{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RMD3TVMVQEUJ6ERPNXLJJGJY3F","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":"57062624cc69b1b35f6a402b4d8481110596e62c04df92075ce1d9b6b4bd2f58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-14T19:58:46Z","title_canon_sha256":"761226b88871a53ce82cfdc8109d149988307f188544888ec75a54145b8a0f1a"},"schema_version":"1.0","source":{"id":"1510.04264","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04264","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04264v3","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04264","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"RMD3TVMVQEUJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RMD3TVMVQEUJ6ERP","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RMD3TVMV","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:f4dbc2a3aac420fc03c1dd16992972a45831a2a32afab948cbb474c07c5f2809","target":"graph","created_at":"2026-05-18T01:21:21Z","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":"The two dimensional Jacobian Conjecture says that a morphism $f:\\mathbb{C}[x,y]\\to \\mathbb{C}[x,y]$ having an invertible Jacobian, is invertible. We show that a morphism $f$ having an invertible Jacobian is invertible, in each of the following two special cases: The degree of $f(x)$ is $\\leq 2$; The $(0,1)$-degrees or $(1,0)$-degrees of all monomials in $f(x)$ are of the same parity. In each case there is no restriction on the degree of $f(y)$ nor on the parity of the $(0,1)$-degrees or $(1,0)$-degrees of its monomials.","authors_text":"Vered Moskowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-14T19:58:46Z","title":"Observations on the two dimensional Jacobian Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04264","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":"sha256:96aefc4b780c68d24f9b0657eb6792a6f5398cca478864c1746d7ff9ff74b168","target":"record","created_at":"2026-05-18T01:21:21Z","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":"57062624cc69b1b35f6a402b4d8481110596e62c04df92075ce1d9b6b4bd2f58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-14T19:58:46Z","title_canon_sha256":"761226b88871a53ce82cfdc8109d149988307f188544888ec75a54145b8a0f1a"},"schema_version":"1.0","source":{"id":"1510.04264","kind":"arxiv","version":3}},"canonical_sha256":"8b07b9d59581289f122f6dd6949938d97a9922d562edbc1b7cb7ef2c8d681270","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b07b9d59581289f122f6dd6949938d97a9922d562edbc1b7cb7ef2c8d681270","first_computed_at":"2026-05-18T01:21:21.251306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:21.251306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gfgpN/3R2WK677duJKb84Dy8HaHX3CnBvNJy/IPVDkhXFw6HMaGL0+oom/KgjKldzyuDPR629GuOMNhjCBOcAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:21.251871Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04264","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96aefc4b780c68d24f9b0657eb6792a6f5398cca478864c1746d7ff9ff74b168","sha256:f4dbc2a3aac420fc03c1dd16992972a45831a2a32afab948cbb474c07c5f2809"],"state_sha256":"546f4858302656cab1931fbf020a8e0a928b001d73535134e6cd1c6130153d77"}