{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7LMPQYGGJ3B65WKLWTK3IZ6RGD","short_pith_number":"pith:7LMPQYGG","canonical_record":{"source":{"id":"1210.6246","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-23T14:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"175b9b16bda74d27ba41e595138ca957bb3fb1961bbe6c19eb6bdcc9c04f7fb6","abstract_canon_sha256":"b2d37a76bed018035a00c52b685ec66f0efd7179f0a0b7ed09b961436b0a9e03"},"schema_version":"1.0"},"canonical_sha256":"fad8f860c64ec3eed94bb4d5b467d130cb67c949ae234edeae346aa788899ca3","source":{"kind":"arxiv","id":"1210.6246","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6246","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6246v3","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6246","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"7LMPQYGGJ3B6","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7LMPQYGGJ3B65WKL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7LMPQYGG","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7LMPQYGGJ3B65WKLWTK3IZ6RGD","target":"record","payload":{"canonical_record":{"source":{"id":"1210.6246","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-23T14:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"175b9b16bda74d27ba41e595138ca957bb3fb1961bbe6c19eb6bdcc9c04f7fb6","abstract_canon_sha256":"b2d37a76bed018035a00c52b685ec66f0efd7179f0a0b7ed09b961436b0a9e03"},"schema_version":"1.0"},"canonical_sha256":"fad8f860c64ec3eed94bb4d5b467d130cb67c949ae234edeae346aa788899ca3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:24.356551Z","signature_b64":"7DUyvys215uRSDSkDMFM2uCg1df/0NZZVb/HgtOS1u+qaDGsKVP8xDgmJz1WTyObZ4PukPcxU5mYWewvTTC5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fad8f860c64ec3eed94bb4d5b467d130cb67c949ae234edeae346aa788899ca3","last_reissued_at":"2026-05-18T03:19:24.355896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:24.355896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.6246","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bi5wIr6zO8maZaR59k4yvFBj7cOBAuk5yyobWEQF6KddBkbOnpYCrrD0D6c5WypufwGdYqcZ+FlxNe7pptdsDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:38:57.408201Z"},"content_sha256":"9f8a0f6ae97ab3082ba59e6071baf2e1ecf0faafe2b4d1e2637e9fdc55c23b64","schema_version":"1.0","event_id":"sha256:9f8a0f6ae97ab3082ba59e6071baf2e1ecf0faafe2b4d1e2637e9fdc55c23b64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7LMPQYGGJ3B65WKLWTK3IZ6RGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Determination of all rational preperiodic points for morphisms of PN","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Benjamin Hutz","submitted_at":"2012-10-23T14:27:52Z","abstract_excerpt":"For a morphism $f:\\P^N \\to \\P^N$, the points whose forward orbit by $f$ is finite are called preperiodic points for $f$. This article presents an algorithm to effectively determine all the rational preperiodic points for $f$ defined over a given number field $K$. This algorithm is implemented in the open-source software Sage for $\\Q$. Additionally, the notion of a dynatomic zero-cycle is generalized to preperiodic points. Along with examining their basic properties, these generalized dynatomic cycles are shown to be effective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6246","kind":"arxiv","version":3},"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":"2026-05-18T03:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDnpjkQJ5XjEteBWk79+PYUjDAtGiKx+R2UZcCUi0wxTPusuRV/nH57dhCABNVeRMfMW/CZPXnPMi7cVhpBiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:38:57.408574Z"},"content_sha256":"c682d0aa1b656e646cb1ac1448766717a842b5369c45dda7186f9e0c520c075d","schema_version":"1.0","event_id":"sha256:c682d0aa1b656e646cb1ac1448766717a842b5369c45dda7186f9e0c520c075d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7LMPQYGGJ3B65WKLWTK3IZ6RGD/bundle.json","state_url":"https://pith.science/pith/7LMPQYGGJ3B65WKLWTK3IZ6RGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7LMPQYGGJ3B65WKLWTK3IZ6RGD/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":"2026-06-20T05:38:57Z","links":{"resolver":"https://pith.science/pith/7LMPQYGGJ3B65WKLWTK3IZ6RGD","bundle":"https://pith.science/pith/7LMPQYGGJ3B65WKLWTK3IZ6RGD/bundle.json","state":"https://pith.science/pith/7LMPQYGGJ3B65WKLWTK3IZ6RGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7LMPQYGGJ3B65WKLWTK3IZ6RGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7LMPQYGGJ3B65WKLWTK3IZ6RGD","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":"b2d37a76bed018035a00c52b685ec66f0efd7179f0a0b7ed09b961436b0a9e03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-23T14:27:52Z","title_canon_sha256":"175b9b16bda74d27ba41e595138ca957bb3fb1961bbe6c19eb6bdcc9c04f7fb6"},"schema_version":"1.0","source":{"id":"1210.6246","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6246","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6246v3","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6246","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"7LMPQYGGJ3B6","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7LMPQYGGJ3B65WKL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7LMPQYGG","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:c682d0aa1b656e646cb1ac1448766717a842b5369c45dda7186f9e0c520c075d","target":"graph","created_at":"2026-05-18T03:19:24Z","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":"For a morphism $f:\\P^N \\to \\P^N$, the points whose forward orbit by $f$ is finite are called preperiodic points for $f$. This article presents an algorithm to effectively determine all the rational preperiodic points for $f$ defined over a given number field $K$. This algorithm is implemented in the open-source software Sage for $\\Q$. Additionally, the notion of a dynatomic zero-cycle is generalized to preperiodic points. Along with examining their basic properties, these generalized dynatomic cycles are shown to be effective.","authors_text":"Benjamin Hutz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-23T14:27:52Z","title":"Determination of all rational preperiodic points for morphisms of PN"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6246","kind":"arxiv","version":3},"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":"sha256:9f8a0f6ae97ab3082ba59e6071baf2e1ecf0faafe2b4d1e2637e9fdc55c23b64","target":"record","created_at":"2026-05-18T03:19:24Z","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":"b2d37a76bed018035a00c52b685ec66f0efd7179f0a0b7ed09b961436b0a9e03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-23T14:27:52Z","title_canon_sha256":"175b9b16bda74d27ba41e595138ca957bb3fb1961bbe6c19eb6bdcc9c04f7fb6"},"schema_version":"1.0","source":{"id":"1210.6246","kind":"arxiv","version":3}},"canonical_sha256":"fad8f860c64ec3eed94bb4d5b467d130cb67c949ae234edeae346aa788899ca3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fad8f860c64ec3eed94bb4d5b467d130cb67c949ae234edeae346aa788899ca3","first_computed_at":"2026-05-18T03:19:24.355896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:24.355896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7DUyvys215uRSDSkDMFM2uCg1df/0NZZVb/HgtOS1u+qaDGsKVP8xDgmJz1WTyObZ4PukPcxU5mYWewvTTC5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:24.356551Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6246","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f8a0f6ae97ab3082ba59e6071baf2e1ecf0faafe2b4d1e2637e9fdc55c23b64","sha256:c682d0aa1b656e646cb1ac1448766717a842b5369c45dda7186f9e0c520c075d"],"state_sha256":"8e4d26e8e6d94a79aa0ce55113be541c2795cf234817605bb7dabbffdb95797a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fItywQps4xA+He28Wo1amdH0cqP+yoJFLvGJkvGrIcKnZF9cxmc8k0DYL4r36R2GIee3E5sbimNKYBajr3rZAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:38:57.410461Z","bundle_sha256":"03a9832f58aec503fdd6b5ae27ad7ab9c1addd4739e530ffbfa4ca62e933f738"}}