{R}^2$. For each point $x_i$, let $R(x_i)$ denote the number of distinct distances from $x_i$ to the other points, that is, $R(x_i) = \#\{|x_j - x_i| : j \neq i\}$. Order the points so that $R(x_1) \leq R(x_2) \leq \cdots \leq R(... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8092",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8092",
"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... | theorem erdos_653 : answer(sorry) ↔ ∃ o : ℕ → ℝ, o =o[atTop] (1 : ℕ → ℝ) ∧
∀ᶠ n in atTop, (1 - o n) * n ≤ maximalDistinctDistancesFrom n | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_653 : answer(sorry) ↔ ∃ o : ℕ → ℝ, o =o[atTop] (1 : ℕ → ℝ) ∧\n ∀ᶠ n in atTop, (1 - o n) * n ≤ maximalDistinctDistancesFrom n",
"target": null,
"source_url": "https://theoremdb.org/statements/P8092",
"format": "declaration-or-fragment",
"sha25... | [] | TheoremDB P8092 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8092",
"url": "https://theoremdb.org/statements/P8092",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8092",
"not... | {
"source_record": "P8092",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:39+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8092,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:50.345Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5234b782-6a3f-4bcd-886b-5f2cf34bcb25","format_issues":null,"number":3400} |
1.0.0 | problem:theoremdb-p8094 | problem | theoremdb-p8094 | Perfect Powers from Products of Disjoint Long Interval Products | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | For a positive integer $r$, let $I_1, I_2, \ldots, I_r$ be intervals of consecutive positive integers, where each $I_i = [I_{1,i}, I_{2,i}]$ for natural numbers $I_{1,i}$ and $I_{2,i}$ with $0 < I_{1,i}$. The intervals are disjoint and ordered, meaning $I_{2,i} < I_{1,j}$ whenever $i < j$. A natural number $n$ is calle... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8094",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8094",
"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... | theorem erdos_930 :
answer(sorry) ↔ ∀ r > 0, ∃ k, ∀ I₁ I₂ : Fin r → ℕ,
(∀ i : Fin r, 0 < I₁ i ∧ I₁ i + k ≤ I₂ i + 1) →
(∀ i j : Fin r, i < j → I₂ i < I₁ j) →
¬ IsPower (∏ i : Fin r, ∏ m ∈ Icc (I₁ i) (I₂ i), m) | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_930 :\n answer(sorry) ↔ ∀ r > 0, ∃ k, ∀ I₁ I₂ : Fin r → ℕ,\n (∀ i : Fin r, 0 < I₁ i ∧ I₁ i + k ≤ I₂ i + 1) →\n (∀ i j : Fin r, i < j → I₂ i < I₁ j) →\n ¬ IsPower (∏ i : Fin r, ∏ m ∈ Icc (I₁ i) (I₂ i), m)",
"target": null,
"source... | [] | TheoremDB P8094 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8094",
"url": "https://theoremdb.org/statements/P8094",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8094",
"not... | {
"source_record": "P8094",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:39+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8094,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
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"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:04.796Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"637dccd5-a182-4757-aacc-59951e8bc06b","format_issues":null,"number":6388} |
1.0.0 | problem:theoremdb-p8096 | problem | theoremdb-p8096 | Non-existence of a ternary-integer monochromatic quantum graph for six vertices and three colours | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "community-map",
"evidence": "Inferred from community field: combinatorics"
}
] | Let $N$ be a positive even integer and let $D$ be a positive integer. A quantum graph with $N$ vertices and $D$ colours is encoded by a weight function $W$ that assigns to each unordered pair of distinct vertices $\{i,j\}$ with $1 \leq i < j \leq N$ and each colour $c \in \{1,\dots,D\}$ a value $W(\{i,j\}, c)$ in a coe... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8096",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8096",
"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... | theorem eqSystem6_no_solution_d3_trinary_int :
answer(sorry) ↔
¬ ∃ W : WeightsN 6 3 ℤ,
(∀ e, W e = (-1 : ℤ) ∨ W e = 0 ∨ W e = 1) ∧
EqSystemN 6 3 W | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem eqSystem6_no_solution_d3_trinary_int :\n answer(sorry) ↔\n ¬ ∃ W : WeightsN 6 3 ℤ,\n (∀ e, W e = (-1 : ℤ) ∨ W e = 0 ∨ W e = 1) ∧\n EqSystemN 6 3 W",
"target": null,
"source_url": "https://theoremdb.org/statements/P8096",
"forma... | [] | TheoremDB P8096 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8096",
"url": "https://theoremdb.org/statements/P8096",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8096",
"not... | {
"source_record": "P8096",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:40+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8096,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:04.270Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a86b2956-9071-4e6f-a97f-2f85a67191fa","format_issues":null,"number":6276} |
