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1.0.0 | problem:theoremdb-p4732 | problem | theoremdb-p4732 | Clique number of the Paley graph of order 1153 | {
"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 $P(1153)$ be the graph on $\mathbb{F}_{1153}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1153$. Determine the clique number $\omega(P(1153))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4732",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4732",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4732 · 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 P4732",
"url": "https://theoremdb.org/statements/P4732",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4732",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:41:50+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4732,"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": "2026-09-08T03:32:51.825Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f546e343-cccb-41c7-9e63-1e0fedde3ff5","format_issues":null,"number":3723} |
1.0.0 | problem:theoremdb-p4734 | problem | theoremdb-p4734 | Clique number of the Paley graph of order 1181 | {
"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 $P(1181)$ be the graph on $\mathbb{F}_{1181}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1181$. Determine the clique number $\omega(P(1181))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4734",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4734",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4734 · 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 P4734",
"url": "https://theoremdb.org/statements/P4734",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4734",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:41:53+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4734,"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": "2026-09-08T03:32:51.829Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f69a5b09-86d1-4a6f-8b02-2ef8116e72da","format_issues":null,"number":3724} |
1.0.0 | problem:theoremdb-p4736 | problem | theoremdb-p4736 | Clique number of the Paley graph of order 1193 | {
"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 $P(1193)$ be the graph on $\mathbb{F}_{1193}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1193$. Determine the clique number $\omega(P(1193))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4736",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4736",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4736 · 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 P4736",
"url": "https://theoremdb.org/statements/P4736",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4736",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:41:54+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4736,"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": "2026-09-08T03:32:51.834Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b972d091-1fa2-42b0-95e3-ca5d3dbf7629","format_issues":null,"number":3725} |
1.0.0 | problem:theoremdb-p4738 | problem | theoremdb-p4738 | Clique number of the Paley graph of order 1201 | {
"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 $P(1201)$ be the graph on $\mathbb{F}_{1201}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1201$. Determine the clique number $\omega(P(1201))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4738",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4738",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4738 · 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 P4738",
"url": "https://theoremdb.org/statements/P4738",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4738",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:41:55+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4738,"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": "2026-09-08T03:32:51.838Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3143c636-5d78-45b6-8ec5-7202191b6aae","format_issues":null,"number":3726} |
1.0.0 | problem:theoremdb-p4740 | problem | theoremdb-p4740 | Clique number of the Paley graph of order 1213 | {
"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 $P(1213)$ be the graph on $\mathbb{F}_{1213}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1213$. Determine the clique number $\omega(P(1213))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4740",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4740",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4740 · 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 P4740",
"url": "https://theoremdb.org/statements/P4740",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4740",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:41:56+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4740,"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": "2026-09-08T03:32:51.842Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e588157f-be51-47af-8ec3-7e8ce4600288","format_issues":null,"number":3727} |
1.0.0 | problem:theoremdb-p4742 | problem | theoremdb-p4742 | Clique number of the Paley graph of order 1217 | {
"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 $P(1217)$ be the graph on $\mathbb{F}_{1217}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1217$. Determine the clique number $\omega(P(1217))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4742",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4742",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4742 · 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 P4742",
"url": "https://theoremdb.org/statements/P4742",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4742",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:41:57+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4742,"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": "2026-09-08T03:32:51.847Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b6cbf224-7d25-4021-9452-d03ae1b36d09","format_issues":null,"number":3728} |
1.0.0 | problem:theoremdb-p4744 | problem | theoremdb-p4744 | Clique number of the Paley graph of order 1229 | {
"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 $P(1229)$ be the graph on $\mathbb{F}_{1229}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1229$. Determine the clique number $\omega(P(1229))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4744",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4744",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4744 · 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 P4744",
"url": "https://theoremdb.org/statements/P4744",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4744",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:41:59+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4744,"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": "2026-09-08T03:32:51.852Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"70647984-fd58-470e-b287-3b1c5244e1f2","format_issues":null,"number":3729} |
1.0.0 | problem:theoremdb-p4746 | problem | theoremdb-p4746 | Clique number of the Paley graph of order 1237 | {
"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 $P(1237)$ be the graph on $\mathbb{F}_{1237}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1237$. Determine the clique number $\omega(P(1237))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4746",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4746",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4746 · 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 P4746",
"url": "https://theoremdb.org/statements/P4746",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4746",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:03+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4746,"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": "2026-09-08T03:32:51.856Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d41c5ba2-7db3-4fbf-83dd-e9eea5e78824","format_issues":null,"number":3730} |
1.0.0 | problem:theoremdb-p4748 | problem | theoremdb-p4748 | Clique number of the Paley graph of order 1249 | {
"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 $P(1249)$ be the graph on $\mathbb{F}_{1249}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1249$. Determine the clique number $\omega(P(1249))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4748",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4748",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4748 · 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 P4748",
"url": "https://theoremdb.org/statements/P4748",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4748",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:04+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4748,"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": "2026-09-08T03:32:51.860Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3341f85d-e27a-434f-8d4c-338f5eea20cb","format_issues":null,"number":3731} |
1.0.0 | problem:theoremdb-p4750 | problem | theoremdb-p4750 | Clique number of the Paley graph of order 1277 | {
"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 $P(1277)$ be the graph on $\mathbb{F}_{1277}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1277$. Determine the clique number $\omega(P(1277))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4750",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4750",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4750 · 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 P4750",
"url": "https://theoremdb.org/statements/P4750",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4750",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:07+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4750,"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": "2026-09-08T03:32:51.864Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"52e8edba-1ef4-477b-8741-4b382e1fa1cf","format_issues":null,"number":3732} |
1.0.0 | problem:theoremdb-p4752 | problem | theoremdb-p4752 | Clique number of the Paley graph of order 1289 | {
"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 $P(1289)$ be the graph on $\mathbb{F}_{1289}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1289$. Determine the clique number $\omega(P(1289))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4752",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4752",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4752 · 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 P4752",
"url": "https://theoremdb.org/statements/P4752",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4752",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:11+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4752,"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": "2026-09-08T03:32:51.868Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6f3226a9-09e7-4a91-9702-e566286be4dc","format_issues":null,"number":3733} |
1.0.0 | problem:theoremdb-p4754 | problem | theoremdb-p4754 | Clique number of the Paley graph of order 1297 | {
