{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BRMZA5ZZVRPV3ASHP7EMEFL2UW","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":"17dfc34571f4c05425f9b8b168a04ee865882fbc7fe3de903a1a84f26a2249dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-01-28T03:36:07Z","title_canon_sha256":"49ce0d69501d10d396a4a7cc510837ee80f1c4fa0be38e4a5cf45d35144719f0"},"schema_version":"1.0","source":{"id":"1001.5094","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.5094","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1001.5094v7","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5094","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"BRMZA5ZZVRPV","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BRMZA5ZZVRPV3ASH","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BRMZA5ZZ","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:c624e1692a8dc41fadaacfbc8ac7493b352e3b85a6c0d4e4263ebd33a2ad8a7e","target":"graph","created_at":"2026-05-18T03:57:37Z","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":"We investigate the structure of the characteristic polynomial det(xI-T) of a transition matrix T that is associated to a train track representative of a pseudo-Anosov map [F] acting on a surface. As a result we obtain three new polynomial invariants of [F], one of them being the product of the other two, and all three being divisors of det(xI-T). The degrees of the new polynomials are invariants of [F ] and we give simple formulas for computing them by a counting argument from an invariant train track. We give examples of genus 2 pseudo-Anosov maps having the same dilatation, and use our invar","authors_text":"Joan Birman, Keiko Kawamuro, Peter Brinkmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-01-28T03:36:07Z","title":"Polynomial invariants of pseudo-Anosov maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5094","kind":"arxiv","version":7},"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":"sha256:3688dcc2e36a9f44c16f937b33fce3137a61c12294170aa2a83ca5a2b2c6dc27","target":"record","created_at":"2026-05-18T03:57:37Z","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":"17dfc34571f4c05425f9b8b168a04ee865882fbc7fe3de903a1a84f26a2249dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-01-28T03:36:07Z","title_canon_sha256":"49ce0d69501d10d396a4a7cc510837ee80f1c4fa0be38e4a5cf45d35144719f0"},"schema_version":"1.0","source":{"id":"1001.5094","kind":"arxiv","version":7}},"canonical_sha256":"0c59907739ac5f5d82477fc8c2157aa599edb3828452d9bee5d1a30b844b117a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c59907739ac5f5d82477fc8c2157aa599edb3828452d9bee5d1a30b844b117a","first_computed_at":"2026-05-18T03:57:37.495308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:37.495308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KCI5zcKfzIIlgtlP5XKK5IBSptyX452yWXlBorU6hntTBLovKv8kvxr83WcTIYcz9tpMJGAO92061ct5HbP3Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:37.495939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.5094","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3688dcc2e36a9f44c16f937b33fce3137a61c12294170aa2a83ca5a2b2c6dc27","sha256:c624e1692a8dc41fadaacfbc8ac7493b352e3b85a6c0d4e4263ebd33a2ad8a7e"],"state_sha256":"b63b21f1d79517aaa68d047a2b29e3e5e44e7cf31eb0836531ac060020e78b1d"}