{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Z5HVP7ZX5U436KMGMSNDEMUTOK","short_pith_number":"pith:Z5HVP7ZX","canonical_record":{"source":{"id":"1409.7883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-28T09:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"6976cd965296a9d50f766d42b448e997e294bb85d568933a8f8498110156d7fe","abstract_canon_sha256":"58008b4566b5114ec6e8966b8727b5c21a3d4e086b757ec73b0c085ec3d7e138"},"schema_version":"1.0"},"canonical_sha256":"cf4f57ff37ed39bf2986649a32329372aea81f93719d26336e09d3f56cbd564a","source":{"kind":"arxiv","id":"1409.7883","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7883","created_at":"2026-05-18T02:41:40Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7883v1","created_at":"2026-05-18T02:41:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7883","created_at":"2026-05-18T02:41:40Z"},{"alias_kind":"pith_short_12","alias_value":"Z5HVP7ZX5U43","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z5HVP7ZX5U436KMG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z5HVP7ZX","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Z5HVP7ZX5U436KMGMSNDEMUTOK","target":"record","payload":{"canonical_record":{"source":{"id":"1409.7883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-28T09:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"6976cd965296a9d50f766d42b448e997e294bb85d568933a8f8498110156d7fe","abstract_canon_sha256":"58008b4566b5114ec6e8966b8727b5c21a3d4e086b757ec73b0c085ec3d7e138"},"schema_version":"1.0"},"canonical_sha256":"cf4f57ff37ed39bf2986649a32329372aea81f93719d26336e09d3f56cbd564a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:40.293417Z","signature_b64":"kl7VNs1Klen/ZbnxN1TIxT7RxyeSVr6opk39/AepHpPrLTgAo3PiOZEOemfQr0srPIu+o55Ae21pEiQKncj3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf4f57ff37ed39bf2986649a32329372aea81f93719d26336e09d3f56cbd564a","last_reissued_at":"2026-05-18T02:41:40.292942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:40.292942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.7883","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":"2026-05-18T02:41:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gKT+GJ0Gqn+iPXEtQh/FcGAZoX4IcYNJXxsq/TmzpFgDF8KooJnxqTlcArAvbOz9xXTNr50SgnQ85wfSkDEvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:45:20.966790Z"},"content_sha256":"4a83fbc691768cd04acef9f85bc49b4e1b7740563f16f57272d9d93a8b617b07","schema_version":"1.0","event_id":"sha256:4a83fbc691768cd04acef9f85bc49b4e1b7740563f16f57272d9d93a8b617b07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Z5HVP7ZX5U436KMGMSNDEMUTOK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the set of fixed points of a polynomial automorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Tomasz Lenarcik, Zbigniew Jelonek","submitted_at":"2014-09-28T09:21:33Z","abstract_excerpt":"Let K be an algebraically closed field of characteristic zero. We say that a polynomial automorphism f : K^n -> K^n is special if the Jacobian of f is equal to 1. We show that every (n - 1)-dimensional component H of the set Fix(f) of fixed points of a non-trivial special polynomial automorphism f : K^n -> K^n is uniruled. Moreover, we show that if f is non-special and H is an (n-1)-dimensional component of the set Fix(f), then H is smooth, irreducible and H = Fix(f) and for K = C the Euler characteristic of H is equal to 1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7883","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":"2026-05-18T02:41:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nS8mltCL0FENJApT45hXI1vOEvhaKkuK0jxyILAH/L7oNtHxpxSpj2QvMErRJJ319GNqsBCQB9jelmB665mHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:45:20.967139Z"},"content_sha256":"fe969702a4c09bd2ed56376b4b22ead6d4f928f3a160d2ce230a2d6b900d229b","schema_version":"1.0","event_id":"sha256:fe969702a4c09bd2ed56376b4b22ead6d4f928f3a160d2ce230a2d6b900d229b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5HVP7ZX5U436KMGMSNDEMUTOK/bundle.json","state_