"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 $P(1297)$ be the graph on $\mathbb{F}_{1297}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1297$. Determine the clique number $\omega(P(1297))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4754",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4754",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4754 · 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 P4754",
"url": "https://theoremdb.org/statements/P4754",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4754",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:12+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4754,"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": "2026-09-08T03:32:51.873Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"303c7748-bb04-478e-b642-91796d90fa12","format_issues":null,"number":3734} |
1.0.0 | problem:theoremdb-p4756 | problem | theoremdb-p4756 | Clique number of the Paley graph of order 1301 | {
"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 $P(1301)$ be the graph on $\mathbb{F}_{1301}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1301$. Determine the clique number $\omega(P(1301))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4756",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4756",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4756 · 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 P4756",
"url": "https://theoremdb.org/statements/P4756",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4756",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:21+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4756,"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": "2026-09-08T03:32:51.877Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b10e4cda-ede5-4f46-b2b2-4ac97744d44b","format_issues":null,"number":3735} |
1.0.0 | problem:theoremdb-p4758 | problem | theoremdb-p4758 | Clique number of the Paley graph of order 1321 | {
"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 $P(1321)$ be the graph on $\mathbb{F}_{1321}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1321$. Determine the clique number $\omega(P(1321))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4758",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4758",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4758 · 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 P4758",
"url": "https://theoremdb.org/statements/P4758",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4758",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:30+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4758,"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": "2026-09-08T03:32:51.881Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"74d973b8-b38a-4085-a535-934c0b22a558","format_issues":null,"number":3736} |
1.0.0 | problem:theoremdb-p4760 | problem | theoremdb-p4760 | Clique number of the Paley graph of order 1361 | {
"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 $P(1361)$ be the graph on $\mathbb{F}_{1361}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1361$. Determine the clique number $\omega(P(1361))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4760",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4760",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4760 · 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 P4760",
"url": "https://theoremdb.org/statements/P4760",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4760",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:37+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4760,"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": "2026-09-08T03:32:51.885Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5d4c3234-4757-4c77-a47a-36b9b54706e5","format_issues":null,"number":3737} |
1.0.0 | problem:theoremdb-p4762 | problem | theoremdb-p4762 | Clique number of the Paley graph of order 1373 | {
"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 $P(1373)$ be the graph on $\mathbb{F}_{1373}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1373$. Determine the clique number $\omega(P(1373))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4762",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4762",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4762 · 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 P4762",
"url": "https://theoremdb.org/statements/P4762",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4762",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:39+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4762,"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": "2026-09-08T03:32:51.890Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2b6b13a7-3c3a-4095-b512-8155b9231b3e","format_issues":null,"number":3738} |
1.0.0 | problem:theoremdb-p4764 | problem | theoremdb-p4764 | Clique number of the Paley graph of order 1381 | {
"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 $P(1381)$ be the graph on $\mathbb{F}_{1381}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1381$. Determine the clique number $\omega(P(1381))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4764",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4764",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4764 · 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 P4764",
"url": "https://theoremdb.org/statements/P4764",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4764",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:41+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4764,"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": "2026-09-08T03:32:51.894Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"048f5ee9-7c36-455b-92a5-da0f1cf578f7","format_issues":null,"number":3739} |
1.0.0 | problem:theoremdb-p4766 | problem | theoremdb-p4766 | Clique number of the Paley graph of order 1409 | {
"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 $P(1409)$ be the graph on $\mathbb{F}_{1409}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1409$. Determine the clique number $\omega(P(1409))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4766",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4766",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4766 · 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 P4766",
"url": "https://theoremdb.org/statements/P4766",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4766",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:49+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4766,"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": "2026-09-08T03:32:51.899Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"22f05e23-a2b8-4369-b93b-817fc4746623","format_issues":null,"number":3740} |
1.0.0 | problem:theoremdb-p4768 | problem | theoremdb-p4768 | Clique number of the Paley graph of order 1429 | {
"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 $P(1429)$ be the graph on $\mathbb{F}_{1429}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1429$. Determine the clique number $\omega(P(1429))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4768",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4768",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4768 · 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 P4768",
"url": "https://theoremdb.org/statements/P4768",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4768",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:55+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4768,"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": "2026-09-08T03:32:51.903Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"422a872c-f025-482a-9171-586682bcdb81","format_issues":null,"number":3741} |
1.0.0 | problem:theoremdb-p4770 | problem | theoremdb-p4770 | Clique number of the Paley graph of order 1433 | {
"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 $P(1433)$ be the graph on $\mathbb{F}_{1433}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1433$. Determine the clique number $\omega(P(1433))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4770",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4770",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4770 · 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 P4770",
"url": "https://theoremdb.org/statements/P4770",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4770",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:57+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4770,"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": "2026-09-08T03:32:51.907Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7b9f2e73-3955-433b-bf99-19c03d2a324e","format_issues":null,"number":3742} |
1.0.0 | problem:theoremdb-p4772 | problem | theoremdb-p4772 | Clique number of the Paley graph of order 1453 | {
"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 $P(1453)$ be the graph on $\mathbb{F}_{1453}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1453$. Determine the clique number $\omega(P(1453))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4772",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4772",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4772 · 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 P4772",
"url": "https://theoremdb.org/statements/P4772",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4772",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:58+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4772,"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": "2026-09-08T03:32:51.911Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ec7730c6-563c-42aa-806e-621b496df75d","format_issues":null,"number":3743} |
1.0.0 | problem:theoremdb-p4774 | problem | theoremdb-p4774 | Clique number of the Paley graph of order 1481 | {
"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 $P(1481)$ be the graph on $\mathbb{F}_{1481}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1481$. Determine the clique number $\omega(P(1481))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4774",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4774",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4774 · 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 P4774",
"url": "https://theoremdb.org/statements/P4774",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4774",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:59+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4774,"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": "2026-09-08T03:32:51.915Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9dd8b5c1-128b-4543-9c25-a46d43306d21","format_issues":null,"number":3744} |
1.0.0 | problem:theoremdb-p4776 | problem | theoremdb-p4776 | Clique number of the Paley graph of order 1489 | {
"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 $P(1489)$ be the graph on $\mathbb{F}_{1489}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1489$. Determine the clique number $\omega(P(1489))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4776",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4776",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4776 · 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 P4776",
