{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3ZTZ4ANC3Z4DFH5INQI7YIMOTW","short_pith_number":"pith:3ZTZ4ANC","canonical_record":{"source":{"id":"1304.0634","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-02T14:09:47Z","cross_cats_sorted":[],"title_canon_sha256":"1ce4e69153c40e2440029718f240259e33595497c2f03127c1d703dfe0393880","abstract_canon_sha256":"946768d3306cffd08bcba48578386ce60b0c1199fc98aace87f62723123aaaaa"},"schema_version":"1.0"},"canonical_sha256":"de679e01a2de78329fa86c11fc218e9d8498d1d8b40a66d58431692165b99600","source":{"kind":"arxiv","id":"1304.0634","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0634","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0634v3","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0634","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"3ZTZ4ANC3Z4D","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3ZTZ4ANC3Z4DFH5I","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3ZTZ4ANC","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3ZTZ4ANC3Z4DFH5INQI7YIMOTW","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0634","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-02T14:09:47Z","cross_cats_sorted":[],"title_canon_sha256":"1ce4e69153c40e2440029718f240259e33595497c2f03127c1d703dfe0393880","abstract_canon_sha256":"946768d3306cffd08bcba48578386ce60b0c1199fc98aace87f62723123aaaaa"},"schema_version":"1.0"},"canonical_sha256":"de679e01a2de78329fa86c11fc218e9d8498d1d8b40a66d58431692165b99600","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:28.423368Z","signature_b64":"MBFTpBD89U6Oq3q2f3f1P3z9MpXHtoffHOLa5j0UlC9+XLHiqZFlsTd9n5oz5fI43owPlo6RmgTEtnVASSkrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de679e01a2de78329fa86c11fc218e9d8498d1d8b40a66d58431692165b99600","last_reissued_at":"2026-05-18T01:18:28.422760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:28.422760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0634","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":"2026-05-18T01:18:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H979ERzIrUGj/oaR+IGjfg5hzSkYy/8k1SnGcZx+Lcb6HmOgEaCC2zkzeXg7vYMQzmDW/1hXymvc9zpx+G4MBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:19:39.466010Z"},"content_sha256":"b1c0ff0e51a72a6ab40dc4f111bb2a0985cb8d85e2cfd64bf61e0bc0d65b1890","schema_version":"1.0","event_id":"sha256:b1c0ff0e51a72a6ab40dc4f111bb2a0985cb8d85e2cfd64bf61e0bc0d65b1890"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3ZTZ4ANC3Z4DFH5INQI7YIMOTW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Irreducibility properties of Keller maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Yan, Michiel de Bondt","submitted_at":"2013-04-02T14:09:47Z","abstract_excerpt":"Jedrzejewicz showed that a polynomial map over a field of characteristic zero is invertible, if and only if the corresponding endomorphism maps irreducible polynomials to irreducible polynomials. Furthermore, he showed that a polynomial map over a field of characteristic zero is a Keller map, if and only if the corresponding endomorphism maps irreducible polynomials to square-free polynomials. We show that the latter endomorphism maps other square-free polynomials to square-free polynomials as well.\n  In connection with the above classification of invertible polynomial maps and the Jacobian Co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0634","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":"2026-05-18T01:18:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QxQ+dOo9spUnetKoeXdWfxNG7uKTl+N2pP6QnI4dI/Jesgk4ML6MrTAqoPlFA0SOT2fpaU/qyGJ+9s30ll8JDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:19:39.466358Z"},"content_sha256":"bf5fb9d0b6cdeec60c344bdb2ee1bc212862b0866dae1c990e679def24c9980a","schema_version":"1.0","event_id":"sha256:bf5fb9d0b6cdeec60c344bdb2ee1bc212862b0866dae1c990e679def24c9980a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ZTZ4ANC3Z4DFH5INQI7YIMOTW/bundle.json","state_url":"https://pith.science/pith/3ZTZ4ANC3Z4DFH5INQI7YIMOTW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ZTZ4ANC3Z4DFH5INQI7YIMOTW/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":"2026-06-05T00:19:39Z","links":{"resolver":"https://pith.science/pith/3ZTZ4ANC3Z4DFH5INQI7YIMOTW","bundle":"https://pith.science/pith/3ZTZ4ANC3Z4DFH5INQI7YIMOTW/bundle.json","state":"https://pith.science/pith/3ZTZ4ANC3Z4DFH5INQI7YIMOTW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ZTZ4ANC3Z4DFH5INQI7YIMOTW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3ZTZ4ANC3Z4DFH5INQI7YIMOTW","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":"946768d3306cffd08bcba48578386ce60b0c1199fc98aace87f62723123aaaaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-02T14:09:47Z","title_canon_sha256":"1ce4e69153c40e2440029718f240259e33595497c2f03127c1d703dfe0393880"},"schema_version":"1.0","source":{"id":"1304.0634","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0634","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0634v3","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0634","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"3ZTZ4ANC3Z4D","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3ZTZ4ANC3Z4DFH5I","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3ZTZ4ANC","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:bf5fb9d0b6cdeec60c344bdb2ee1bc212862b0866dae1c990e679def24c9980a","target":"graph","created_at":"2026-05-18T01:18:28Z","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":"Jedrzejewicz showed that a polynomial map over a field of characteristic zero is invertible, if and only if the corresponding endomorphism maps irreducible polynomials to irreducible polynomials. Furthermore, he showed that a polynomial map over a field of characteristic zero is a Keller map, if and only if the corresponding endomorphism maps irreducible polynomials to square-free polynomials. We show that the latter endomorphism maps other square-free polynomials to square-free polynomials as well.\n  In connection with the above classification of invertible polynomial maps and the Jacobian Co","authors_text":"Dan Yan, Michiel de Bondt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-02T14:09:47Z","title":"Irreducibility properties of Keller maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0634","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:b1c0ff0e51a72a6ab40dc4f111bb2a0985cb8d85e2cfd64bf61e0bc0d65b1890","target":"record","created_at":"2026-05-18T01:18:28Z","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":"946768d3306cffd08bcba48578386ce60b0c1199fc98aace87f62723123aaaaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-02T14:09:47Z","title_canon_sha256":"1ce4e69153c40e2440029718f240259e33595497c2f03127c1d703dfe0393880"},"schema_version":"1.0","source":{"id":"1304.0634","kind":"arxiv","version":3}},"canonical_sha256":"de679e01a2de78329fa86c11fc218e9d8498d1d8b40a66d58431692165b99600","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de679e01a2de78329fa86c11fc218e9d8498d1d8b40a66d58431692165b99600","first_computed_at":"2026-05-18T01:18:28.422760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:28.422760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MBFTpBD89U6Oq3q2f3f1P3z9MpXHtoffHOLa5j0UlC9+XLHiqZFlsTd9n5oz5fI43owPlo6RmgTEtnVASSkrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:28.423368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0634","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1c0ff0e51a72a6ab40dc4f111bb2a0985cb8d85e2cfd64bf61e0bc0d65b1890","sha256:bf5fb9d0b6cdeec60c344bdb2ee1bc212862b0866dae1c990e679def24c9980a"],"state_sha256":"b072a4d1bb8259a71df894c21624a68d7efe943d6c342b9f726d24793ea833ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fhKWoGzfaGboIiOgxkBaCVcbWCrmeaUy5UndLFWIwhNeqGsfPmEYRXxMFzSp0erI0E+uO9DhBOl1Hkaj8VBRDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:19:39.468398Z","bundle_sha256":"5580b9aac4fe76e1ac03122decc7455f93535af25abf30dd52ec0406e06713de"}}