{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:MV7T6YVLANIR4MOVJ4BPDHPAZG","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":"4edf707ba3ca2b17795151d0436263ee39e77424899f2f03b881a8f54908eba6","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"1997-02-21T00:00:00Z","title_canon_sha256":"152cb86c5a7093c3ccc05987c16032aae9ef1293541c7c6e9eee748d0eeb2b08"},"schema_version":"1.0","source":{"id":"math/9702229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9702229","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/9702229v1","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9702229","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"MV7T6YVLANIR","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"MV7T6YVLANIR4MOV","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"MV7T6YVL","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:dc9e2ea9cdce2a638d3b9d4fb07cc4d8db452ba141d98ee42020eb03deb48f93","target":"graph","created_at":"2026-05-18T01:05:37Z","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":"Let P(x) be a germ at the origin of an analytic function in C^n, where x = (x_1,..., x_n), and let\n  \\xi = \\xi_1(x) d/dx_1 + ... + \\xi_n(x) d/dx_n\n  be a germ at the origin of an analytic vector field. Suppose that \\xi(0) != 0, and let \\gamma be a trajectory of \\xi through the origin. Suppose that P|_\\gamma /\\equiv 0, and let \\mu(P|_\\gamma) be the multiplicity of a zero of P|_\\gamma at the origin. Let\n  \\xi P = \\xi_1 dP/dx_1 + ... + \\xi_n dP/dx_n\n  be derivative of P in the direction of \\xi, and let \\xi^kP be the kth iteration of this derivative.\n  We give a formula (Theorem 1) for \\mu(P|_\\gam","authors_text":"Andrei Gabrielov (Purdue University)","cross_cats":[],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"1997-02-21T00:00:00Z","title":"Multiplicity of a zero of an analytic function on a trajectory of a vector field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9702229","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":"sha256:5093f11c0996c538bf41bc35cf413b47964d14a515969dbbfb7b99c7b389569b","target":"record","created_at":"2026-05-18T01:05:37Z","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":"4edf707ba3ca2b17795151d0436263ee39e77424899f2f03b881a8f54908eba6","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"1997-02-21T00:00:00Z","title_canon_sha256":"152cb86c5a7093c3ccc05987c16032aae9ef1293541c7c6e9eee748d0eeb2b08"},"schema_version":"1.0","source":{"id":"math/9702229","kind":"arxiv","version":1}},"canonical_sha256":"657f3f62ab03511e31d54f02f19de0c9869fdb241479f5e126d3b1f32d5307fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"657f3f62ab03511e31d54f02f19de0c9869fdb241479f5e126d3b1f32d5307fe","first_computed_at":"2026-05-18T01:05:37.104419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:37.104419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AVXArSiCwpp+nPynmClBKxllS5mExgcfdizN4maw3Qa73y8FRFUfYCdqyB8hqaEPsMe7pmhe77iB3VCwj0qRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:37.105038Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9702229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5093f11c0996c538bf41bc35cf413b47964d14a515969dbbfb7b99c7b389569b","sha256:dc9e2ea9cdce2a638d3b9d4fb07cc4d8db452ba141d98ee42020eb03deb48f93"],"state_sha256":"93c9b6ab1ea7286cc3ac17085b7abd2e534f7d585a3a4a65fb42b7db46271557"}