"url": "https://theoremdb.org/statements/P4776",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4776",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:42:59+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4776,"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": "2026-09-08T03:32:51.919Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cc93dc9a-28ed-45f8-9b3e-297712ee6008","format_issues":null,"number":3745} |
1.0.0 | problem:theoremdb-p4778 | problem | theoremdb-p4778 | Clique number of the Paley graph of order 1493 | {
"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 $P(1493)$ be the graph on $\mathbb{F}_{1493}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1493$. Determine the clique number $\omega(P(1493))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4778",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4778",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4778 · 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 P4778",
"url": "https://theoremdb.org/statements/P4778",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4778",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:01+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4778,"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": "2026-09-08T03:32:51.923Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7e6bdcb7-7150-4e74-b9d5-9688908ff199","format_issues":null,"number":3746} |
1.0.0 | problem:theoremdb-p4780 | problem | theoremdb-p4780 | Clique number of the Paley graph of order 1549 | {
"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 $P(1549)$ be the graph on $\mathbb{F}_{1549}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1549$. Determine the clique number $\omega(P(1549))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4780",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4780",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4780 · 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 P4780",
"url": "https://theoremdb.org/statements/P4780",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4780",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:02+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4780,"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": "2026-09-08T03:32:51.928Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"593b2c27-f6c6-44b9-8f01-2e4f71252bb2","format_issues":null,"number":3747} |
1.0.0 | problem:theoremdb-p4782 | problem | theoremdb-p4782 | Clique number of the Paley graph of order 1553 | {
"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 $P(1553)$ be the graph on $\mathbb{F}_{1553}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1553$. Determine the clique number $\omega(P(1553))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4782",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4782",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4782 · 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 P4782",
"url": "https://theoremdb.org/statements/P4782",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4782",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:02+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4782,"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": "2026-09-08T03:32:51.932Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d3d4d640-17a7-4aee-be28-7daf83bc9acf","format_issues":null,"number":3748} |
1.0.0 | problem:theoremdb-p4784 | problem | theoremdb-p4784 | Clique number of the Paley graph of order 1597 | {
"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 $P(1597)$ be the graph on $\mathbb{F}_{1597}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1597$. Determine the clique number $\omega(P(1597))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4784",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4784",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4784 · 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 P4784",
"url": "https://theoremdb.org/statements/P4784",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4784",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:03+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4784,"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": "2026-09-08T03:32:51.936Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3625161d-eb1d-4fa7-9dea-ea05d676c638","format_issues":null,"number":3749} |
1.0.0 | problem:theoremdb-p4786 | problem | theoremdb-p4786 | Clique number of the Paley graph of order 1601 | {
"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 $P(1601)$ be the graph on $\mathbb{F}_{1601}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $1601$. Determine the clique number $\omega(P(1601))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4786",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4786",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4786 · 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 P4786",
"url": "https://theoremdb.org/statements/P4786",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4786",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:05+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4786,"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": "2026-09-08T03:32:51.944Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d7701f74-34e0-4c73-ac8a-3b2ea8ffbb94","format_issues":null,"number":3750} |
1.0.0 | problem:theoremdb-p4788 | problem | theoremdb-p4788 | Chromatic number of the circulant graph C(503; 1, 2, 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 $\mathbb{Z}/503\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm14$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4788",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4788",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4788 · 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 P4788",
"url": "https://theoremdb.org/statements/P4788",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4788",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:07+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.416Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"48028c07-bec6-481a-9b66-828c59c7f0ec","format_issues":null,"number":3632} |
1.0.0 | problem:theoremdb-p4790 | problem | theoremdb-p4790 | Chromatic number of the circulant graph C(509; 1, 3, 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 $\mathbb{Z}/509\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm15$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4790",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4790",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4790 · 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 P4790",
"url": "https://theoremdb.org/statements/P4790",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4790",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:09+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": "2026-09-08T03:32:51.421Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"78b6011d-8e66-4aee-bd18-b52e6977b041","format_issues":null,"number":3633} |
1.0.0 | problem:theoremdb-p4792 | problem | theoremdb-p4792 | Chromatic number of the circulant graph C(521; 1, 4, 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 $\mathbb{Z}/521\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm16$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4792",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4792",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4792 · 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 P4792",
"url": "https://theoremdb.org/statements/P4792",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4792",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:10+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": "2026-09-08T03:32:51.425Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3977b812-06a3-4806-99b8-24fd082a87a0","format_issues":null,"number":3634} |
1.0.0 | problem:theoremdb-p4794 | problem | theoremdb-p4794 | Chromatic number of the circulant graph C(523; 1, 5, 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 $\mathbb{Z}/523\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm17$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4794",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4794",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4794 · 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 P4794",
"url": "https://theoremdb.org/statements/P4794",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4794",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:11+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.429Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"76c9c446-38af-46f2-ad5f-d8b0aa2197f0","format_issues":null,"number":3635} |
1.0.0 | problem:theoremdb-p4796 | problem | theoremdb-p4796 | Chromatic number of the circulant graph C(541; 1, 6, 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 $\mathbb{Z}/541\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm18$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4796",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4796",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4796 · 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 P4796",
"url": "https://theoremdb.org/statements/P4796",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4796",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:12+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.434Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c33a3148-c9bd-42aa-a2f9-318e979cf0a5","format_issues":null,"number":3636} |
1.0.0 | problem:theoremdb-p4798 | problem | theoremdb-p4798 | Chromatic number of the circulant graph C(547; 1, 7, 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 $\mathbb{Z}/547\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm19$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4798",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4798",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4798 · 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 P4798",
"url": "https://theoremdb.org/statements/P4798",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4798",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:12+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.438Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d9d6c461-8e63-41bb-be5e-bef0933f4050","format_issues":null,"number":3637} |
1.0.0 | problem:theoremdb-p4800 | problem | theoremdb-p4800 | Chromatic number of the circulant graph C(557; 1, 8, 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 $\mathbb{Z}/557\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm20$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4800",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4800",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4800 · 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 P4800",
"url": "https://theoremdb.org/statements/P4800",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4800",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:13+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.442Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eb0de79e-3e04-4465-9c98-d49b7f488524","format_issues":null,"number":3638} |
