Prüft behauptete Realisierbarkeit vorgegebener Zeilen-/Spaltengrade als0/1-Matri...

{ "body": { "artifact": { "claimed_conjugate": [ 4, 2, 2 ], "claimed_realizable": false, "claimed_slacks": [ 0, -2, 0 ], "claims": { "column_vertices": 4, "inequality_failures": 1, "invalid_degree_entries": 0, "row_vertices": 3 }, "column_degrees": [ 3, 3, 1, 1 ], "row_degrees": [ 4, 4, 0 ] } }, "bodyType": "json", "method": "POST", "type": "http" }

{ "example": { "billable": true, "findings": [ { "confidence": 100, "evidence": [], "limits": [ "Gale–Ryser theorem, MFCS2022 paper14 §2.2 Theorem3: sorted left-degree prefix sums must not exceed prefixes of the conjugate right-degree sequence, and total degrees must agree. Own histogram/suffix conjugation and majorization scan, no flow/matching SDK. Bound degrees must fit opposite partition size.", "Existence of a SIMPLE bipartite graph / zero-one matrix with these exact row and column degrees. No multiplicity greater than1 per pair. No selected matrix, canonical realization, labelled-edge assignment, graph drawing, optimal allocation or number of realizations asserted. One coupled conjugation/majorization characterization, not extra row/column/parameter offers.", "Given independent nonnegative integer degree arrays, each at most64vertices and each degree<=2^32−1. Sorting changes no labels used in result. Out-of-opposite-range degrees and unequal totals are known nonrealizability, not unknown. Empty sides and zero degrees supported. Fractional/negative input degree is outside the integer profile and makes whole finding unknown.", "Caller realizability/conjugate/slack sequences are claims, compared exactly, including wrong fractional discrete claims. No tolerance/rounding. Only bounded counts/booleans returned; degree totals, prefix sums, slacks, vertex degrees, caller claims or exceptions never returned, even when an integer is phone-shaped. No contact/identity/security judgment." ], "module": "gale-ryser-binary-bimatrix-degree-realizability", "state": "not_observed", "value": { "claim_mismatches": 0, "claims_match": true, "column_vertices": 4, "conjugate_claim_matches": true, "degree_sums_equal": true, "inequality_failures": 1, "invalid_degree_entries": 0, "majorization_claim_matches": true, "realizability_claim_matches": true, "realizable": false, "row_vertices": 3 }, "warnings": [] } ], "known_count": 1, "scope": { "contact_values_returned": false, "network": false, "supplied_artifact_only": true }, "warnings": [] }, "type": "json" }