{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KS4LHJZ2WXGEYPBGJTHKZQIZHR","short_pith_number":"pith:KS4LHJZ2","schema_version":"1.0","canonical_sha256":"54b8b3a73ab5cc4c3c264cceacc1193c4ed9a71611ee9dc301b808693202cc82","source":{"kind":"arxiv","id":"2406.12166","version":1},"attestation_state":"computed","paper":{"title":"Universal polynomials for multi-singularity loci of maps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Toru Ohmoto","submitted_at":"2024-06-18T00:36:12Z","abstract_excerpt":"In the present paper, we prove the existence of universal polynomials which express multi-singularity loci classes of prescribed types for proper morphisms between smooth schemes over an algebraically closed field of characteristic zero -- we call them Thom polynomials for multi-singularity types of maps. It has been referred to as the Thom-Kazarian principle and unsolved for a long time. This result solidifies the foundation for a general enumerative theory of singularities of maps which is applicable to a broad range of problems in classical and modern algebraic geometry. In particular, it w"},"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":"2406.12166","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-06-18T00:36:12Z","cross_cats_sorted":[],"title_canon_sha256":"e547a0c65dc16803b8730a93e8646e47315885d5eef854c6479384d6fe948412","abstract_canon_sha256":"3504f325f4537024a30cf79bcef6bea5d1d5f8c95173120deea00acc15b5ce91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:33:07.341564Z","signature_b64":"LaI2kArNVWUKLvD7YD7WIRHagjnqbtrIlXHBzLQOzP/rGWln1nqIBFa/qxlIbJriaNheWH/stKdvMaxv2GkXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54b8b3a73ab5cc4c3c264cceacc1193c4ed9a71611ee9dc301b808693202cc82","last_reissued_at":"2026-07-05T08:33:07.341135Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:33:07.341135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal polynomials for multi-singularity loci of maps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Toru Ohmoto","submitted_at":"2024-06-18T00:36:12Z","abstract_excerpt":"In the present paper, we prove the existence of universal polynomials which express multi-singularity loci classes of prescribed types for proper morphisms between smooth schemes over an algebraically closed field of characteristic zero -- we call them Thom polynomials for multi-singularity types of maps. It has been referred to as the Thom-Kazarian principle and unsolved for a long time. This result solidifies the foundation for a general enumerative theory of singularities of maps which is applicable to a broad range of problems in classical and modern algebraic geometry. In particular, it w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.12166","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.12166/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2406.12166","created_at":"2026-07-05T08:33:07.341201+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.12166v1","created_at":"2026-07-05T08:33:07.341201+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.12166","created_at":"2026-07-05T08:33:07.341201+00:00"},{"alias_kind":"pith_short_12","alias_value":"KS4LHJZ2WXGE","created_at":"2026-07-05T08:33:07.341201+00:00"},{"alias_kind":"pith_short_16","alias_value":"KS4LHJZ2WXGEYPBG","created_at":"2026-07-05T08:33:07.341201+00:00"},{"alias_kind":"pith_short_8","alias_value":"KS4LHJZ2","created_at":"2026-07-05T08:33:07.341201+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/KS4LHJZ2WXGEYPBGJTHKZQIZHR","json":"https://pith.science/pith/KS4LHJZ2WXGEYPBGJTHKZQIZHR.json","graph_json":"https://pith.science/api/pith-number/KS4LHJZ2WXGEYPBGJTHKZQIZHR/graph.json","events_json":"https://pith.science/api/pith-number/KS4LHJZ2WXGEYPBGJTHKZQIZHR/events.json","paper":"https://pith.science/paper/KS4LHJZ2"},"agent_actions":{"view_html":"https://pith.science/pith/KS4LHJZ2WXGEYPBGJTHKZQIZHR","download_json":"https://pith.science/pith/KS4LHJZ2WXGEYPBGJTHKZQIZHR.json","view_paper":"https://pith.science/paper/KS4LHJZ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.12166&json=true","fetch_graph":"https://pith.science/api/pith-number/KS4LHJZ2WXGEYPBGJTHKZQIZHR/graph.json","fetch_events":"https://pith.science/api/pith-number/KS4LHJZ2WXGEYPBGJTHKZQIZHR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KS4LHJZ2WXGEYPBGJTHKZQIZHR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KS4LHJZ2WXGEYPBGJTHKZQIZHR/action/storage_attestation","attest_author":"https://pith.science/pith/KS4LHJZ2WXGEYPBGJTHKZQIZHR/action/author_attestation","sign_citation":"https://pith.science/pith/KS4LHJZ2WXGEYPBGJTHKZQIZHR/action/citation_signature","submit_replication":"https://pith.science/pith/KS4LHJZ2WXGEYPBGJTHKZQIZHR/action/replication_record"}},"created_at":"2026-07-05T08:33:07.341201+00:00","updated_at":"2026-07-05T08:33:07.341201+00:00"}