1.0.0 | problem:theoremdb-p8098 | problem | theoremdb-p8098 | The Base-10 Lychrel Conjecture | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | For a positive integer $n$, let $\operatorname{rev}_{10}(n)$ denote the integer obtained by writing $n$ in base $10$ and reversing the order of its digits. Define the Lychrel iteration by $a_0 = n$ and $a_{k+1} = a_k + \operatorname{rev}_{10}(a_k)$ for $k \geq 0$. A positive integer $n$ is called a base-$10$ Lychrel nu... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8098",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8098",
"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... | theorem no_lychrel_numbers_base10 :
answer(sorry) ↔ ∀ n : ℕ, 0 < n → ¬ IsLychrel10 n | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem no_lychrel_numbers_base10 :\n answer(sorry) ↔ ∀ n : ℕ, 0 < n → ¬ IsLychrel10 n",
"target": null,
"source_url": "https://theoremdb.org/statements/P8098",
"format": "declaration-or-fragment",
"sha256": "19ac8124fc4eff52786da3058e053e5cadd365589084457... | [] | TheoremDB P8098 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8098",
"url": "https://theoremdb.org/statements/P8098",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8098",
"not... | {
"source_record": "P8098",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:40+00:00","display_standard":{"formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8098,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reaso... | [
"formalization-contains-placeholder",
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"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:06.375Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"42eade55-36a3-4e24-82d4-9790146a6d3c","format_issues":null,"number":6729} |
1.0.0 | problem:theoremdb-p8100 | problem | theoremdb-p8100 | A density question for infinite B₂[2] sets | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "community-map",
"evidence": "Inferred from community field: combinatorics"
}
] | A set $A \subseteq \mathbb{N}$ is called a $B_2[g]$ set if for every natural number $n$, the equation $a + a' = n$ with $a \leq a'$ and $a, a' \in A$ has at most $g$ solutions. Let $A$ be an infinite $B_2[2]$ set. Must $\liminf_{N \to \infty} |A \cap \{0, 1, \ldots, N-1\}| \cdot N^{-1/2} = 0$? | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8100",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8100",
"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... | theorem erdos_158 : answer(sorry) ↔ ∀ A : Set ℕ, A.Infinite → B2 2 A →
liminf (fun N : ℕ => (A ∩ .Iio N).ncard * (N : ℝ) ^ (- 1 / 2 : ℝ)) atTop = 0 | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_158 : answer(sorry) ↔ ∀ A : Set ℕ, A.Infinite → B2 2 A →\n liminf (fun N : ℕ => (A ∩ .Iio N).ncard * (N : ℝ) ^ (- 1 / 2 : ℝ)) atTop = 0",
"target": null,
"source_url": "https://theoremdb.org/statements/P8100",
"format": "declaration-or-fragment",... | [] | TheoremDB P8100 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8100",
"url": "https://theoremdb.org/statements/P8100",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8100",
"not... | {
"source_record": "P8100",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:41+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8100,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:49.078Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3a6e6698-0a1c-4fc9-badb-bb68221d5864","format_issues":null,"number":3127} |
1.0.0 | problem:theoremdb-p8102 | problem | theoremdb-p8102 | Packing of Reciprocal-Sized Rectangles into the Unit Square | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For each natural number $n$, let $R_n$ denote a rectangle with side lengths $\frac{1}{n+1}$ and $\frac{1}{n+2}$. A placement of $R_n$ in the plane is specified by a choice of starting point $(a_n, b_n) \in \mathbb{R}^2$ and a rotation angle $\theta_n$; the placed rectangle consists of all points obtained from the stand... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8102",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8102",
"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... | theorem rectangles_pack_unit_square :
answer(sorry) ↔ ∃ c : Configuration, (∀ n, (c.rect n).toSet ⊆ unitSquare) ∧ c.IsPacking | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem rectangles_pack_unit_square :\n answer(sorry) ↔ ∃ c : Configuration, (∀ n, (c.rect n).toSet ⊆ unitSquare) ∧ c.IsPacking",
"target": null,
"source_url": "https://theoremdb.org/statements/P8102",
"format": "declaration-or-fragment",
"sha256": "ab51dc... | [] | TheoremDB P8102 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8102",
"url": "https://theoremdb.org/statements/P8102",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8102",
"not... | {