url":"https://pith.science/pith/Z5HVP7ZX5U436KMGMSNDEMUTOK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5HVP7ZX5U436KMGMSNDEMUTOK/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":"2026-06-27T04:45:20Z","links":{"resolver":"https://pith.science/pith/Z5HVP7ZX5U436KMGMSNDEMUTOK","bundle":"https://pith.science/pith/Z5HVP7ZX5U436KMGMSNDEMUTOK/bundle.json","state":"https://pith.science/pith/Z5HVP7ZX5U436KMGMSNDEMUTOK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5HVP7ZX5U436KMGMSNDEMUTOK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z5HVP7ZX5U436KMGMSNDEMUTOK","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":"58008b4566b5114ec6e8966b8727b5c21a3d4e086b757ec73b0c085ec3d7e138","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-28T09:21:33Z","title_canon_sha256":"6976cd965296a9d50f766d42b448e997e294bb85d568933a8f8498110156d7fe"},"schema_version":"1.0","source":{"id":"1409.7883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7883","created_at":"2026-05-18T02:41:40Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7883v1","created_at":"2026-05-18T02:41:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7883","created_at":"2026-05-18T02:41:40Z"},{"alias_kind":"pith_short_12","alias_value":"Z5HVP7ZX5U43","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z5HVP7ZX5U436KMG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z5HVP7ZX","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:fe969702a4c09bd2ed56376b4b22ead6d4f928f3a160d2ce230a2d6b900d229b","target":"graph","created_at":"2026-05-18T02:41:40Z","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 K be an algebraically closed field of characteristic zero. We say that a polynomial automorphism f : K^n -> K^n is special if the Jacobian of f is equal to 1. We show that every (n - 1)-dimensional component H of the set Fix(f) of fixed points of a non-trivial special polynomial automorphism f : K^n -> K^n is uniruled. Moreover, we show that if f is non-special and H is an (n-1)-dimensional component of the set Fix(f), then H is smooth, irreducible and H = Fix(f) and for K = C the Euler characteristic of H is equal to 1.","authors_text":"Tomasz Lenarcik, Zbigniew Jelonek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-28T09:21:33Z","title":"On the set of fixed points of a polynomial automorphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7883","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":"sha256:4a83fbc691768cd04acef9f85bc49b4e1b7740563f16f57272d9d93a8b617b07","target":"record","created_at":"2026-05-18T02:41:40Z","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":"58008b4566b5114ec6e8966b8727b5c21a3d4e086b757ec73b0c085ec3d7e138","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-28T09:21:33Z","title_canon_sha256":"6976cd965296a9d50f766d42b448e997e294bb85d568933a8f8498110156d7fe"},"schema_version":"1.0","source":{"id":"1409.7883","kind":"arxiv","version":1}},"canonical_sha256":"cf4f57ff37ed39bf2986649a32329372aea81f93719d26336e09d3f56cbd564a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf4f57ff37ed39bf2986649a32329372aea81f93719d26336e09d3f56cbd564a","first_computed_at":"2026-05-18T02:41:40.292942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:40.292942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kl7VNs1Klen/ZbnxN1TIxT7RxyeSVr6opk39/AepHpPrLTgAo3PiOZEOemfQr0srPIu+o55Ae21pEiQKncj3Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:40.293417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a83fbc691768cd04acef9f85bc49b4e1b7740563f16f57272d9d93a8b617b07","sha256:fe969702a4c09bd2ed56376b4b22ead6d4f928f3a160d2ce230a2d6b900d229b"],"state_sha256":"b79a4a39d3e5e7aec29de115f7aeb093ce3853ff4f7be4f6cc03d2315de3a55b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xj9l6LUOJSRE1zjdSeswMKfGgjpZymg4SMHk48PkKwazuaJVTHriohAh1tFDsKRYzy+6YB+1y2HRtOR4gJtfAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T04:45:20.969092Z","bundle_sha256":"906316ddca2442170c7310fb53e2cc29c874efbb732efebda596d19deaa100c6"}}