{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UCPKLMNEOCEPINCPDPEZN52WMM","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":"8810ee2aa5bce6a2ffea77651ba7016267209ddaaf417e269d34785f532b8732","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-24T18:44:12Z","title_canon_sha256":"f8912d28fbc2e594b8748a746347378df94f370da0672569c007d86c77d70898"},"schema_version":"1.0","source":{"id":"1803.09147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.09147","created_at":"2026-05-18T00:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1803.09147v1","created_at":"2026-05-18T00:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09147","created_at":"2026-05-18T00:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"UCPKLMNEOCEP","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UCPKLMNEOCEPINCP","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UCPKLMNE","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:db5f24564645fe1da49671c6777ab0371ffcf21c940e31f67ec6351a8dcef0ed","target":"graph","created_at":"2026-05-18T00:20:12Z","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 his monograph \"Le\\c{c}ons sur les syst\\`emes orthogonaux et les coordonn\\'ees curvilignes. Principes de g\\'eom\\'etrie analytique\", 1910, Darboux stated three theorems providing local existence and uniqueness of solutions to first order systems of the type \\[\\partial_{x_i} u_\\alpha(x)=f^\\alpha_i(x,u(x)),\\quad i\\in I_\\alpha\\subseteq\\{1,\\dots,n\\}.\\] For a given point $\\bar x\\in \\mathbb{R}^n$ it is assumed that the values of the unknown $u_\\alpha$ are given locally near $\\bar x$ along $\\{x\\,|\\, x_i=\\bar x_i \\, \\text{for each}\\, i\\in I_\\alpha\\}$. The more general of the theorems, Th\\'eor\\`eme II","authors_text":"Helge Kristian Jenssen, Irina A. Kogan, Michael Benfield","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-24T18:44:12Z","title":"A generalization of an integrability theorem of Darboux"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09147","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":"sha256:3563b33eb17772b6fde459c64299640a49166393d5a59f089c45920bcc039061","target":"record","created_at":"2026-05-18T00:20:12Z","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":"8810ee2aa5bce6a2ffea77651ba7016267209ddaaf417e269d34785f532b8732","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-24T18:44:12Z","title_canon_sha256":"f8912d28fbc2e594b8748a746347378df94f370da0672569c007d86c77d70898"},"schema_version":"1.0","source":{"id":"1803.09147","kind":"arxiv","version":1}},"canonical_sha256":"a09ea5b1a47088f4344f1bc996f75663119b0e1cd00ac784d51e4c0bcfbf208e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a09ea5b1a47088f4344f1bc996f75663119b0e1cd00ac784d51e4c0bcfbf208e","first_computed_at":"2026-05-18T00:20:12.500049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:12.500049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dObTnvrPDCQcl0o1vEBDvKdJpw2VWvOy+wi0dFLfKBegxilcdKzBtjD/UxcLjb7jUciVVxeFqWac6kg0osoTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:12.500489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.09147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3563b33eb17772b6fde459c64299640a49166393d5a59f089c45920bcc039061","sha256:db5f24564645fe1da49671c6777ab0371ffcf21c940e31f67ec6351a8dcef0ed"],"state_sha256":"8ed783839036d5817a3cacad914daadf85cbee667813ae7eabd5f38eb5274898"}