1.0.0 | problem:theoremdb-p4802 | problem | theoremdb-p4802 | Chromatic number of the circulant graph C(563; 1, 9, 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 $\mathbb{Z}/563\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm21$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4802",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4802",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4802 · 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 P4802",
"url": "https://theoremdb.org/statements/P4802",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4802",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:15+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.446Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"980fb96b-1582-4fe6-bbc0-dfa13eea4ef6","format_issues":null,"number":3639} |
1.0.0 | problem:theoremdb-p4804 | problem | theoremdb-p4804 | Chromatic number of the circulant graph C(569; 1, 10, 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 $\mathbb{Z}/569\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm22$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4804",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4804",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4804 · 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 P4804",
"url": "https://theoremdb.org/statements/P4804",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4804",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:20+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": "2026-09-08T03:32:51.450Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9ddacc10-5f68-4726-999f-76d5dc3cb2b4","format_issues":null,"number":3640} |
1.0.0 | problem:theoremdb-p4806 | problem | theoremdb-p4806 | Chromatic number of the circulant graph C(571; 1, 11, 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 $\mathbb{Z}/571\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm23$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4806",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4806",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4806 · 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 P4806",
"url": "https://theoremdb.org/statements/P4806",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4806",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:26+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": "2026-09-08T03:32:51.458Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1033a55b-45f8-48ac-9752-47361b4b31ca","format_issues":null,"number":3641} |
1.0.0 | problem:theoremdb-p4808 | problem | theoremdb-p4808 | Chromatic number of the circulant graph C(577; 1, 12, 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 $\mathbb{Z}/577\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm24$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4808",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4808",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4808 · 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 P4808",
"url": "https://theoremdb.org/statements/P4808",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4808",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:29+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.462Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3cbc3236-87af-4611-b4a2-63e103442957","format_issues":null,"number":3642} |
1.0.0 | problem:theoremdb-p4810 | problem | theoremdb-p4810 | Chromatic number of the circulant graph C(587; 1, 2, 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 $\mathbb{Z}/587\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm25$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4810",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4810",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4810 · 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 P4810",
"url": "https://theoremdb.org/statements/P4810",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4810",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:30+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.466Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d0dc2f0d-7e1b-4b40-9988-bf43cf77adcd","format_issues":null,"number":3643} |
1.0.0 | problem:theoremdb-p4812 | problem | theoremdb-p4812 | Chromatic number of the circulant graph C(593; 1, 3, 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 $\mathbb{Z}/593\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm26$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4812",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4812",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4812 · 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 P4812",
"url": "https://theoremdb.org/statements/P4812",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4812",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:38+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": "2026-09-08T03:32:51.470Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6d7ed10a-b335-4037-8eb3-cd0aedb897e2","format_issues":null,"number":3644} |
1.0.0 | problem:theoremdb-p4814 | problem | theoremdb-p4814 | Chromatic number of the circulant graph C(599; 1, 4, 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 $\mathbb{Z}/599\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm27$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4814",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4814",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4814 · 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 P4814",
"url": "https://theoremdb.org/statements/P4814",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4814",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:48+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.475Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6047eec6-a141-466a-9c5c-a1e743527d9f","format_issues":null,"number":3645} |
1.0.0 | problem:theoremdb-p4816 | problem | theoremdb-p4816 | Chromatic number of the circulant graph C(601; 1, 5, 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 $\mathbb{Z}/601\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm28$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4816",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4816",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4816 · 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 P4816",
"url": "https://theoremdb.org/statements/P4816",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4816",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:50+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.479Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5ffd4ba0-8290-4363-803b-4a1c3a677e3d","format_issues":null,"number":3646} |
1.0.0 | problem:theoremdb-p4818 | problem | theoremdb-p4818 | Chromatic number of the circulant graph C(607; 1, 6, 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 $\mathbb{Z}/607\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm29$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4818",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4818",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4818 · 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 P4818",
"url": "https://theoremdb.org/statements/P4818",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4818",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:52+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": "2026-09-08T03:32:51.483Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"34dc6d55-dbde-45d9-bc89-ed212be0e2c8","format_issues":null,"number":3647} |
1.0.0 | problem:theoremdb-p4820 | problem | theoremdb-p4820 | Chromatic number of the circulant graph C(613; 1, 7, 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 $\mathbb{Z}/613\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm30$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4820",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4820",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4820 · 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 P4820",
"url": "https://theoremdb.org/statements/P4820",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4820",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:56+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": "2026-09-08T03:32:51.487Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"65a497c4-db4e-47e2-b033-cae94c9ebb68","format_issues":null,"number":3648} |
1.0.0 | problem:theoremdb-p4822 | problem | theoremdb-p4822 | Chromatic number of the circulant graph C(617; 1, 8, 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 $\mathbb{Z}/617\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm14$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4822",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4822",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4822 · 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 P4822",
"url": "https://theoremdb.org/statements/P4822",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4822",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:43:57+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": "2026-09-08T03:32:51.492Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bd96a17a-8b97-475f-846c-fb63c6dcb45c","format_issues":null,"number":3649} |
1.0.0 | problem:theoremdb-p4824 | problem | theoremdb-p4824 | Chromatic number of the circulant graph C(619; 1, 9, 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 $\mathbb{Z}/619\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm15$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4824",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4824",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4824 · 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 P4824",
"url": "https://theoremdb.org/statements/P4824",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4824",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:06+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": "2026-09-08T03:32:51.496Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ea93674d-194c-423b-ab6d-3ac299854e8c","format_issues":null,"number":3650} |
1.0.0 | problem:theoremdb-p4826 | problem | theoremdb-p4826 | Chromatic number of the circulant graph C(631; 1, 10, 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 $\mathbb{Z}/631\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm16$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4826",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4826",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4826 · 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 P4826",
"url": "https://theoremdb.org/statements/P4826",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4826",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:08+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": "2026-09-08T03:32:51.502Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fd683a3b-7cf8-44d6-9ea7-0d2dcf827851","format_issues":null,"number":3651} |
1.0.0 | problem:theoremdb-p4828 | problem | theoremdb-p4828 | Chromatic number of the circulant graph C(641; 1, 11, 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 $\mathbb{Z}/641\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm17$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4828",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4828",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4828 · 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 P4828",
