{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:W7A6V6HQA4PFGO6FLBD7C3T5P4","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":"20f4f6ecf2a0906b386a6f77d82430018ffa5f018c6ac96d30113bd4852eeebb","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2001-01-01T00:00:00Z","title_canon_sha256":"20610c5d7dff403440eebf0e7eda76545fd291cf74eddf3d459cbbd843533a3c"},"schema_version":"1.0","source":{"id":"math/0101268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0101268","created_at":"2026-05-18T03:47:10Z"},{"alias_kind":"arxiv_version","alias_value":"math/0101268v1","created_at":"2026-05-18T03:47:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0101268","created_at":"2026-05-18T03:47:10Z"},{"alias_kind":"pith_short_12","alias_value":"W7A6V6HQA4PF","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"W7A6V6HQA4PFGO6F","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"W7A6V6HQ","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:f1f424255aafabff0042e0b1ed3dd3b4fa767d5fd7955f4591076df22493b1a8","target":"graph","created_at":"2026-05-18T03:47:10Z","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 present a new approach to Morse theory based on the de Rham-Federer theory of currents. The full classical theory is derived in a transparent way. The methods carry over uniformly to the equivariant and the holomorphic settings. Moreover, the methods are substantially stronger than the classical ones and have interesting applications to geometry. They lead, for example, to formulae relating characteristic forms and singularities of bundle maps.","authors_text":"F. Reese Harvey, H. Blaine Lawson, jr","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2001-01-01T00:00:00Z","title":"Finite volume flows and Morse theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101268","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:a01cf09da3798d6e0fa4af626ec788b08afe2451bfb715f8088780b2933f5033","target":"record","created_at":"2026-05-18T03:47:10Z","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":"20f4f6ecf2a0906b386a6f77d82430018ffa5f018c6ac96d30113bd4852eeebb","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2001-01-01T00:00:00Z","title_canon_sha256":"20610c5d7dff403440eebf0e7eda76545fd291cf74eddf3d459cbbd843533a3c"},"schema_version":"1.0","source":{"id":"math/0101268","kind":"arxiv","version":1}},"canonical_sha256":"b7c1eaf8f0071e533bc55847f16e7d7f3494760a7ffcfc7b153f12980a82f0d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7c1eaf8f0071e533bc55847f16e7d7f3494760a7ffcfc7b153f12980a82f0d0","first_computed_at":"2026-05-18T03:47:10.566153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:10.566153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q91yhS/AUaSnDlaif1oi9oWfjkr6YEMEjCDn8uKdCXojKDlxqSS7Vfp5mj3Y8oHXCLGw5jltJXOdrnHjGarGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:10.566714Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0101268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a01cf09da3798d6e0fa4af626ec788b08afe2451bfb715f8088780b2933f5033","sha256:f1f424255aafabff0042e0b1ed3dd3b4fa767d5fd7955f4591076df22493b1a8"],"state_sha256":"3e8d381cf697ddca4641d46d841fef2a94a79d28ef37d54f2e3ef5eb202fa5e4"}