{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6AR7FTO4MNLQ5XGRXWKIAFFAEO","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":"b2ab3c4ba89bdb703a7d83d3f1481e24a10878917d80131a07b2c5a49c6ee196","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AG","submitted_at":"2012-03-16T03:13:06Z","title_canon_sha256":"976a8a5fd8383291d8ebad0883840ef81ac5f1ad68d35c535a6f2f6dc976cfba"},"schema_version":"1.0","source":{"id":"1203.3609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3609","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3609v1","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3609","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"6AR7FTO4MNLQ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6AR7FTO4MNLQ5XGR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6AR7FTO4","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:6d48da9f10e9fb2ad7574b77bcac221947fb3d310421f75581ed2a48cbeeaef7","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":"In this paper, we first show that homogeneous Keller maps are injective on lines through the origin. We subsequently formulate a generalization, which is that under some conditions, a polynomial endomorphism with $r$ homogeneous parts of positive degree does not have $r$ times the same image point on a line through the origin, in case its Jacobian determinant does not vanish anywhere on that line. As a consequence, a Keller map of degree $r$ does not take the same values on $r > 1$ collinear points, provided $r$ is a unit in the base field.\n  Next, we show that for invertible maps $x + H$ of d","authors_text":"Dan Yan, Michiel de Bondt","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AG","submitted_at":"2012-03-16T03:13:06Z","title":"Some remarks on the Jacobian conjecture and polynomial endomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3609","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:e5fd92dbedbcc5b8ca7dc7a6d45af377a2b5ee916c4654aa50508dac2dcdbca8","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":"b2ab3c4ba89bdb703a7d83d3f1481e24a10878917d80131a07b2c5a49c6ee196","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AG","submitted_at":"2012-03-16T03:13:06Z","title_canon_sha256":"976a8a5fd8383291d8ebad0883840ef81ac5f1ad68d35c535a6f2f6dc976cfba"},"schema_version":"1.0","source":{"id":"1203.3609","kind":"arxiv","version":1}},"canonical_sha256":"f023f2cddc63570edcd1bd948014a023ad0f1330a396d941aac40b5f40c4df52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f023f2cddc63570edcd1bd948014a023ad0f1330a396d941aac40b5f40c4df52","first_computed_at":"2026-05-18T01:18:28.467354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:28.467354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Lkcu7+AeIKhnwSVSshSgX1OlFqvNpRl4jlD1c+hnFuqY+MXJrqttc/tcLkHOCSfvo5KA0WFezpwBrzZMuizAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:28.467833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5fd92dbedbcc5b8ca7dc7a6d45af377a2b5ee916c4654aa50508dac2dcdbca8","sha256:6d48da9f10e9fb2ad7574b77bcac221947fb3d310421f75581ed2a48cbeeaef7"],"state_sha256":"7484a77382b95913e764f3ff81242ce5dc91e70e12b27d357fa8c85966e16942"}