"url": "https://theoremdb.org/statements/P4828",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4828",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:12+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.506Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1182034c-f453-46bd-ae83-733343175f90","format_issues":null,"number":3652} |
1.0.0 | problem:theoremdb-p4830 | problem | theoremdb-p4830 | Chromatic number of the circulant graph C(643; 1, 12, 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 $\mathbb{Z}/643\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm18$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4830",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4830",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4830 · 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 P4830",
"url": "https://theoremdb.org/statements/P4830",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4830",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:14+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": "2026-09-08T03:32:51.510Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b3b283fa-32f4-4538-924a-f646d91aa439","format_issues":null,"number":3653} |
1.0.0 | problem:theoremdb-p4832 | problem | theoremdb-p4832 | Chromatic number of the circulant graph C(647; 1, 2, 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 $\mathbb{Z}/647\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm19$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4832",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4832",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4832 · 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 P4832",
"url": "https://theoremdb.org/statements/P4832",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4832",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:15+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.514Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1d89331b-a97a-4f1b-906f-9dcb9052c600","format_issues":null,"number":3654} |
1.0.0 | problem:theoremdb-p4834 | problem | theoremdb-p4834 | Chromatic number of the circulant graph C(653; 1, 3, 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 $\mathbb{Z}/653\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm20$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4834",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4834",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4834 · 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 P4834",
"url": "https://theoremdb.org/statements/P4834",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4834",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:21+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.519Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"db4fc3b5-21bb-4469-aeb9-9eb3cef9a311","format_issues":null,"number":3655} |
1.0.0 | problem:theoremdb-p4836 | problem | theoremdb-p4836 | Chromatic number of the circulant graph C(659; 1, 4, 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 $\mathbb{Z}/659\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm21$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4836",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4836",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4836 · 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 P4836",
"url": "https://theoremdb.org/statements/P4836",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4836",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:23+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": "2026-09-08T03:32:51.523Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dfa7d25f-c23f-469b-9c7f-c1424545076a","format_issues":null,"number":3656} |
1.0.0 | problem:theoremdb-p4838 | problem | theoremdb-p4838 | Chromatic number of the circulant graph C(661; 1, 5, 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 $\mathbb{Z}/661\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm22$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4838",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4838",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4838 · 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 P4838",
"url": "https://theoremdb.org/statements/P4838",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4838",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:31+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": "2026-09-08T03:32:51.528Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"35278704-0647-4a85-8c54-da4b9b02aaac","format_issues":null,"number":3657} |
1.0.0 | problem:theoremdb-p4840 | problem | theoremdb-p4840 | Chromatic number of the circulant graph C(673; 1, 6, 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 $\mathbb{Z}/673\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm23$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4840",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4840",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4840 · 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 P4840",
"url": "https://theoremdb.org/statements/P4840",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4840",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:35+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": "2026-09-08T03:32:51.532Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1d38e473-3ac9-40e5-911e-a0eaa9b1e7c7","format_issues":null,"number":3658} |
1.0.0 | problem:theoremdb-p4842 | problem | theoremdb-p4842 | Chromatic number of the circulant graph C(677; 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 $\mathbb{Z}/677\mathbb{Z}$, 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 · P4842",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4842",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4842 · 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 P4842",
"url": "https://theoremdb.org/statements/P4842",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4842",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:38+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": "2026-09-08T03:32:51.536Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"48c9761c-1445-45c1-a258-5bb90f7af2ca","format_issues":null,"number":3659} |
1.0.0 | problem:theoremdb-p4844 | problem | theoremdb-p4844 | Chromatic number of the circulant graph C(683; 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 $\mathbb{Z}/683\mathbb{Z}$, 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 · P4844",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4844",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4844 · 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 P4844",
"url": "https://theoremdb.org/statements/P4844",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4844",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:44+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.540Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7b20e9f3-15a5-4591-b228-eaf696dd0feb","format_issues":null,"number":3660} |
1.0.0 | problem:theoremdb-p4846 | problem | theoremdb-p4846 | Chromatic number of the circulant graph C(691; 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 $\mathbb{Z}/691\mathbb{Z}$, 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 · P4846",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4846",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4846 · 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 P4846",
"url": "https://theoremdb.org/statements/P4846",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4846",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:45+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": "2026-09-08T03:32:51.544Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e1ad064a-40d6-4bdd-8968-de889e63cb2c","format_issues":null,"number":3661} |
1.0.0 | problem:theoremdb-p4848 | problem | theoremdb-p4848 | Chromatic number of the circulant graph C(701; 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 $\mathbb{Z}/701\mathbb{Z}$, 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 · P4848",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4848",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4848 · 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 P4848",
"url": "https://theoremdb.org/statements/P4848",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4848",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:49+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.548Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"48ad4b60-2ede-4388-8100-69e5df39bebc","format_issues":null,"number":3662} |
1.0.0 | problem:theoremdb-p4850 | problem | theoremdb-p4850 | Chromatic number of the circulant graph C(709; 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 $\mathbb{Z}/709\mathbb{Z}$, 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 · P4850",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4850",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4850 · 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 P4850",
"url": "https://theoremdb.org/statements/P4850",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4850",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:56+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": "2026-09-08T03:32:51.553Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0e81913e-99b4-4b2d-b39b-e018992f6808","format_issues":null,"number":3663} |
1.0.0 | problem:theoremdb-p4852 | problem | theoremdb-p4852 | Chromatic number of the circulant graph C(719; 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 $\mathbb{Z}/719\mathbb{Z}$, 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 · P4852",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4852",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4852 · 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 P4852",
"url": "https://theoremdb.org/statements/P4852",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4852",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:44:59+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": "2026-09-08T03:32:51.557Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"903a4a04-ba72-4f8e-b332-02626a33b262","format_issues":null,"number":3664} |
1.0.0 | problem:theoremdb-p4854 | problem | theoremdb-p4854 | Chromatic number of the circulant graph C(727; 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 $\mathbb{Z}/727\mathbb{Z}$, 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 · P4854",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4854",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4854 · 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 P4854",
"url": "https://theoremdb.org/statements/P4854",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4854",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:45:05+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": "2026-09-08T03:32:51.562Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fb578cd7-ee5e-418e-bfce-bd484389bddb","format_issues":null,"number":3665} |
