{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NUMHMBRATWCSSEMJAPGIHPH6RD","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":"c9ded87ffb15101287077b95a1c9fe882490d656dffb73e8d72a35dbc471123a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-02T04:56:55Z","title_canon_sha256":"7321aa87f4894fc8042e2bc641b02566f46c602848df5c10e21e4ac69c34bffe"},"schema_version":"1.0","source":{"id":"1202.0362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0362","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0362v2","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0362","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"pith_short_12","alias_value":"NUMHMBRATWCS","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NUMHMBRATWCSSEMJ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NUMHMBRA","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:4a01ac8b1fb58d5445c936a29e3cf6b27def9869f4ae4559f3fdd583af2c1b05","target":"graph","created_at":"2026-05-18T03:55:46Z","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 rationality of the Artin-Mazur zeta function of a dynamical system defined by a polynomial self-map of A^1(k), where k is the algebraic closure of the finite field F_p. The zeta functions of the maps f(x)=x^m for (p,m)=1 and f(x)=x^{p^m}+ax for nonzero a in F_{p^m}, p odd, are shown to be transcendental.","authors_text":"Andrew Bridy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-02T04:56:55Z","title":"Transcendence of the Artin-Mazur Zeta Function for Polynomial Maps of A^1(F_p)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0362","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":"sha256:232eb4069af73f925f72c4513594b75c81b6213d925bb8d926911d3dcc3aa33b","target":"record","created_at":"2026-05-18T03:55:46Z","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":"c9ded87ffb15101287077b95a1c9fe882490d656dffb73e8d72a35dbc471123a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-02T04:56:55Z","title_canon_sha256":"7321aa87f4894fc8042e2bc641b02566f46c602848df5c10e21e4ac69c34bffe"},"schema_version":"1.0","source":{"id":"1202.0362","kind":"arxiv","version":2}},"canonical_sha256":"6d187606209d8529118903cc83bcfe88e9e19466e4f10cabc4d9da36ec39bfe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d187606209d8529118903cc83bcfe88e9e19466e4f10cabc4d9da36ec39bfe5","first_computed_at":"2026-05-18T03:55:46.540519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:46.540519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ClsRAygAWU1fUNEC4vtjMfzfsVWkQT7M2t57aElJATj6W32m7e26YihPGKENmjVqeW5jos8G10Ia8djogASACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:46.540899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:232eb4069af73f925f72c4513594b75c81b6213d925bb8d926911d3dcc3aa33b","sha256:4a01ac8b1fb58d5445c936a29e3cf6b27def9869f4ae4559f3fdd583af2c1b05"],"state_sha256":"eee1795db92165b39e2903dc8237358dae1647616069091cf051297fa612825d"}