{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:7FHZ77VZ2MFFU4CN5PKECDECNX","short_pith_number":"pith:7FHZ77VZ","canonical_record":{"source":{"id":"2006.12869","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-23T10:04:26Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"272b963c94490e3e303dc083f2624dab6b2062f7086866026c120ddd44a9cc0a","abstract_canon_sha256":"c19cc186c3ddd71da6b0b607d61b0498aa0fae8e8bf1ef74cce0eb983124e314"},"schema_version":"1.0"},"canonical_sha256":"f94f9ffeb9d30a5a704debd4410c826df5151f050008b3b9ed1d7a68611880e5","source":{"kind":"arxiv","id":"2006.12869","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.12869","created_at":"2026-07-05T04:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"2006.12869v3","created_at":"2026-07-05T04:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.12869","created_at":"2026-07-05T04:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"7FHZ77VZ2MFF","created_at":"2026-07-05T04:42:53Z"},{"alias_kind":"pith_short_16","alias_value":"7FHZ77VZ2MFFU4CN","created_at":"2026-07-05T04:42:53Z"},{"alias_kind":"pith_short_8","alias_value":"7FHZ77VZ","created_at":"2026-07-05T04:42:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:7FHZ77VZ2MFFU4CN5PKECDECNX","target":"record","payload":{"canonical_record":{"source":{"id":"2006.12869","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-23T10:04:26Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"272b963c94490e3e303dc083f2624dab6b2062f7086866026c120ddd44a9cc0a","abstract_canon_sha256":"c19cc186c3ddd71da6b0b607d61b0498aa0fae8e8bf1ef74cce0eb983124e314"},"schema_version":"1.0"},"canonical_sha256":"f94f9ffeb9d30a5a704debd4410c826df5151f050008b3b9ed1d7a68611880e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:42:53.141983Z","signature_b64":"q4uKmGN2RLJHjAZYAucnPkGk2E2A39wv11HdG0V2sYOLoG/oepJdy/TwI63w0YHxNHhTy9JEKdCozou4HJVhBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f94f9ffeb9d30a5a704debd4410c826df5151f050008b3b9ed1d7a68611880e5","last_reissued_at":"2026-07-05T04:42:53.141597Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:42:53.141597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.12869","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":"2026-07-05T04:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9x1YF9lv7NQXZgHVrrdS3wHVoC/vCI3bIg6KCwjwIuFewmPGS65Pc/HFJVgSEgnX9y32i5zC9mimTjtVnVZEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:40:56.933476Z"},"content_sha256":"3da1fab1aa753cf2d3fe366cc3e262bd7a6d0159fedb7fb028a2058f28b3240a","schema_version":"1.0","event_id":"sha256:3da1fab1aa753cf2d3fe366cc3e262bd7a6d0159fedb7fb028a2058f28b3240a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:7FHZ77VZ2MFFU4CN5PKECDECNX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimally critical endomorphisms of P^N","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Patrick Ingram","submitted_at":"2020-06-23T10:04:26Z","abstract_excerpt":"We study the dynamics of the map endomorphism of N-dimensional projective space defined by f(X)=AX^d, where A is a matrix and d is at least 2. When d>N^2+N+1, we show that the critical height of such a morphism is comparable to its height in moduli space, confirming a case of a natural generalization of a conjecture of Silverman."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.12869","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.12869/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ylr6fqAJvwedBvR4wowBKPMJUIvEp/txUARAwhmOTf44GYwOqVQ6xQxYhYxSqc24KAe4EbwCwb+O2aKW9dGPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:40:56.933979Z"},"content_sha256":"749d57c69ab5b325c1f6f1f5f66324693f965160b0760e5805a59ef6faa5e8c4","schema_version":"1.0","event_id":"sha256:749d57c69ab5b325c1f6f1f5f66324693f965160b0760e5805a59ef6faa5e8c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FHZ77VZ2MFFU4CN5PKECDECNX/bundle.json","state_url":"https://pith.science/pith/7FHZ77VZ2MFFU4CN5PKECDECNX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FHZ77VZ2MFFU4CN5PKECDECNX/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":"2026-08-13T21:40:56Z","links":{"resolver":"https://pith.science/pith/7FHZ77VZ2MFFU4CN5PKECDECNX","bundle":"https://pith.science/pith/7FHZ77VZ2MFFU4CN5PKECDECNX/bundle.json","state":"https://pith.science/pith/7FHZ77VZ2MFFU4CN5PKECDECNX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FHZ77VZ2MFFU4CN5PKECDECNX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:7FHZ77VZ2MFFU4CN5PKECDECNX","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":"c19cc186c3ddd71da6b0b607d61b0498aa0fae8e8bf1ef74cce0eb983124e314","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-23T10:04:26Z","title_canon_sha256":"272b963c94490e3e303dc083f2624dab6b2062f7086866026c120ddd44a9cc0a"},"schema_version":"1.0","source":{"id":"2006.12869","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.12869","created_at":"2026-07-05T04:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"2006.12869v3","created_at":"2026-07-05T04:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.12869","created_at":"2026-07-05T04:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"7FHZ77VZ2MFF","created_at":"2026-07-05T04:42:53Z"},{"alias_kind":"pith_short_16","alias_value":"7FHZ77VZ2MFFU4CN","created_at":"2026-07-05T04:42:53Z"},{"alias_kind":"pith_short_8","alias_value":"7FHZ77VZ","created_at":"2026-07-05T04:42:53Z"}],"graph_snapshots":[{"event_id":"sha256:749d57c69ab5b325c1f6f1f5f66324693f965160b0760e5805a59ef6faa5e8c4","target":"graph","created_at":"2026-07-05T04:42:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2006.12869/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the dynamics of the map endomorphism of N-dimensional projective space defined by f(X)=AX^d, where A is a matrix and d is at least 2. When d>N^2+N+1, we show that the critical height of such a morphism is comparable to its height in moduli space, confirming a case of a natural generalization of a conjecture of Silverman.","authors_text":"Patrick Ingram","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-23T10:04:26Z","title":"Minimally critical endomorphisms of P^N"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.12869","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":"sha256:3da1fab1aa753cf2d3fe366cc3e262bd7a6d0159fedb7fb028a2058f28b3240a","target":"record","created_at":"2026-07-05T04:42:53Z","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":"c19cc186c3ddd71da6b0b607d61b0498aa0fae8e8bf1ef74cce0eb983124e314","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-23T10:04:26Z","title_canon_sha256":"272b963c94490e3e303dc083f2624dab6b2062f7086866026c120ddd44a9cc0a"},"schema_version":"1.0","source":{"id":"2006.12869","kind":"arxiv","version":3}},"canonical_sha256":"f94f9ffeb9d30a5a704debd4410c826df5151f050008b3b9ed1d7a68611880e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f94f9ffeb9d30a5a704debd4410c826df5151f050008b3b9ed1d7a68611880e5","first_computed_at":"2026-07-05T04:42:53.141597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:42:53.141597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q4uKmGN2RLJHjAZYAucnPkGk2E2A39wv11HdG0V2sYOLoG/oepJdy/TwI63w0YHxNHhTy9JEKdCozou4HJVhBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:42:53.141983Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.12869","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3da1fab1aa753cf2d3fe366cc3e262bd7a6d0159fedb7fb028a2058f28b3240a","sha256:749d57c69ab5b325c1f6f1f5f66324693f965160b0760e5805a59ef6faa5e8c4"],"state_sha256":"d3989ca87443cf3c329c93cb8f2092f5487f843abc45b34f5a10c001d57aa223"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5pjLbb1eXZT3k5pxsmy+fbu88jdYtGJyDnd0ZxDM4e20xEu5S5zfzxmV8msGf9IWNcVHb5eBK7Tv8hn1RSTsDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T21:40:56.968056Z","bundle_sha256":"3ff5f185ec8877f16f971b9974d36c32d752a09d0b0bb148c87aee1b20e0a612"}}