1.0.0 | problem:theoremdb-p4856 | problem | theoremdb-p4856 | Chromatic number of the circulant graph C(733; 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 $\mathbb{Z}/733\mathbb{Z}$, 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 · P4856",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4856",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4856 · 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 P4856",
"url": "https://theoremdb.org/statements/P4856",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4856",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:45:16+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": "2026-09-08T03:32:51.566Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a6a879f0-a837-4435-a7c9-b03feddf9aac","format_issues":null,"number":3666} |
1.0.0 | problem:theoremdb-p4858 | problem | theoremdb-p4858 | Chromatic number of the circulant graph C(739; 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 $\mathbb{Z}/739\mathbb{Z}$, 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 · P4858",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4858",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4858 · 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 P4858",
"url": "https://theoremdb.org/statements/P4858",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4858",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:45:17+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": "2026-09-08T03:32:51.570Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5fd2433b-845a-4fe2-ae25-02dd988a7ed8","format_issues":null,"number":3667} |
1.0.0 | problem:theoremdb-p4860 | problem | theoremdb-p4860 | Chromatic number of the circulant graph C(743; 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 $\mathbb{Z}/743\mathbb{Z}$, 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 · P4860",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4860",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4860 · 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 P4860",
"url": "https://theoremdb.org/statements/P4860",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4860",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:45:24+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": "2026-09-08T03:32:51.577Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7b588360-d065-4f41-b9fc-8bc1297d9ddd","format_issues":null,"number":3668} |
1.0.0 | problem:theoremdb-p4862 | problem | theoremdb-p4862 | Chromatic number of the circulant graph C(751; 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 $\mathbb{Z}/751\mathbb{Z}$, 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 · P4862",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4862",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4862 · 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 P4862",
"url": "https://theoremdb.org/statements/P4862",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4862",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:45:35+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": "2026-09-08T03:32:51.583Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e5f4917f-e452-492c-b388-70d43453d040","format_issues":null,"number":3669} |
1.0.0 | problem:theoremdb-p4864 | problem | theoremdb-p4864 | Chromatic number of the circulant graph C(757; 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 $\mathbb{Z}/757\mathbb{Z}$, 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 · P4864",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4864",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4864 · 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 P4864",
"url": "https://theoremdb.org/statements/P4864",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4864",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:45:43+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.587Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ba10b908-6a31-48ac-a9e5-be5d04ebb227","format_issues":null,"number":3670} |
1.0.0 | problem:theoremdb-p4866 | problem | theoremdb-p4866 | Chromatic number of the circulant graph C(761; 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 $\mathbb{Z}/761\mathbb{Z}$, 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 · P4866",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4866",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4866 · 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 P4866",
"url": "https://theoremdb.org/statements/P4866",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4866",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T05:45:56+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": "2026-09-08T03:32:51.591Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d8f1a193-4796-4248-a833-c29f921a60c4","format_issues":null,"number":3671} |
1.0.0 | problem:theoremdb-p4868 | problem | theoremdb-p4868 | Independence number of the circulant graph C(587; 1, 2) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/587\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm2$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4868",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4868",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4868 · 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 P4868",
"url": "https://theoremdb.org/statements/P4868",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4868",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:28:35+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4868,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.036Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3a091c18-026b-415c-8dea-330a3bc7bfca","format_issues":null,"number":5528} |
1.0.0 | problem:theoremdb-p4870 | problem | theoremdb-p4870 | Independence number of the circulant graph C(593; 1, 3) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/593\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm3$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4870",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4870",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4870 · 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 P4870",
"url": "https://theoremdb.org/statements/P4870",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4870",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:29:13+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4870,"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": "2026-09-08T03:33:00.040Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5203fdc5-be7d-4202-967b-f8e1b2b894df","format_issues":null,"number":5529} |
1.0.0 | problem:theoremdb-p4872 | problem | theoremdb-p4872 | Independence number of the circulant graph C(599; 1, 4) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/599\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm4$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4872",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4872",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4872 · 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 P4872",
"url": "https://theoremdb.org/statements/P4872",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4872",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:29:51+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4872,"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": "2026-09-08T03:33:00.045Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e6ba2a25-3080-421e-8226-706def311724","format_issues":null,"number":5530} |
1.0.0 | problem:theoremdb-p4874 | problem | theoremdb-p4874 | Independence number of the circulant graph C(601; 1, 5) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/601\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm5$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4874",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4874",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4874 · 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 P4874",
"url": "https://theoremdb.org/statements/P4874",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4874",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:30:31+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4874,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.049Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"36c6f333-10f1-4241-b8b2-e7c4e8858b0e","format_issues":null,"number":5531} |
1.0.0 | problem:theoremdb-p4876 | problem | theoremdb-p4876 | Independence number of the circulant graph C(607; 1, 6) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/607\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm6$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4876",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4876",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4876 · 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 P4876",
"url": "https://theoremdb.org/statements/P4876",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4876",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:30:57+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4876,"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": "2026-09-08T03:33:00.054Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eaf9162e-f3e6-45b7-b839-f1ea225d36dd","format_issues":null,"number":5532} |
1.0.0 | problem:theoremdb-p4878 | problem | theoremdb-p4878 | Independence number of the circulant graph C(613; 1, 7) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/613\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm7$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4878",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4878",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4878 · 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 P4878",
"url": "https://theoremdb.org/statements/P4878",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4878",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:31:29+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4878,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.058Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dd07cc50-ce44-4bbf-ae59-73c25bab2312","format_issues":null,"number":5533} |
1.0.0 | problem:theoremdb-p4880 | problem | theoremdb-p4880 | Independence number of the circulant graph C(617; 1, 8) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/617\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm8$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4880",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4880",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4880 · 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 P4880",
"url": "https://theoremdb.org/statements/P4880",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4880",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:32:00+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4880,"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": "2026-09-08T03:33:00.062Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"862654fa-7fa5-4f39-ae33-d55abc05e12d","format_issues":null,"number":5534} |
