{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:INJNHKXKOYFVOMU7NNZHUMSMCF","short_pith_number":"pith:INJNHKXK","schema_version":"1.0","canonical_sha256":"4352d3aaea760b57329f6b727a324c116586d37a59bd43eabe96209d3ea5f330","source":{"kind":"arxiv","id":"1103.3236","version":1},"attestation_state":"computed","paper":{"title":"Milnor Fibrations and the Thom Property for maps $f \\bar g$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anne Pichon, Jos\\'e Seade","submitted_at":"2011-03-16T17:20:42Z","abstract_excerpt":"We prove that every map-germ ${f \\bar g}: (\\C^n,\\0) {\\to}(\\C,0)$ with an isolated critical value at 0 has the Thom $a_{f \\bar g}$-property. This extends Hironaka's theorem for holomorphic mappings to the case of map-germs $f \\bar g$ and it implies that every such map-germ has a Milnor-L\\^e fibration defined on a Milnor tube. One thus has a locally trivial fibration $\\phi: \\mathbb S_\\e \\setminus K \\to \\mathbb S^1$ for every sufficiently small sphere around $\\0$, where $K$ is the link of $f \\bar g$ and in a neighbourhood of $K$ the projection map $\\phi$ is given by $f \\bar g / | f \\bar g|$."},"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":"1103.3236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-16T17:20:42Z","cross_cats_sorted":[],"title_canon_sha256":"e3936610e604b2ce87287fe24f7484c4da9f49c91aa001641aff32efae099e87","abstract_canon_sha256":"089494951dcb61287958fae823dcdd873cffe75dc42b318969b2b1ef6d441feb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:44.547080Z","signature_b64":"MV/Yby6raDxWvYYfTzGWEmfJ214U9x7i5sEDisBBE7pgoFgp5W4HmVVx81RjQmC+pXt7oAqn8PF9JYDgt6ygBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4352d3aaea760b57329f6b727a324c116586d37a59bd43eabe96209d3ea5f330","last_reissued_at":"2026-05-18T04:26:44.546406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:44.546406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Milnor Fibrations and the Thom Property for maps $f \\bar g$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anne Pichon, Jos\\'e Seade","submitted_at":"2011-03-16T17:20:42Z","abstract_excerpt":"We prove that every map-germ ${f \\bar g}: (\\C^n,\\0) {\\to}(\\C,0)$ with an isolated critical value at 0 has the Thom $a_{f \\bar g}$-property. This extends Hironaka's theorem for holomorphic mappings to the case of map-germs $f \\bar g$ and it implies that every such map-germ has a Milnor-L\\^e fibration defined on a Milnor tube. One thus has a locally trivial fibration $\\phi: \\mathbb S_\\e \\setminus K \\to \\mathbb S^1$ for every sufficiently small sphere around $\\0$, where $K$ is the link of $f \\bar g$ and in a neighbourhood of $K$ the projection map $\\phi$ is given by $f \\bar g / | f \\bar g|$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3236","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":""},"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":"1103.3236","created_at":"2026-05-18T04:26:44.546511+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.3236v1","created_at":"2026-05-18T04:26:44.546511+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3236","created_at":"2026-05-18T04:26:44.546511+00:00"},{"alias_kind":"pith_short_12","alias_value":"INJNHKXKOYFV","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"INJNHKXKOYFVOMU7","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"INJNHKXK","created_at":"2026-05-18T12:26:32.869790+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/INJNHKXKOYFVOMU7NNZHUMSMCF","json":"https://pith.science/pith/INJNHKXKOYFVOMU7NNZHUMSMCF.json","graph_json":"https://pith.science/api/pith-number/INJNHKXKOYFVOMU7NNZHUMSMCF/graph.json","events_json":"https://pith.science/api/pith-number/INJNHKXKOYFVOMU7NNZHUMSMCF/events.json","paper":"https://pith.science/paper/INJNHKXK"},"agent_actions":{"view_html":"https://pith.science/pith/INJNHKXKOYFVOMU7NNZHUMSMCF","download_json":"https://pith.science/pith/INJNHKXKOYFVOMU7NNZHUMSMCF.json","view_paper":"https://pith.science/paper/INJNHKXK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.3236&json=true","fetch_graph":"https://pith.science/api/pith-number/INJNHKXKOYFVOMU7NNZHUMSMCF/graph.json","fetch_events":"https://pith.science/api/pith-number/INJNHKXKOYFVOMU7NNZHUMSMCF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/INJNHKXKOYFVOMU7NNZHUMSMCF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/INJNHKXKOYFVOMU7NNZHUMSMCF/action/storage_attestation","attest_author":"https://pith.science/pith/INJNHKXKOYFVOMU7NNZHUMSMCF/action/author_attestation","sign_citation":"https://pith.science/pith/INJNHKXKOYFVOMU7NNZHUMSMCF/action/citation_signature","submit_replication":"https://pith.science/pith/INJNHKXKOYFVOMU7NNZHUMSMCF/action/replication_record"}},"created_at":"2026-05-18T04:26:44.546511+00:00","updated_at":"2026-05-18T04:26:44.546511+00:00"}