"source_record": "P8102",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:41+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8102,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:04.733Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3e06e87c-adc0-4451-ab68-7b1d9d64d4b1","format_issues":null,"number":6374} |
1.0.0 | problem:theoremdb-p8104 | problem | theoremdb-p8104 | Existence of a Transversal in Every Order-11 Latin Square | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "community-map",
"evidence": "Inferred from community field: combinatorics"
}
] | A Latin square of order $n$ is an $n \times n$ array filled with $n$ different symbols, each occurring exactly once in each row and exactly once in each column. A transversal of a Latin square is a set of $n$ cells, one in each row, one in each column, and containing each symbol exactly once. Does every Latin square of... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8104",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8104",
"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... | theorem latinSquareOrder11Transversal : answer(sorry) ↔
∀ (L : LatinSquare 11), ∃ σ, IsTransversal L σ | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem latinSquareOrder11Transversal : answer(sorry) ↔\n ∀ (L : LatinSquare 11), ∃ σ, IsTransversal L σ",
"target": null,
"source_url": "https://theoremdb.org/statements/P8104",
"format": "declaration-or-fragment",
"sha256": "3f62c175c6d18fa50c6f892e9927e... | [] | TheoremDB P8104 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8104",
"url": "https://theoremdb.org/statements/P8104",
"note": null,
"sort_order": 0
},
{
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"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8104",
"not... | {
"source_record": "P8104",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:42+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8104,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:58.555Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b95f1de6-bac5-4077-86cb-5de1a20d1f6b","format_issues":null,"number":5207} |
1.0.0 | problem:theoremdb-p8106 | problem | theoremdb-p8106 | Asymptotic equivalence of the subset sum threshold to the cube-root linearithmic bound | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "community-map",
"evidence": "Inferred from community field: combinatorics"
}
] | For each positive integer $n$, define the subset sum threshold $h(n)$ to be the largest integer $m$ such that for every set $A$ of $n$ integers, there exists a subset $B \subseteq A$ with $|B| \geq m$ having the following property: if two nonempty subsets of $B$ have equal sums, then they have equal cardinalities. Is i... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8106",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8106",
"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... | theorem erdos_789.variants.cube_root_linearithmic :
(fun n ↦ (subsetSumThreshold n : ℝ)) =Θ[atTop]
fun n ↦ (n * Real.log n) ^ ((1 : ℝ) / 3) | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_789.variants.cube_root_linearithmic :\n (fun n ↦ (subsetSumThreshold n : ℝ)) =Θ[atTop]\n fun n ↦ (n * Real.log n) ^ ((1 : ℝ) / 3)",
"target": null,
"source_url": "https://theoremdb.org/statements/P8106",
"format": "declaration-or-fragment",
... | [] | TheoremDB P8106 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8106",
"url": "https://theoremdb.org/statements/P8106",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8106",
"not... | {
"source_record": "P8106",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:42+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8106,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:50.025Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"08d22844-ee45-437f-8ee2-7bbfbec8925c","format_issues":null,"number":3335} |
1.0.0 | problem:theoremdb-p8108 | problem | theoremdb-p8108 | Unbounded rank conjecture for elliptic curves over the rationals | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | An elliptic curve over $\mathbb{Q}$ is, up to isomorphism, a smooth projective curve given by a Weierstrass equation $y^2 = x^3 + Ax + B$ with $A, B \in \mathbb{Z}$, where the discriminant $4A^3 + 27B^2 \neq 0$ and the pair $(A,B)$ is reduced in the sense that for every prime $p$, it is not the case that both $p^4 \mid... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8108",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8108",
"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... | theorem unbounded_rank_conjecture (n : ℕ) : ∃ E : RatEllipticCurve, n ≤ E.rank | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem unbounded_rank_conjecture (n : ℕ) : ∃ E : RatEllipticCurve, n ≤ E.rank",
"target": null,
"source_url": "https://theoremdb.org/statements/P8108",
"format": "declaration-or-fragment",
"sha256": "4162e80bde07377c97b22c686be7d627c940018d305b56a1057064c7a4... | [] | TheoremDB P8108 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8108",
"url": "https://theoremdb.org/statements/P8108",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8108",
