{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QF2WLQQTLASCO66V3M4KLYRLTI","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":"bdb085941ab7c7a4dc112f1b4264eb6547668be080bcfb78464cea9400797fc5","cross_cats_sorted":["math.AC","math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-25T01:18:26Z","title_canon_sha256":"ac43e721729c9612538b510eb6f965edaa7e5239a7ed7fc82a8d7672a3815cc4"},"schema_version":"1.0","source":{"id":"1303.6011","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6011","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6011v1","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6011","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"QF2WLQQTLASC","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QF2WLQQTLASCO66V","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QF2WLQQT","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:a364c275d7a0033804ff29c93d33bf68beb72b4fa020925cd5cec3796da57519","target":"graph","created_at":"2026-05-18T02:48:47Z","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":"We establish an invertibility criterion for free polynomials and free functions evaluated on some tuples of matrices. We show that if the derivative is nonsingular on some domain closed with respect to direct sums and similarity, the function must be invertible. Thus, as a corollary, we establish the Jacobian conjecture in this context. Furthermore, our result holds for commutative polynomials evaluated on tuples of commuting matrices.","authors_text":"J. E. Pascoe","cross_cats":["math.AC","math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-25T01:18:26Z","title":"The inverse function theorem and the resolution of the Jacobian conjecture in free analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6011","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":"sha256:55e5ea19cfba25d87e43f8c5a04635e6480b0b4168d616fd07bc7e342da50696","target":"record","created_at":"2026-05-18T02:48:47Z","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":"bdb085941ab7c7a4dc112f1b4264eb6547668be080bcfb78464cea9400797fc5","cross_cats_sorted":["math.AC","math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-25T01:18:26Z","title_canon_sha256":"ac43e721729c9612538b510eb6f965edaa7e5239a7ed7fc82a8d7672a3815cc4"},"schema_version":"1.0","source":{"id":"1303.6011","kind":"arxiv","version":1}},"canonical_sha256":"817565c2135824277bd5db38a5e22b9a30440b8f3e3f6b1bbb2e661596b5392b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"817565c2135824277bd5db38a5e22b9a30440b8f3e3f6b1bbb2e661596b5392b","first_computed_at":"2026-05-18T02:48:47.073780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:47.073780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d5P/MzF3IhuNEu/H8YhW3ZLMBIjn280+GkvehE8ywjllDtPkpco68t7/u9KIC9jf/9UIB+5Ktd08P1lGuJitAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:47.074409Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6011","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55e5ea19cfba25d87e43f8c5a04635e6480b0b4168d616fd07bc7e342da50696","sha256:a364c275d7a0033804ff29c93d33bf68beb72b4fa020925cd5cec3796da57519"],"state_sha256":"008c623937ac7cb19f0d66e28fd59b663c98a36fd1a4a0f71114ad0468f9537e"}