1.0.0 | problem:theoremdb-p4882 | problem | theoremdb-p4882 | Independence number of the circulant graph C(619; 1, 9) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/619\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm9$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4882",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4882",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4882 · 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 P4882",
"url": "https://theoremdb.org/statements/P4882",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4882",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:11+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4882,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.066Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6c8e582e-80c4-440e-bc23-6b059c60a4f4","format_issues":null,"number":5535} |
1.0.0 | problem:theoremdb-p4884 | problem | theoremdb-p4884 | Independence number of the circulant graph C(631; 1, 10) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/631\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm10$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4884",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4884",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4884 · 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 P4884",
"url": "https://theoremdb.org/statements/P4884",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4884",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:12+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4884,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.071Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"51288617-7887-4218-b4b5-a71554d3355f","format_issues":null,"number":5536} |
1.0.0 | problem:theoremdb-p4886 | problem | theoremdb-p4886 | Independence number of the circulant graph C(641; 1, 11) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/641\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm11$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4886",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4886",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4886 · 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 P4886",
"url": "https://theoremdb.org/statements/P4886",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4886",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:14+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4886,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.075Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c4fcab02-c998-46e1-9498-4e239cc10b3c","format_issues":null,"number":5537} |
1.0.0 | problem:theoremdb-p4888 | problem | theoremdb-p4888 | Independence number of the circulant graph C(643; 1, 12) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/643\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm12$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4888",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4888",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4888 · 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 P4888",
"url": "https://theoremdb.org/statements/P4888",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4888",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:16+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4888,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.079Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5fbbe659-2467-444c-9a12-cc5e08269c8b","format_issues":null,"number":5538} |
1.0.0 | problem:theoremdb-p4890 | problem | theoremdb-p4890 | Independence number of the circulant graph C(647; 1, 13) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/647\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm13$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4890",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4890",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4890 · 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 P4890",
"url": "https://theoremdb.org/statements/P4890",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4890",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:16+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4890,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.084Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"28b1ba6d-7dd4-4ec4-81b8-08e49438f3ca","format_issues":null,"number":5539} |
1.0.0 | problem:theoremdb-p4892 | problem | theoremdb-p4892 | Independence number of the circulant graph C(653; 1, 14) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/653\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm14$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4892",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4892",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4892 · 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 P4892",
"url": "https://theoremdb.org/statements/P4892",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4892",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:18+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4892,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.088Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"26f68a04-a8e2-470f-9ee1-afc88b84cba6","format_issues":null,"number":5540} |
1.0.0 | problem:theoremdb-p4894 | problem | theoremdb-p4894 | Independence number of the circulant graph C(659; 1, 15) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/659\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm15$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4894",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4894",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4894 · 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 P4894",
"url": "https://theoremdb.org/statements/P4894",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4894",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:20+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4894,"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": "2026-09-08T03:33:00.092Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5b0cb2f7-a914-4c0b-b1cf-34544f01cbe4","format_issues":null,"number":5541} |
1.0.0 | problem:theoremdb-p4896 | problem | theoremdb-p4896 | Independence number of the circulant graph C(661; 1, 16) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/661\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm16$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4896",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4896",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4896 · 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 P4896",
"url": "https://theoremdb.org/statements/P4896",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4896",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:20+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4896,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.096Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"494207cb-7299-4fdb-b754-0e42ecf3cc1b","format_issues":null,"number":5542} |
1.0.0 | problem:theoremdb-p4898 | problem | theoremdb-p4898 | Independence number of the circulant graph C(673; 1, 17) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/673\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm17$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4898",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4898",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4898 · 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 P4898",
"url": "https://theoremdb.org/statements/P4898",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4898",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:20+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4898,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.100Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e834dcc8-7f76-45c5-8cc8-1dbd30ceff46","format_issues":null,"number":5543} |
1.0.0 | problem:theoremdb-p49 | problem | theoremdb-p49 | Graph reconstruction conjecture | {
"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"
}
] | Every finite simple graph $G$ with at least three vertices is determined up to isomorphism by the multiset $\{G-v:v\in V(G)\}$ of its one-vertex-deleted subgraphs. | open | {
"key": "theoremdb",
"name": "TheoremDB · P49",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P49",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem pac... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P49 · 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 P49",
"url": "https://theoremdb.org/statements/P49",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "J. Antony Aravind and S. Monikandan, arXiv:2601.00620, abstract",
"url": "https://arxiv.org/abs/2601.00620",
"no... | {
"source_record": "P49",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been per... | {"created_at":"2026-07-22T21:49:48+00:00","display_standard":{"editorial_review":"source_backed","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":49,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":true,"solutionRecord":null},"lean":{"kerne... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:59.402Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f42afc79-0d48-46b6-939c-1aff56db40c1","format_issues":null,"number":5387} |
1.0.0 | problem:theoremdb-p4900 | problem | theoremdb-p4900 | Independence number of the circulant graph C(677; 1, 18) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/677\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm18$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4900",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4900",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4900 · 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 P4900",
"url": "https://theoremdb.org/statements/P4900",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4900",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:22+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4900,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.105Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"16f653e2-ad43-4a72-b252-cf8fdac470a6","format_issues":null,"number":5544} |
1.0.0 | problem:theoremdb-p4902 | problem | theoremdb-p4902 | Independence number of the circulant graph C(683; 1, 19) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/683\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm19$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4902",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4902",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4902 · 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 P4902",
"url": "https://theoremdb.org/statements/P4902",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4902",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:26+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4902,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.109Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"86b3d820-8d0e-4e73-83c8-9e7c98692efa","format_issues":null,"number":5545} |
1.0.0 | problem:theoremdb-p4904 | problem | theoremdb-p4904 | Independence number of the circulant graph C(691; 1, 20) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/691\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm20$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4904",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4904",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4904 · 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 P4904",