"not... | {
"source_record": "P8108",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:43+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8108,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:07.140Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ee5069d1-aca5-42f8-9638-d3db1aaab81e","format_issues":null,"number":6895} |
1.0.0 | problem:theoremdb-p8110 | problem | theoremdb-p8110 | Asymptotic behavior of the minimum triangle area function for point sets in the unit disk | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For each positive integer $n$, let $\alpha(n)$ denote the supremum, over all sets $S$ of $n$ points in the closed unit disk in $\mathbb{R}^2$ that are not collinear, of the minimum area of a triangle determined by three distinct points of $S$. Determine a function $f: \mathbb{N} \to \mathbb{R}$ such that $\alpha(n)$ is... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8110",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8110",
"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... | theorem erdos_507.equivalent:
α ~[atTop] (answer(sorry) : ℕ → ℝ) | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_507.equivalent:\n α ~[atTop] (answer(sorry) : ℕ → ℝ)",
"target": null,
"source_url": "https://theoremdb.org/statements/P8110",
"format": "declaration-or-fragment",
"sha256": "85f9fbc5b6c2fcea10953443c46bf767dee7413c9c32b110c54906fd1d2dedc9",
... | [] | TheoremDB P8110 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8110",
"url": "https://theoremdb.org/statements/P8110",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8110",
"not... | {
"source_record": "P8110",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:44+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8110,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:49.916Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0cfe7ea1-e81a-452d-854a-ef911587749a","format_issues":null,"number":3313} |
1.0.0 | problem:theoremdb-p8112 | problem | theoremdb-p8112 | Representability of binomial coefficients by exactly $t$ pairs | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | For a positive integer $a$, let $S(a)$ denote the set of natural numbers $n$ for which there exists an integer $k$ with $1 \leq k \leq \frac{n}{2}$ such that $\binom{n}{k} = a$. Is it true that for every integer $t \geq 1$, there exists a positive integer $a$ such that the cardinality of $S(a)$ equals exactly $t$? | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8112",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8112",
"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... | theorem erdos_849 : answer(sorry) ↔
∀ t ≥ 1, ∃ a : ℕ,
{n : ℕ | ∃ k ≥ 1, 2 * k ≤ n ∧ choose n k = a}.ncard = t | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_849 : answer(sorry) ↔\n ∀ t ≥ 1, ∃ a : ℕ,\n {n : ℕ | ∃ k ≥ 1, 2 * k ≤ n ∧ choose n k = a}.ncard = t",
"target": null,
"source_url": "https://theoremdb.org/statements/P8112",
"format": "declaration-or-fragment",
"sha256": "a611fd535e8d737... | [] | TheoremDB P8112 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8112",
"url": "https://theoremdb.org/statements/P8112",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8112",
"not... | {
"source_record": "P8112",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:44+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8112,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:05.627Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d7597f14-9c63-4681-9406-b3e535b7c31e","format_issues":null,"number":6568} |
1.0.0 | problem:theoremdb-p8114 | problem | theoremdb-p8114 | Minimal asymptotic additive bases and their complements of higher order | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "community-map",
"evidence": "Inferred from community field: combinatorics"
}
] | Let $k$ be a positive integer. A set $A \subseteq \mathbb{N}$ is called an *asymptotic additive basis of order $k$* if every sufficiently large natural number can be written as the sum of $k$ elements of $A$ (not necessarily distinct). A set $A \subseteq \mathbb{N}$ is called a *minimal asymptotic additive basis of ord... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8114",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8114",
"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... | theorem erdos_881 :
answer(sorry) ↔ ∀ (k : ℕ) (A : Set ℕ),
IsMinimalAsymptoticAddBasisOfOrder k A →
∃ (B : Set ℕ), B ⊆ A ∧ B.Infinite ∧
(A \ B).IsAsymptoticAddBasisOfOrder (k + 1) | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_881 :\n answer(sorry) ↔ ∀ (k : ℕ) (A : Set ℕ),\n IsMinimalAsymptoticAddBasisOfOrder k A →\n ∃ (B : Set ℕ), B ⊆ A ∧ B.Infinite ∧\n (A \\ B).IsAsymptoticAddBasisOfOrder (k + 1)",
"target": null,
"source_url": "https://theoremdb.org... | [] | TheoremDB P8114 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8114",
