{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:TZO6N2PNUMS3ZGRKXVBZYCS4AY","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":"727b48f80b5555c93f6b29d3535f35a781ab54207cc139d6f534bb33378280c0","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.AG","submitted_at":"2006-02-14T14:23:58Z","title_canon_sha256":"d13f5157b73f50561f397c6508bf42982fd0e61df2f3191aed2b03a0d5302f60"},"schema_version":"1.0","source":{"id":"math/0602301","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0602301","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0602301v2","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0602301","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"TZO6N2PNUMS3","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"TZO6N2PNUMS3ZGRK","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"TZO6N2PN","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:c820736ff50de1f2351f70ec7bb9865976719d56c38f10a46c820cfcb68707d8","target":"graph","created_at":"2026-05-18T01:05:22Z","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":"This is a review article on the Gauss-Manin system associated to the complete intersection singularities of projection. We show how the logarithmic vector fields appear as coefficients to the Gauss-Manin system.\n We examine further how the multiplication table on the Jacobian quotient module calculates the logarithmic vector fields tangent to the discriminant and the bifurcation set . As applications, we establish signature formulae for Euler characteristics of real hypersurfaces and real complete intersections by means of these fields.","authors_text":"Susumu Tanab\\'e","cross_cats":["math.CV"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2006-02-14T14:23:58Z","title":"Logarithmic vector fields and multiplication table"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602301","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":"sha256:388a0191cc47f9bd75d95350cdf94e8a80fc46beb11e7effe9400e8079613306","target":"record","created_at":"2026-05-18T01:05:22Z","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":"727b48f80b5555c93f6b29d3535f35a781ab54207cc139d6f534bb33378280c0","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.AG","submitted_at":"2006-02-14T14:23:58Z","title_canon_sha256":"d13f5157b73f50561f397c6508bf42982fd0e61df2f3191aed2b03a0d5302f60"},"schema_version":"1.0","source":{"id":"math/0602301","kind":"arxiv","version":2}},"canonical_sha256":"9e5de6e9eda325bc9a2abd439c0a5c0636ce673a4792c626615a5f0696d3a012","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e5de6e9eda325bc9a2abd439c0a5c0636ce673a4792c626615a5f0696d3a012","first_computed_at":"2026-05-18T01:05:22.780917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:22.780917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WwN2NZcOqkJqSEx+vjuqC5bwDkaoxB5Yxrd7QZGBcQm6CqJhOgIx0w8Qqs7BQ+iamR2sXyt9qM3chU//yim+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:22.781486Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0602301","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:388a0191cc47f9bd75d95350cdf94e8a80fc46beb11e7effe9400e8079613306","sha256:c820736ff50de1f2351f70ec7bb9865976719d56c38f10a46c820cfcb68707d8"],"state_sha256":"5fea61778e8c254748f0d2ab01f387a97074fc1c5744dcc801aa0f5a2398e670"}