{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:L3F24RTIX6MZPJXXYJEKVYBFKB","short_pith_number":"pith:L3F24RTI","canonical_record":{"source":{"id":"1403.2293","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-10T16:27:34Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"e619db6e0d6075682ddb768d0241348af5c96cbff8ad63d0dbeec30b05270116","abstract_canon_sha256":"2f96a6b5c01cbb45220089d5a7913bec68cbf5787c5b078026f526b1bcaae799"},"schema_version":"1.0"},"canonical_sha256":"5ecbae4668bf9997a6f7c248aae025507498174f516370e633083fac04d877fe","source":{"kind":"arxiv","id":"1403.2293","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2293","created_at":"2026-05-18T01:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2293v5","created_at":"2026-05-18T01:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2293","created_at":"2026-05-18T01:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"L3F24RTIX6MZ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L3F24RTIX6MZPJXX","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L3F24RTI","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:L3F24RTIX6MZPJXXYJEKVYBFKB","target":"record","payload":{"canonical_record":{"source":{"id":"1403.2293","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-10T16:27:34Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"e619db6e0d6075682ddb768d0241348af5c96cbff8ad63d0dbeec30b05270116","abstract_canon_sha256":"2f96a6b5c01cbb45220089d5a7913bec68cbf5787c5b078026f526b1bcaae799"},"schema_version":"1.0"},"canonical_sha256":"5ecbae4668bf9997a6f7c248aae025507498174f516370e633083fac04d877fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:06.943686Z","signature_b64":"HQiYnj6BDZOPi/BEX5jnGny6852SCbZ4exloapU8cHuB97uhNdfh5CQxO5VzYHsmHVj0fYdT0MDtCnrobcRdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ecbae4668bf9997a6f7c248aae025507498174f516370e633083fac04d877fe","last_reissued_at":"2026-05-18T01:33:06.942949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:06.942949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.2293","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B40cUvo57TTBgX5EKncMOTB7NVaeoXpB2lVxHCEXUVe4DVbS+eNuNiTmQIEsXPBdppiYoMOmuCNVoQ58sugaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:06:38.969694Z"},"content_sha256":"b63c47cc21a7252f9b66ace8509b2c331957f3eb0b7578dc0fdcfb425bfd23f3","schema_version":"1.0","event_id":"sha256:b63c47cc21a7252f9b66ace8509b2c331957f3eb0b7578dc0fdcfb425bfd23f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:L3F24RTIX6MZPJXXYJEKVYBFKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Preperiodic points for rational functions defined over a global field in terms of good reductions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Jung-Kyu Canci, Laura Paladino","submitted_at":"2014-03-10T16:27:34Z","abstract_excerpt":"Let $\\phi$ be an endomorphism of the projective line defined over a global field $K$. We prove a bound for the cardinality of the set of $K$-rational preperiodic points for $\\phi$ in terms of the number of places of bad reduction. The result is completely new in the function fields case and it is an improvement of the number fields case. An important tool is an $S$-unit equation theorem in 2 variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2293","kind":"arxiv","version":5},"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":"2026-05-18T01:33:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfvUeeYwr1ENdjKAePAgF8D6bSq77EHh9mBnYLWXuHpCf6BttVaoL1Izn/4FC0DZanoX5nDP3H9DVSDxzbynBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:06:38.970032Z"},"content_sha256":"754d44e143d47f0d7d71386af3a3baf032cf722e6e68686fa7d43b0c14c897c5","schema_version":"1.0","event_id":"sha256:754d44e143d47f0d7d71386af3a3baf032cf722e6e68686fa7d43b0c14c897c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3F24RTIX6MZPJXXYJEKVYBFKB/bundle.json","state_url":"https://pith.science/pith/L3F24RTIX6MZPJXXYJEKVYBFKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3F24RTIX6MZPJXXYJEKVYBFKB/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":"2026-06-24T09:06:38Z","links":{"resolver":"https://pith.science/pith/L3F24RTIX6MZPJXXYJEKVYBFKB","bundle":"https://pith.science/pith/L3F24RTIX6MZPJXXYJEKVYBFKB/bundle.json","state":"https://pith.science/pith/L3F24RTIX6MZPJXXYJEKVYBFKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3F24RTIX6MZPJXXYJEKVYBFKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L3F24RTIX6MZPJXXYJEKVYBFKB","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":"2f96a6b5c01cbb45220089d5a7913bec68cbf5787c5b078026f526b1bcaae799","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-10T16:27:34Z","title_canon_sha256":"e619db6e0d6075682ddb768d0241348af5c96cbff8ad63d0dbeec30b05270116"},"schema_version":"1.0","source":{"id":"1403.2293","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2293","created_at":"2026-05-18T01:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2293v5","created_at":"2026-05-18T01:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2293","created_at":"2026-05-18T01:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"L3F24RTIX6MZ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L3F24RTIX6MZPJXX","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L3F24RTI","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:754d44e143d47f0d7d71386af3a3baf032cf722e6e68686fa7d43b0c14c897c5","target":"graph","created_at":"2026-05-18T01:33:06Z","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":"Let $\\phi$ be an endomorphism of the projective line defined over a global field $K$. We prove a bound for the cardinality of the set of $K$-rational preperiodic points for $\\phi$ in terms of the number of places of bad reduction. The result is completely new in the function fields case and it is an improvement of the number fields case. An important tool is an $S$-unit equation theorem in 2 variables.","authors_text":"Jung-Kyu Canci, Laura Paladino","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-10T16:27:34Z","title":"Preperiodic points for rational functions defined over a global field in terms of good reductions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2293","kind":"arxiv","version":5},"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:b63c47cc21a7252f9b66ace8509b2c331957f3eb0b7578dc0fdcfb425bfd23f3","target":"record","created_at":"2026-05-18T01:33:06Z","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":"2f96a6b5c01cbb45220089d5a7913bec68cbf5787c5b078026f526b1bcaae799","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-10T16:27:34Z","title_canon_sha256":"e619db6e0d6075682ddb768d0241348af5c96cbff8ad63d0dbeec30b05270116"},"schema_version":"1.0","source":{"id":"1403.2293","kind":"arxiv","version":5}},"canonical_sha256":"5ecbae4668bf9997a6f7c248aae025507498174f516370e633083fac04d877fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ecbae4668bf9997a6f7c248aae025507498174f516370e633083fac04d877fe","first_computed_at":"2026-05-18T01:33:06.942949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:06.942949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HQiYnj6BDZOPi/BEX5jnGny6852SCbZ4exloapU8cHuB97uhNdfh5CQxO5VzYHsmHVj0fYdT0MDtCnrobcRdCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:06.943686Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2293","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b63c47cc21a7252f9b66ace8509b2c331957f3eb0b7578dc0fdcfb425bfd23f3","sha256:754d44e143d47f0d7d71386af3a3baf032cf722e6e68686fa7d43b0c14c897c5"],"state_sha256":"79a3cf2b6dd315733b185ceac00d8f6b96408fc0ef433738c6dce3bc5adad265"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EHbnGqG+cf3lrPzNgp0tsLrF8t2AsWQJOevY2ASATlrl6mG1j0P4AeU0yG6gfQskvbW3Qs96wkyUph8pKfJJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T09:06:38.971956Z","bundle_sha256":"7a6772f1b8c615d06f4afedc32ec169fbfe220a86166124d2ea43a797b4db7bf"}}