"url": "https://theoremdb.org/statements/P8114",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8114",
"not... | {
"source_record": "P8114",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:44+00:00","display_standard":{"formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8114,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reaso... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:03.886Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"617e7e61-0871-43ff-8a22-a5dc2e85d883","format_issues":null,"number":6192} |
1.0.0 | problem:theoremdb-p8116 | problem | theoremdb-p8116 | Asymptotic lower bound for the monotone distinct-sums function | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | For each positive integer $n$, let $h(n)$ denote the largest integer $k$ for which there exist integers $1 \le a_1 \le a_2 \le \dots \le a_k \le n$ such that all sums of the form $\sum_{i=u}^{v} a_i$ with $1 \le u \le v \le k$ are distinct. Determine whether there exists an explicit function $g : \mathbb{N} \to \mathbb... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8116",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8116",
"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... | theorem erdos_357.variants.monotone.parts.ii.littleO_version :
(answer(sorry) : ℕ → ℝ) =o[atTop] (fun n ↦ (h n : ℝ)) | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_357.variants.monotone.parts.ii.littleO_version :\n (answer(sorry) : ℕ → ℝ) =o[atTop] (fun n ↦ (h n : ℝ))",
"target": null,
"source_url": "https://theoremdb.org/statements/P8116",
"format": "declaration-or-fragment",
"sha256": "0e659d97554b8b7... | [] | TheoremDB P8116 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8116",
"url": "https://theoremdb.org/statements/P8116",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8116",
"not... | {
"source_record": "P8116",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:45+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8116,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:50.332Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"86eb78d8-2d82-4c48-97d5-5c08c9c7d64b","format_issues":null,"number":3398} |
1.0.0 | problem:theoremdb-p8118 | problem | theoremdb-p8118 | Non-existence of monochromatic quantum graphs with twelve vertices and three colours over the complex numbers | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "community-map",
"evidence": "Inferred from community field: combinatorics"
}
] | Let $N = 12$ and $D = 3$. A weight function on the complete graph $K_N$ with $D$ colours and coefficients in a ring $\alpha$ assigns to every unordered pair of distinct vertices $\{i, j\}$ with $i, j \in \{0, 1, \dots, N-1\}$ and $i < j$ a $D$-tuple of weights in $\alpha$, one for each colour. For a given assignment of... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8118",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8118",
"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... | theorem eqSystem12_no_solution_d3 :
answer(sorry) ↔
¬ ∃ W : WeightsN 12 3 ℂ, EqSystemN 12 3 W | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem eqSystem12_no_solution_d3 :\n answer(sorry) ↔\n ¬ ∃ W : WeightsN 12 3 ℂ, EqSystemN 12 3 W",
"target": null,
"source_url": "https://theoremdb.org/statements/P8118",
"format": "declaration-or-fragment",
"sha256": "ffb8a3a469efccf944f99d262522a9c... | [] | TheoremDB P8118 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
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"citation": "TheoremDB P8118",
"url": "https://theoremdb.org/statements/P8118",
"note": null,
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},
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"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8118",
"not... | {
"source_record": "P8118",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:46+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8118,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:04.396Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d07367bd-bc86-45c4-894b-eb841cc79ec5","format_issues":null,"number":6301} |
1.0.0 | problem:theoremdb-p8120 | problem | theoremdb-p8120 | Infinitude of primes with exactly three set bits in binary | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | For a natural number $p$, say that $p$ has exactly three set bits in its binary representation if the binary expansion of $p$ contains precisely three digits equal to $1$. Let $A$ denote the set of prime numbers that have exactly three set bits in their binary representation. Is $A$ infinite? Equivalently, are there in... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8120",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8120",
"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... | theorem conjectureA81091 :
answer(sorry) ↔ Set.Infinite {p : ℕ | A p} | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem conjectureA81091 :\n answer(sorry) ↔ Set.Infinite {p : ℕ | A p}",
