Prüft behaupteten gemeinsamen Rückkehrperioden-GGT und kanonische zyklische Phas...

{ "body": { "artifact": { "claimed_phases": [ 0, 1, 2, 1, 2, 0 ], "claims": { "aperiodic": false, "directed_edges": 8, "period": 3, "vertices": 6 }, "edges": [ [ 0, 1 ], [ 1, 2 ], [ 2, 0 ], [ 0, 3 ], [ 3, 4 ], [ 4, 0 ], [ 4, 5 ], [ 5, 3 ] ], "vertices": 6 } }, "bodyType": "json", "method": "POST", "type": "http" }

{ "example": { "billable": true, "findings": [ { "confidence": 100, "evidence": [], "limits": [ "Levin/Peres Markov Chains and Mixing Times2nded §1.3 Lemma1.6 and Exercise1.6: irreducible finite support has common period equal gcd of positive return-walk lengths, partition into cyclic classes advancing+1 per edge. Own graph support algorithm: forward/reverse reachability, exact gcd of depth[u]+1−depth[v] over all edges, residue-class correspondence. No Markov/graph SDK or probability solver.", "Closed strongly connected directed support graph with positive outdegree at every vertex,1..64anonymous index vertices. Unit edge traversal steps; no weights/delays/probabilities needed. Duplicate edge entries have support-set semantics; selfloops allowed and force period1. Reducible graphs/empty return support outside premise=>whole unknown, no fabricated zero period.", "Claimed cyclic phases are canonical walk-length residues from vertex0 modulo computed period, with phase0at root. Edge order and chosen spanning traversal do not change these residues. Every edge advances one phase. Exact discrete period/phase/count claims including wrong fractions compare without tolerance.", "Period is combinatorial return-time support, not target-hit probability, actual runtime oscillation, a measured mixing time, stationary distribution, convergence guarantee or workflow safety verdict. No extra service per component/dimension/transition weight.", "Only bounded vertex/edge/period counts and booleans returned. No edge list, phase IDs, raw numeric claims or exceptions returned. No customer/contact/URL values, identity or legal/security judgments. At most4096input edges." ], "module": "irreducible-directed-walk-period-cyclic-classes", "state": "not_observed", "value": { "aperiodic": false, "claim_mismatches": 0, "claims_match": true, "directed_edges": 8, "period": 3, "phase_claim_matches": true, "vertices": 6 }, "warnings": [] } ], "known_count": 1, "scope": { "contact_values_returned": false, "network": false, "supplied_artifact_only": true }, "warnings": [] }, "type": "json" }