{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:T3E2A32KI64CBX6PGIPD7TITYF","short_pith_number":"pith:T3E2A32K","canonical_record":{"source":{"id":"1904.04942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-09T22:49:55Z","cross_cats_sorted":["math.AG","math.DS"],"title_canon_sha256":"807bb4985fd994003649c23c8ceb88ce13ea0390c279cfa41c45f9eaa210e561","abstract_canon_sha256":"420e097382d407cdedf1937de3ef4a492929039b2549756a6fe7e87620d71519"},"schema_version":"1.0"},"canonical_sha256":"9ec9a06f4a47b820dfcf321e3fcd13c1433bd22e81d35337c7483f7532faa222","source":{"kind":"arxiv","id":"1904.04942","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04942","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04942v1","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04942","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"pith_short_12","alias_value":"T3E2A32KI64C","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T3E2A32KI64CBX6P","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T3E2A32K","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:T3E2A32KI64CBX6PGIPD7TITYF","target":"record","payload":{"canonical_record":{"source":{"id":"1904.04942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-09T22:49:55Z","cross_cats_sorted":["math.AG","math.DS"],"title_canon_sha256":"807bb4985fd994003649c23c8ceb88ce13ea0390c279cfa41c45f9eaa210e561","abstract_canon_sha256":"420e097382d407cdedf1937de3ef4a492929039b2549756a6fe7e87620d71519"},"schema_version":"1.0"},"canonical_sha256":"9ec9a06f4a47b820dfcf321e3fcd13c1433bd22e81d35337c7483f7532faa222","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:57.620667Z","signature_b64":"t5yJh57U4FW+SOYPuz0qfwmuKEw7COdbFm5Gj2UKk9NpTJyBvXuj5AEx1o6Pt3TNOaXeD6ktfEwJxnnVej0yAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ec9a06f4a47b820dfcf321e3fcd13c1433bd22e81d35337c7483f7532faa222","last_reissued_at":"2026-05-17T23:48:57.620211Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:57.620211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.04942","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"blUXegc+bWNZTPhs+pGQpbrbTEfEIKghvGxhCf1EJXdfdwSwFh05Un0/Bz/gsMXnex6BJBn/Kg7NnkVlNIBvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:55:56.018283Z"},"content_sha256":"613992db459079d3eccfaf5bb0eb9870f1ff4c954a4b007e42a0baa7e9a77a2b","schema_version":"1.0","event_id":"sha256:613992db459079d3eccfaf5bb0eb9870f1ff4c954a4b007e42a0baa7e9a77a2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:T3E2A32KI64CBX6PGIPD7TITYF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamically affine maps in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.NT","authors_text":"Gunther Cornelissen, Jakub Byszewski, Lois van der Meijden, Marc Houben","submitted_at":"2019-04-09T22:49:55Z","abstract_excerpt":"We study fixed points of iterates of dynamically affine maps (a generalisation of Latt\\`es maps) over algebraically closed fields of positive characteristic $p$. We present and study certain hypotheses that imply a dichotomy for the Artin-Mazur zeta function of the dynamical system: it is either rational or non-holonomic, depending on specific characteristics of the map. We also study the algebraicity of the so-called tame zeta function, the generating function for periodic points of order coprime to $p$. We then verify these hypotheses for dynamically affine maps on the projective line, gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04942","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TDetpiNBLJlU0/bb2qOsM0TX7lJzVRR5xHEJytA+0jhWnF547E5/XBVaCuAAggKCNFPUSCZLAniDVLnuIEaBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:55:56.018741Z"},"content_sha256":"d092ff21b4ab861c72c5b567688c5f354498d12120bd038fa1fe4ab6d9db6c39","schema_version":"1.0","event_id":"sha256:d092ff21b4ab861c72c5b567688c5f354498d12120bd038fa1fe4ab6d9db6c39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3E2A32KI64CBX6PGIPD7TITYF/bundle.json","state_url":"https://pith.science/pith/T3E2A32KI64CBX6PGIPD7TITYF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