"target": null,
"source_url": "https://theoremdb.org/statements/P8120",
"format": "declaration-or-fragment",
"sha256": "74c676394ac01177c37d8394112abaeeed3dacb787c17bf1c47fa1cb6c2cd6... | [] | TheoremDB P8120 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8120",
"url": "https://theoremdb.org/statements/P8120",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8120",
"not... | {
"source_record": "P8120",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:49+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8120,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:01.225Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1a531d26-a4c9-4664-804e-697aa3ffe2d5","format_issues":null,"number":5685} |
1.0.0 | problem:theoremdb-p8122 | problem | theoremdb-p8122 | Powerful Numbers in Products of Consecutive Integers | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | Let $k \geq 3$ be an integer and let $n$ be a positive integer. A positive integer $N$ is called powerful if for every prime $p$ dividing $N$, we have $p^2$ also divides $N$. Consider the product of $k$ consecutive integers starting from $n+1$, that is, the product $(n+1)(n+2)\cdots(n+k)$. Must there always exist a pri... | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8122",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8122",
"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... | theorem erdos_137 : answer(sorry) ↔ ∀ k ≥ 3, ∀ n, ¬ (∏ x ∈ Finset.Ioc n (n + k), x).Powerful | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem erdos_137 : answer(sorry) ↔ ∀ k ≥ 3, ∀ n, ¬ (∏ x ∈ Finset.Ioc n (n + k), x).Powerful",
"target": null,
"source_url": "https://theoremdb.org/statements/P8122",
"format": "declaration-or-fragment",
"sha256": "1c487570328bfc47b26302762f1e95fcbf5af1284979... | [] | TheoremDB P8122 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8122",
"url": "https://theoremdb.org/statements/P8122",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8122",
"not... | {
"source_record": "P8122",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:50+00:00","display_standard":{"formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8122,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","reaso... | [
"formalization-contains-placeholder",
"formalization-not-compiled-during-export",
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:05.008Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9c6f1f6f-0fa1-4aed-b65d-96b7b798f116","format_issues":null,"number":6433} |
1.0.0 | problem:theoremdb-p8124 | problem | theoremdb-p8124 | The rational distance problem for the unit square | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | Let the unit square have vertices at $(0,0)$, $(1,0)$, $(1,1)$, and $(0,1)$. Does there exist a point $P$ in the plane such that the Euclidean distance from $P$ to each of the four vertices of the unit square is a rational number? | unassessed | {
"key": "theoremdb",
"name": "TheoremDB · P8124",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P8124",
"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... | theorem rational_distance_problem :
answer(sorry) ↔ ∃ P : ℝ² , ∀ i, ¬ Irrational (dist P (UnitSquareCorners i)) | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "theorem rational_distance_problem :\n answer(sorry) ↔ ∃ P : ℝ² , ∀ i, ¬ Irrational (dist P (UnitSquareCorners i))",
"target": null,
"source_url": "https://theoremdb.org/statements/P8124",
"format": "declaration-or-fragment",
"sha256": "a65b44f4c1727c0fa0a0... | [] | TheoremDB P8124 · Candidate awaiting source review | 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.
This record is in the source backlog; its novelty and unresolved status have not passed source review. | null | published | incremental | hard | [
"source-candidate",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P8124",
"url": "https://theoremdb.org/statements/P8124",
"note": null,
"sort_order": 0
},
{
"kind": "formalization",
"citation": "Source formal statement (not locally verified)",
"url": "https://theoremdb.org/statements/P8124",
"not... | {
"source_record": "P8124",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source candidate · not reviewed",
"note": "Full public directory statement. Source lane: backlog; source resolution: open. Source verification claims are attributed only; no local Lean verification has be... | {"created_at":"2026-08-17T18:34:52+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_assessed"},"lean_verified":false,"problem_number":8124,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{... | [
"formalization-contains-placeholder",
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"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:06.736Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dcdf4b08-6e81-4d46-923c-8a65387b37d2","format_issues":null,"number":6806} |
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