{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6TPLQ45CJTMC6NBC3I3A2FZSYY","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":"2d619d0ae947e8f1bf13c19e5c73677b81634f4c5c1d921a530285901672291d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-26T08:34:15Z","title_canon_sha256":"feb1ee22d2e5df7f6c5ab2035121cf5cb0beabbfce54d607c0fcdf938d336419"},"schema_version":"1.0","source":{"id":"0905.4135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4135","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4135v1","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4135","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"6TPLQ45CJTMC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6TPLQ45CJTMC6NBC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6TPLQ45C","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:21b09e0fe46b06157e9d73b994c6520a8adf252dc30a8d8f2a795daaa6cc09f8","target":"graph","created_at":"2026-05-18T02:13:37Z","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 study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e., map-independent) distribution function R(x)=1-e^{-x}(1+x) has been conjectured to exist, for the normalized cycle lengths of the reduced map in the large field limit (J. A. G. Roberts and F. Vivaldi, Nonlinearity 18 (2005) 2171-2192). We show that these statistics correspond to those of a composition of two random involutions, having an appropriate number of f","authors_text":"Franco Vivaldi, John A. G. Roberts","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-26T08:34:15Z","title":"A combinatorial model for reversible rational maps over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4135","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":"sha256:7783feb9cc5cb707451492f2cb227ee47b6e4e90ea22136bdd775a769aec7753","target":"record","created_at":"2026-05-18T02:13:37Z","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":"2d619d0ae947e8f1bf13c19e5c73677b81634f4c5c1d921a530285901672291d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-26T08:34:15Z","title_canon_sha256":"feb1ee22d2e5df7f6c5ab2035121cf5cb0beabbfce54d607c0fcdf938d336419"},"schema_version":"1.0","source":{"id":"0905.4135","kind":"arxiv","version":1}},"canonical_sha256":"f4deb873a24cd82f3422da360d1732c628b5cc18f5e4b3f819f0c72ce3194ad0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4deb873a24cd82f3422da360d1732c628b5cc18f5e4b3f819f0c72ce3194ad0","first_computed_at":"2026-05-18T02:13:37.587084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:37.587084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5uookLwB2VHJMFtdMp+gTKC4ia7WPKdSNUkihLMYSiqDN4f9J6mBfaC2bEx1n+amizecxv3+bsygYa+A2TuRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:37.587710Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.4135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7783feb9cc5cb707451492f2cb227ee47b6e4e90ea22136bdd775a769aec7753","sha256:21b09e0fe46b06157e9d73b994c6520a8adf252dc30a8d8f2a795daaa6cc09f8"],"state_sha256":"f696a2dc82c024838d3018785d2d053185446f2d6a3edf8c293dc77af60847f6"}