3E2A32KI64CBX6PGIPD7TITYF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T13:55:56Z","links":{"resolver":"https://pith.science/pith/T3E2A32KI64CBX6PGIPD7TITYF","bundle":"https://pith.science/pith/T3E2A32KI64CBX6PGIPD7TITYF/bundle.json","state":"https://pith.science/pith/T3E2A32KI64CBX6PGIPD7TITYF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3E2A32KI64CBX6PGIPD7TITYF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T3E2A32KI64CBX6PGIPD7TITYF","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":"420e097382d407cdedf1937de3ef4a492929039b2549756a6fe7e87620d71519","cross_cats_sorted":["math.AG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-09T22:49:55Z","title_canon_sha256":"807bb4985fd994003649c23c8ceb88ce13ea0390c279cfa41c45f9eaa210e561"},"schema_version":"1.0","source":{"id":"1904.04942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04942","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04942v1","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04942","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"pith_short_12","alias_value":"T3E2A32KI64C","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T3E2A32KI64CBX6P","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T3E2A32K","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:d092ff21b4ab861c72c5b567688c5f354498d12120bd038fa1fe4ab6d9db6c39","target":"graph","created_at":"2026-05-17T23:48:57Z","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 fixed points of iterates of dynamically affine maps (a generalisation of Latt\\`es maps) over algebraically closed fields of positive characteristic $p$. We present and study certain hypotheses that imply a dichotomy for the Artin-Mazur zeta function of the dynamical system: it is either rational or non-holonomic, depending on specific characteristics of the map. We also study the algebraicity of the so-called tame zeta function, the generating function for periodic points of order coprime to $p$. We then verify these hypotheses for dynamically affine maps on the projective line, gener","authors_text":"Gunther Cornelissen, Jakub Byszewski, Lois van der Meijden, Marc Houben","cross_cats":["math.AG","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-09T22:49:55Z","title":"Dynamically affine maps in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04942","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":"sha256:613992db459079d3eccfaf5bb0eb9870f1ff4c954a4b007e42a0baa7e9a77a2b","target":"record","created_at":"2026-05-17T23:48:57Z","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":"420e097382d407cdedf1937de3ef4a492929039b2549756a6fe7e87620d71519","cross_cats_sorted":["math.AG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-09T22:49:55Z","title_canon_sha256":"807bb4985fd994003649c23c8ceb88ce13ea0390c279cfa41c45f9eaa210e561"},"schema_version":"1.0","source":{"id":"1904.04942","kind":"arxiv","version":1}},"canonical_sha256":"9ec9a06f4a47b820dfcf321e3fcd13c1433bd22e81d35337c7483f7532faa222","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ec9a06f4a47b820dfcf321e3fcd13c1433bd22e81d35337c7483f7532faa222","first_computed_at":"2026-05-17T23:48:57.620211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:57.620211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t5yJh57U4FW+SOYPuz0qfwmuKEw7COdbFm5Gj2UKk9NpTJyBvXuj5AEx1o6Pt3TNOaXeD6ktfEwJxnnVej0yAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:57.620667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.04942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:613992db459079d3eccfaf5bb0eb9870f1ff4c954a4b007e42a0baa7e9a77a2b","sha256:d092ff21b4ab861c72c5b567688c5f354498d12120bd038fa1fe4ab6d9db6c39"],"state_sha256":"6683c71758facd1bc7aa07fe1229a911f7cd3918ce304af116b655363207995f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TerIfKtJC7iZva0QByDn03v6oLFe4KszM/twDjpDi+wdUIxitYgfHgWvzAdXNwc7jDaLMJR6xr+9BmQssDRyAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:55:56.020833Z","bundle_sha256":"73552ba33f4d4904259c8aa84a93d838e1ac3fcb4f8ad62b62a498f0afe85528"}}