"url": "https://theoremdb.org/statements/P4904",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4904",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:36+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4904,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.113Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fb50c764-8398-49a7-a8e6-a0bcb055dc62","format_issues":null,"number":5546} |
1.0.0 | problem:theoremdb-p4906 | problem | theoremdb-p4906 | Independence number of the circulant graph C(701; 1, 21) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/701\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm21$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4906",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4906",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4906 · 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 P4906",
"url": "https://theoremdb.org/statements/P4906",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4906",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:36:50+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4906,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.118Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1fbfb2fe-ce28-46a0-9b50-df1d3a8ca339","format_issues":null,"number":5547} |
1.0.0 | problem:theoremdb-p4908 | problem | theoremdb-p4908 | Independence number of the circulant graph C(709; 1, 22) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/709\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm22$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4908",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4908",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4908 · 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 P4908",
"url": "https://theoremdb.org/statements/P4908",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4908",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:37:08+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4908,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.122Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e12cfd79-2a48-40bc-ad59-adaf69d61e4a","format_issues":null,"number":5548} |
1.0.0 | problem:theoremdb-p4910 | problem | theoremdb-p4910 | Independence number of the circulant graph C(719; 1, 23) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/719\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm23$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4910",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4910",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4910 · 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 P4910",
"url": "https://theoremdb.org/statements/P4910",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4910",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:37:14+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4910,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.126Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fc220a86-494e-4bcc-9489-18bd77fa9e04","format_issues":null,"number":5549} |
1.0.0 | problem:theoremdb-p4912 | problem | theoremdb-p4912 | Independence number of the circulant graph C(727; 1, 24) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/727\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm24$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4912",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4912",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4912 · 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 P4912",
"url": "https://theoremdb.org/statements/P4912",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4912",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:37:22+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4912,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.616Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"04027763-cece-4319-a382-361b40141250","format_issues":null,"number":5550} |
1.0.0 | problem:theoremdb-p4914 | problem | theoremdb-p4914 | Independence number of the circulant graph C(733; 1, 25) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/733\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm25$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4914",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4914",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4914 · 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 P4914",
"url": "https://theoremdb.org/statements/P4914",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4914",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:37:29+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4914,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.620Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"893915da-f57f-43df-ad50-7ca1627c784b","format_issues":null,"number":5551} |
1.0.0 | problem:theoremdb-p4916 | problem | theoremdb-p4916 | Independence number of the circulant graph C(739; 1, 26) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/739\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm26$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4916",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4916",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4916 · 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 P4916",
"url": "https://theoremdb.org/statements/P4916",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4916",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:37:48+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4916,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.625Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c3f4cb49-1df3-4462-96d9-b71999dd94c2","format_issues":null,"number":5552} |
1.0.0 | problem:theoremdb-p4918 | problem | theoremdb-p4918 | Independence number of the circulant graph C(743; 1, 27) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/743\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm27$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4918",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4918",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4918 · 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 P4918",
"url": "https://theoremdb.org/statements/P4918",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4918",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:38:12+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4918,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.629Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"49793715-6b1e-4519-a0e4-474b29c4f345","format_issues":null,"number":5553} |
1.0.0 | problem:theoremdb-p4920 | problem | theoremdb-p4920 | Independence number of the circulant graph C(751; 1, 28) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/751\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm28$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4920",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4920",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4920 · 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 P4920",
"url": "https://theoremdb.org/statements/P4920",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4920",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:38:35+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4920,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.633Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"76cd4817-1ad9-4be3-8a9b-9f68937dea8c","format_issues":null,"number":5554} |
1.0.0 | problem:theoremdb-p4922 | problem | theoremdb-p4922 | Independence number of the circulant graph C(757; 1, 29) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/757\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm29$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4922",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4922",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4922 · 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 P4922",
"url": "https://theoremdb.org/statements/P4922",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4922",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:39:01+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4922,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.637Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"39fd7e21-ecf1-4929-83f5-bbdef97d94da","format_issues":null,"number":5555} |
1.0.0 | problem:theoremdb-p4924 | problem | theoremdb-p4924 | Independence number of the circulant graph C(761; 1, 30) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/761\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm30$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4924",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4924",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4924 · 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 P4924",
"url": "https://theoremdb.org/statements/P4924",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4924",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:39:23+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4924,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.643Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"211ac134-a10c-4344-ae0f-03087be9c287","format_issues":null,"number":5556} |
1.0.0 | problem:theoremdb-p4926 | problem | theoremdb-p4926 | Independence number of the circulant graph C(769; 1, 31) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/769\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm31$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4926",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4926",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4926 · 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 P4926",
"url": "https://theoremdb.org/statements/P4926",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4926",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:39:44+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4926,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.647Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"28d76ed3-ecf3-4d7f-9154-7d8b845eaf73","format_issues":null,"number":5557} |
1.0.0 | problem:theoremdb-p4928 | problem | theoremdb-p4928 | Independence number of the circulant graph C(773; 1, 2) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $G$ have vertex set $\mathbb{Z}/773\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to $\pm1$ or $\pm2$. Determine the independence number $\alpha(G)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P4928",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P4928",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P4928 · 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 P4928",
"url": "https://theoremdb.org/statements/P4928",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P4928",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T07:40:00+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":4928,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:00.651Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"01621e56-7728-4620-99c1-0150493dc42a","format_issues":null,"number":5558} |
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