{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:TZO6N2PNUMS3ZGRKXVBZYCS4AY","short_pith_number":"pith:TZO6N2PN","schema_version":"1.0","canonical_sha256":"9e5de6e9eda325bc9a2abd439c0a5c0636ce673a4792c626615a5f0696d3a012","source":{"kind":"arxiv","id":"math/0602301","version":2},"attestation_state":"computed","paper":{"title":"Logarithmic vector fields and multiplication table","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Susumu Tanab\\'e","submitted_at":"2006-02-14T14:23:58Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0602301","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-02-14T14:23:58Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"d13f5157b73f50561f397c6508bf42982fd0e61df2f3191aed2b03a0d5302f60","abstract_canon_sha256":"727b48f80b5555c93f6b29d3535f35a781ab54207cc139d6f534bb33378280c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:22.781486Z","signature_b64":"WwN2NZcOqkJqSEx+vjuqC5bwDkaoxB5Yxrd7QZGBcQm6CqJhOgIx0w8Qqs7BQ+iamR2sXyt9qM3chU//yim+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e5de6e9eda325bc9a2abd439c0a5c0636ce673a4792c626615a5f0696d3a012","last_reissued_at":"2026-05-18T01:05:22.780917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:22.780917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Logarithmic vector fields and multiplication table","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Susumu Tanab\\'e","submitted_at":"2006-02-14T14:23:58Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602301","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0602301","created_at":"2026-05-18T01:05:22.781004+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0602301v2","created_at":"2026-05-18T01:05:22.781004+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0602301","created_at":"2026-05-18T01:05:22.781004+00:00"},{"alias_kind":"pith_short_12","alias_value":"TZO6N2PNUMS3","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"TZO6N2PNUMS3ZGRK","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"TZO6N2PN","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TZO6N2PNUMS3ZGRKXVBZYCS4AY","json":"https://pith.science/pith/TZO6N2PNUMS3ZGRKXVBZYCS4AY.json","graph_json":"https://pith.science/api/pith-number/TZO6N2PNUMS3ZGRKXVBZYCS4AY/graph.json","events_json":"https://pith.science/api/pith-number/TZO6N2PNUMS3ZGRKXVBZYCS4AY/events.json","paper":"https://pith.science/paper/TZO6N2PN"},"agent_actions":{"view_html":"https://pith.science/pith/TZO6N2PNUMS3ZGRKXVBZYCS4AY","download_json":"https://pith.science/pith/TZO6N2PNUMS3ZGRKXVBZYCS4AY.json","view_paper":"https://pith.science/paper/TZO6N2PN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0602301&json=true","fetch_graph":"https://pith.science/api/pith-number/TZO6N2PNUMS3ZGRKXVBZYCS4AY/graph.json","fetch_events":"https://pith.science/api/pith-number/TZO6N2PNUMS3ZGRKXVBZYCS4AY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TZO6N2PNUMS3ZGRKXVBZYCS4AY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TZO6N2PNUMS3ZGRKXVBZYCS4AY/action/storage_attestation","attest_author":"https://pith.science/pith/TZO6N2PNUMS3ZGRKXVBZYCS4AY/action/author_attestation","sign_citation":"https://pith.science/pith/TZO6N2PNUMS3ZGRKXVBZYCS4AY/action/citation_signature","submit_replication":"https://pith.science/pith/TZO6N2PNUMS3ZGRKXVBZYCS4AY/action/replication_record"}},"created_at":"2026-05-18T01:05:22.781004+00:00","updated_at":"2026-05-18T01:05:22.781004+00:00"}