{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BDUGMFV5LJRRW2NJI3DH75G62T","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":"7792be111b86ceee5d9a7de6f9b8ff1e1c3046d29820bfba9d18cbd8ccbef06a","cross_cats_sorted":["math.AG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-11T18:25:18Z","title_canon_sha256":"70e4269a51e2f71a530929ac8980a5957fa3a84e405095bf446f1ebe8551acc6"},"schema_version":"1.0","source":{"id":"1307.3205","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3205","created_at":"2026-05-18T03:00:26Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3205v2","created_at":"2026-05-18T03:00:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3205","created_at":"2026-05-18T03:00:26Z"},{"alias_kind":"pith_short_12","alias_value":"BDUGMFV5LJRR","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BDUGMFV5LJRRW2NJ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BDUGMFV5","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:419034501a922b64d94d19ee4f2f3194b8faae495e7fdd3a31a0349060a5d8a2","target":"graph","created_at":"2026-05-18T03:00:26Z","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 dynamical systems induced by birational automorphisms on smooth cubic surfaces defined over a number field $K$. In particular we are interested in the product of non-commuting birational Geiser involutions of the cubic surface. We present results describing the sets of $K$ and $\\bar{K}$-periodic points of the system, and give a necessary and sufficient condition for a dynamical local-global property called strong residual periodicity. Finally, we give a dynamical result relating to the Mordell--Weil problem on cubic surfaces.","authors_text":"Solomon Vishkautsan","cross_cats":["math.AG","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-11T18:25:18Z","title":"Arithmetic dynamics on smooth cubic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3205","kind":"arxiv","version":2},"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":"sha256:226628feb39bf62613d5fb3dd47055027bdf0a2b53a75f7aa7e2e5a8e91c30b5","target":"record","created_at":"2026-05-18T03:00:26Z","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":"7792be111b86ceee5d9a7de6f9b8ff1e1c3046d29820bfba9d18cbd8ccbef06a","cross_cats_sorted":["math.AG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-11T18:25:18Z","title_canon_sha256":"70e4269a51e2f71a530929ac8980a5957fa3a84e405095bf446f1ebe8551acc6"},"schema_version":"1.0","source":{"id":"1307.3205","kind":"arxiv","version":2}},"canonical_sha256":"08e86616bd5a631b69a946c67ff4ded4cf21679fcfe7dc6ed3d05697a9f86983","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08e86616bd5a631b69a946c67ff4ded4cf21679fcfe7dc6ed3d05697a9f86983","first_computed_at":"2026-05-18T03:00:26.135997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:26.135997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LfNcDhmKnnPaDUv7irUDdzBToPDeK8AyDi6CN9oDJ1IjozzWuhfQ8vRqb99hjRwZRrZVpAoO8bJnRvSpQ10SDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:26.137039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3205","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:226628feb39bf62613d5fb3dd47055027bdf0a2b53a75f7aa7e2e5a8e91c30b5","sha256:419034501a922b64d94d19ee4f2f3194b8faae495e7fdd3a31a0349060a5d8a2"],"state_sha256":"1c9d678116c7c6d82c5246aa9e7569778e00b734135b2dc9869d2665bd6f6f20"}