Prüft die exakt behauptete Zahl zulässiger beschrifteter Graphfärbungen unter al...

{ "body": { "artifact": { "claimed_cardinality": "30", "claims": { "connected_components": 1, "distinct_nonloop_edges": 5, "loop_vertices": 0, "proper_colorings_exist": true, "unique_proper_coloring": false, "vertices": 5 }, "edges": [ [ 0, 1 ], [ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 0 ] ], "number_of_colors": 3, "vertex_count": 5 } }, "bodyType": "json", "method": "POST", "type": "http" }

{ "example": { "billable": true, "findings": [ { "confidence": 100, "evidence": [], "limits": [ "Chromatic-polynomial evaluation: exact number of maps from fixed labelled graph vertices to q labelled colors such that endpoints of every edge differ. A loop gives0; duplicate/parallel undirected edges impose the same constraint once; empty graph on0vertices has one empty coloring even forq0.", "Own dynamic programming over vertex subsets: partition into independent color classes using the unique block containing the lowest remaining vertex; weight each k-block partition by q(q-1)...(q-k+1). No enumeration over q^n assignments and no final-result SDK. No graph automorphism quotient, symmetry deduplication or unconstrained Burnside orbit count.", "Maximum10vertices/256edge records, q0..2^31-1. Exact BigInt cardinality and claimed decimal integer comparison; exact counters/booleans. Does not choose a coloring or minimum color count, prove an external scheduling/security/legal property, or return color/token identities.", "Only bounded structural counters and boolean facts leave the adapter. No number-of-colors premise, actual/claimed cardinality, raw edges/assignments, contact values or exception text returned." ], "module": "graph-chromatic-proper-coloring-cardinality", "state": "not_observed", "value": { "claim_mismatches": 0, "claimed_cardinality_match": true, "claims_match": true, "connected_components": 1, "distinct_nonloop_edges": 5, "loop_vertices": 0, "proper_colorings_exist": true, "unique_proper_coloring": false, "vertices": 5 }, "warnings": [] } ], "known_count": 1, "scope": { "contact_values_returned": false, "network": false, "supplied_artifact_only": true }, "warnings": [] }, "type": "json" }