{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IYDIPHTCBSNFZNOJBGQMVFHQ2P","short_pith_number":"pith:IYDIPHTC","canonical_record":{"source":{"id":"1011.5155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-23T16:40:01Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3493f34def33123133d847d235729610cbaae4cabae2b6039bb352d4dc63675b","abstract_canon_sha256":"7804e7de6fc08bc81891b8875ea8a33bec07f54df8fbb3ea52306e0409809361"},"schema_version":"1.0"},"canonical_sha256":"4606879e620c9a5cb5c909a0ca94f0d3d2443e2df06919c5fdc950bfcbcabd11","source":{"kind":"arxiv","id":"1011.5155","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5155","created_at":"2026-05-18T04:24:27Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5155v3","created_at":"2026-05-18T04:24:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5155","created_at":"2026-05-18T04:24:27Z"},{"alias_kind":"pith_short_12","alias_value":"IYDIPHTCBSNF","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IYDIPHTCBSNFZNOJ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IYDIPHTC","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IYDIPHTCBSNFZNOJBGQMVFHQ2P","target":"record","payload":{"canonical_record":{"source":{"id":"1011.5155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-23T16:40:01Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3493f34def33123133d847d235729610cbaae4cabae2b6039bb352d4dc63675b","abstract_canon_sha256":"7804e7de6fc08bc81891b8875ea8a33bec07f54df8fbb3ea52306e0409809361"},"schema_version":"1.0"},"canonical_sha256":"4606879e620c9a5cb5c909a0ca94f0d3d2443e2df06919c5fdc950bfcbcabd11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:27.440472Z","signature_b64":"O62LgeRjjtsTXT6iGNrQEcLlTky2E9fSKRi6VB3Z5EnmF9AokAO60tNWOWk27xAPiK07X8heEuI6YdIwQGmaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4606879e620c9a5cb5c909a0ca94f0d3d2443e2df06919c5fdc950bfcbcabd11","last_reissued_at":"2026-05-18T04:24:27.439886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:27.439886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.5155","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":"2026-05-18T04:24:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rju7kofiqWFTZwzT/qYazX5po/vRTc7MhxxIrlvo8Bts0vsJEhATAMHeviZIgsUCk+mywoecB4OJwg+KoIr3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:38:22.699297Z"},"content_sha256":"8ad3033d9f89e63d4a8a974cb84bb3fabd6de9cca9b3991f14cd1a8982c3cb6c","schema_version":"1.0","event_id":"sha256:8ad3033d9f89e63d4a8a974cb84bb3fabd6de9cca9b3991f14cd1a8982c3cb6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IYDIPHTCBSNFZNOJBGQMVFHQ2P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effectivity of Dynatomic cycles for morphisms of projective varieties using deformation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Benjamin Hutz","submitted_at":"2010-11-23T16:40:01Z","abstract_excerpt":"Given an endomorphism of a projective variety, by intersecting the graph and the diagonal varieties we can determine the set of periodic points. In an effort to determine the periodic points of a given minimal period, we follow a construction similar to cyclotomic polynomials. The resulting zero-cycle is called a dynatomic cycle and the points in its support are called formal periodic points. This article gives a proof of the effectivity of dynatomic cycles for morphisms of projective varieties using methods from deformation theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5155","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":"2026-05-18T04:24:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8clLHykT/4uPcmU8YTBK96Pb0DwkQ07Bn6mRHdlCTAdARRMGe8ese7VZ1W3XxCFW1S/tn23wTcwczgO8akX9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:38:22.699669Z"},"content_sha256":"9f3daf03ffe6d66c436b2ba58033ef6dddbcf24fc143025ad2dd80f40558fbfe","schema_version":"1.0","event_id":"sha256:9f3daf03ffe6d66c436b2ba58033ef6dddbcf24fc143025ad2dd80f40558fbfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IYDIPHTCBSNFZNOJBGQMVFHQ2P/bundle.json","state_url":"https://pith.science/pith/IYDIPHTCBSNFZNOJBGQMVFHQ2P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IYDIPHTCBSNFZNOJBGQMVFHQ2P/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":"2026-06-20T06:38:22Z","links":{"resolver":"https://pith.science/pith/IYDIPHTCBSNFZNOJBGQMVFHQ2P","bundle":"https://pith.science/pith/IYDIPHTCBSNFZNOJBGQMVFHQ2P/bundle.json","state":"https://pith.science/pith/IYDIPHTCBSNFZNOJBGQMVFHQ2P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IYDIPHTCBSNFZNOJBGQMVFHQ2P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IYDIPHTCBSNFZNOJBGQMVFHQ2P","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":"7804e7de6fc08bc81891b8875ea8a33bec07f54df8fbb3ea52306e0409809361","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-23T16:40:01Z","title_canon_sha256":"3493f34def33123133d847d235729610cbaae4cabae2b6039bb352d4dc63675b"},"schema_version":"1.0","source":{"id":"1011.5155","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5155","created_at":"2026-05-18T04:24:27Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5155v3","created_at":"2026-05-18T04:24:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5155","created_at":"2026-05-18T04:24:27Z"},{"alias_kind":"pith_short_12","alias_value":"IYDIPHTCBSNF","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IYDIPHTCBSNFZNOJ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IYDIPHTC","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:9f3daf03ffe6d66c436b2ba58033ef6dddbcf24fc143025ad2dd80f40558fbfe","target":"graph","created_at":"2026-05-18T04:24:27Z","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":"Given an endomorphism of a projective variety, by intersecting the graph and the diagonal varieties we can determine the set of periodic points. In an effort to determine the periodic points of a given minimal period, we follow a construction similar to cyclotomic polynomials. The resulting zero-cycle is called a dynatomic cycle and the points in its support are called formal periodic points. This article gives a proof of the effectivity of dynatomic cycles for morphisms of projective varieties using methods from deformation theory.","authors_text":"Benjamin Hutz","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-23T16:40:01Z","title":"Effectivity of Dynatomic cycles for morphisms of projective varieties using deformation theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5155","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":"sha256:8ad3033d9f89e63d4a8a974cb84bb3fabd6de9cca9b3991f14cd1a8982c3cb6c","target":"record","created_at":"2026-05-18T04:24:27Z","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":"7804e7de6fc08bc81891b8875ea8a33bec07f54df8fbb3ea52306e0409809361","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-23T16:40:01Z","title_canon_sha256":"3493f34def33123133d847d235729610cbaae4cabae2b6039bb352d4dc63675b"},"schema_version":"1.0","source":{"id":"1011.5155","kind":"arxiv","version":3}},"canonical_sha256":"4606879e620c9a5cb5c909a0ca94f0d3d2443e2df06919c5fdc950bfcbcabd11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4606879e620c9a5cb5c909a0ca94f0d3d2443e2df06919c5fdc950bfcbcabd11","first_computed_at":"2026-05-18T04:24:27.439886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:27.439886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O62LgeRjjtsTXT6iGNrQEcLlTky2E9fSKRi6VB3Z5EnmF9AokAO60tNWOWk27xAPiK07X8heEuI6YdIwQGmaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:27.440472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.5155","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ad3033d9f89e63d4a8a974cb84bb3fabd6de9cca9b3991f14cd1a8982c3cb6c","sha256:9f3daf03ffe6d66c436b2ba58033ef6dddbcf24fc143025ad2dd80f40558fbfe"],"state_sha256":"37b67884034a2948778d7ef976a9dd0c80ca8562308d64238280979ee4593a63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DtD4xWRE9dj+y0/l+2Pray3sZ7G5qZh5ngjh4UqDZbl19HfGmVZaiu7k6Hs26EaxjNc4Wtnn/+RFQ5pBd/qUBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:38:22.701675Z","bundle_sha256":"40ca3e338e28646de1c2f1236629176603d5920ee1287ca6276b504286b816d1"}}