{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O7JXBJDMVKUTGZDBMCAFWSOSJV","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":"de862a3cb974b7d342fed0dbb56c836f9ea9febc658bcbef0aa980be5c92346a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-25T18:18:49Z","title_canon_sha256":"de90beeda5a44bf678b785593bbbda03d3365773d1fc3bdf87a5bc5b30767fa6"},"schema_version":"1.0","source":{"id":"1309.6598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6598","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6598v1","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6598","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"O7JXBJDMVKUT","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O7JXBJDMVKUTGZDB","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O7JXBJDM","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:85d2632d74498423e2c02f5998d9e8c4908ca1e998dfb78a6f74fba74bddf4a0","target":"graph","created_at":"2026-05-18T03:12:20Z","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 the dynamics of maps arising from the composition of two non-commuting involution on a K3 surface. These maps are a particular example of reversible maps, i.e., maps with a time reversing symmetry. The combinatorics of the cycle distribution of two non-commuting involutions on a finite phase space was studied by Roberts and Vivaldi. We show that the dynamical systems of these K3 surfaces satisfy the hypotheses of their results, providing a description of the cycle distribution of the rational points over finite fields. Furthermore, we extend the involutions to include the case where t","authors_text":"Benjamin Hutz, Joao Alberto de Faria","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-25T18:18:49Z","title":"Combinatorics of cycle lengths on Wehler K3 Surfaces over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6598","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":"sha256:4997f97001664143bf8a406dc5c46716ec99e313da84f9e53b07b07c6278617a","target":"record","created_at":"2026-05-18T03:12:20Z","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":"de862a3cb974b7d342fed0dbb56c836f9ea9febc658bcbef0aa980be5c92346a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-25T18:18:49Z","title_canon_sha256":"de90beeda5a44bf678b785593bbbda03d3365773d1fc3bdf87a5bc5b30767fa6"},"schema_version":"1.0","source":{"id":"1309.6598","kind":"arxiv","version":1}},"canonical_sha256":"77d370a46caaa933646160805b49d24d50f9ef0ab491d784426713e415706a09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77d370a46caaa933646160805b49d24d50f9ef0ab491d784426713e415706a09","first_computed_at":"2026-05-18T03:12:20.596623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:20.596623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ITYxN/yw0w1hf+g/93XxnaOmQjLrhJo0T74VyhBM43d1MsVbguib+g8b/J0Yclemk4TYEmdYSrN093r6lBZqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:20.597284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4997f97001664143bf8a406dc5c46716ec99e313da84f9e53b07b07c6278617a","sha256:85d2632d74498423e2c02f5998d9e8c4908ca1e998dfb78a6f74fba74bddf4a0"],"state_sha256":"40770dd1b2a0175114f4dd191e8b9db846fd00aca72d44a0555cb8fe7480dd18"}