{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JY32DM5AWZ5AT5PGKC5TXJ2X7Z","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":"7204530d97b4e1540c304117377467943c423ee2d08b78652ff962b9fcd9e3e2","cross_cats_sorted":["math.AP","math.CA","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-14T10:53:44Z","title_canon_sha256":"35cf4722d9e15d5c6a34cfefb0f9ab733d77b6e2a6388ed5dbc6b5789a1e0800"},"schema_version":"1.0","source":{"id":"1203.3045","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3045","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3045v2","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3045","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"JY32DM5AWZ5A","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JY32DM5AWZ5AT5PG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JY32DM5A","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:7dc45a50d156ad043777e4a01fc2a37149b0de6e69e216dad167e9d70491f2da","target":"graph","created_at":"2026-05-18T01:03:31Z","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 investigate the structure of fully non-linear P.D.E.'s in holomorphic functions, with emphasis on the functorial generalisation of so called \"irregular\" O.D.E.'s. Highlights are an implicit function theorem removing the perturbation conditions of Nash-Moser type, best possible existence results when the singularity of the linearised P.D.E. is at worst bi-dimensional, and various, again optimal, corollaries on existence of centre manifolds and conjugation to normal form of 3-dimensional vector fields.","authors_text":"Daniel Panazzolo, Michael McQuillan","cross_cats":["math.AP","math.CA","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-14T10:53:44Z","title":"(1 + d/dz)^(-1)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3045","kind":"arxiv","version":2},"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":"sha256:92e81179b255c31992de594ed903e01a0b7521ffaf2d154435bf243e4c1966a6","target":"record","created_at":"2026-05-18T01:03:31Z","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":"7204530d97b4e1540c304117377467943c423ee2d08b78652ff962b9fcd9e3e2","cross_cats_sorted":["math.AP","math.CA","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-14T10:53:44Z","title_canon_sha256":"35cf4722d9e15d5c6a34cfefb0f9ab733d77b6e2a6388ed5dbc6b5789a1e0800"},"schema_version":"1.0","source":{"id":"1203.3045","kind":"arxiv","version":2}},"canonical_sha256":"4e37a1b3a0b67a09f5e650bb3ba757fe62016610c3a521bbf248895cba214b89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e37a1b3a0b67a09f5e650bb3ba757fe62016610c3a521bbf248895cba214b89","first_computed_at":"2026-05-18T01:03:31.351384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:31.351384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lhijB94cQ6by8HcUYUfwdNOgbSo4hf9sWtZLPD+dzqqDYlB24bXLYfznn/0dIQgVp6bj6u83NCEsTSqbRUtzAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:31.352006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3045","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92e81179b255c31992de594ed903e01a0b7521ffaf2d154435bf243e4c1966a6","sha256:7dc45a50d156ad043777e4a01fc2a37149b0de6e69e216dad167e9d70491f2da"],"state_sha256":"fe7847f0d66e133ec9849839b794261e38b3da5b04d3f7d65f086dd8a5319f44"}