{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:2FAAX3TGGGTBZVZZ4LLSPKSGOD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2f949605f8b2f0f6c3e8e28fe556415549bb6283655131a84d0373fc1d224b71","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.CO","submitted_at":"2007-10-25T18:07:34Z","title_canon_sha256":"af5edcfa0592b589b061121a9e01307e15f77abd6f7c77f3af71fb3876c69622"},"schema_version":"1.0","source":{"id":"0710.4792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.4792","created_at":"2026-05-18T03:34:12Z"},{"alias_kind":"arxiv_version","alias_value":"0710.4792v1","created_at":"2026-05-18T03:34:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.4792","created_at":"2026-05-18T03:34:12Z"},{"alias_kind":"pith_short_12","alias_value":"2FAAX3TGGGTB","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"2FAAX3TGGGTBZVZZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"2FAAX3TG","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:897395f9c6e7744d369d268c4a0ba1cfa11a8dd5c1960975c13365429e06ce5e","target":"graph","created_at":"2026-05-18T03:34:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let M_n be the n! * n! matrix indexed by permutations of S_n, defined by M_n(sigma,tau)=1 if every descent of tau^{-1} is also a descent of sigma, and M_n(sigma,tau)=0 otherwise. We prove the following result, conjectured by P. Dehornoy: the characteristic polynomial P_n(x)=|xI-M_n| of M_n divides P_{n+1}(x) in Z[x].","authors_text":"Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon","cross_cats":["math.GR"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2007-10-25T18:07:34Z","title":"Sur une conjecture de Dehornoy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.4792","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:79166724aac850f0586c7f9b04651bde09a21bc3320a22a050d37d34b3abdd80","target":"record","created_at":"2026-05-18T03:34:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2f949605f8b2f0f6c3e8e28fe556415549bb6283655131a84d0373fc1d224b71","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.CO","submitted_at":"2007-10-25T18:07:34Z","title_canon_sha256":"af5edcfa0592b589b061121a9e01307e15f77abd6f7c77f3af71fb3876c69622"},"schema_version":"1.0","source":{"id":"0710.4792","kind":"arxiv","version":1}},"canonical_sha256":"d1400bee6631a61cd739e2d727aa4670e05d8a6eeab809c4733219b02f2020f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1400bee6631a61cd739e2d727aa4670e05d8a6eeab809c4733219b02f2020f3","first_computed_at":"2026-05-18T03:34:12.578274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:12.578274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"unI1HSMVaJygodKy1akBCwk9cTHOAr6fVrPE5HnWFrJveQ0QizDawPbPMPVhfq6CXKu/Eouil9i39Qe2eScTAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:12.578751Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.4792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79166724aac850f0586c7f9b04651bde09a21bc3320a22a050d37d34b3abdd80","sha256:897395f9c6e7744d369d268c4a0ba1cfa11a8dd5c1960975c13365429e06ce5e"],"state_sha256":"039320246ac82acc8772359b1cc1c22258771514958214fd3614492b10c7e78e"}