{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QCFHQ2H7ZW423WIKN2EVMGQAXX","short_pith_number":"pith:QCFHQ2H7","schema_version":"1.0","canonical_sha256":"808a7868ffcdb9add90a6e89561a00bdf4cb4e7038b6f9fdb982ffaf7e5037a9","source":{"kind":"arxiv","id":"1409.5053","version":1},"attestation_state":"computed","paper":{"title":"Fibrations structure and degree formulae for Milnor fibers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Antonio Andrade (ICMC), Nicolas Dutertre (I2M), Raimundo N. Ara\\'ujo Dos Santos (ICMC), Ying Chen (ICMC)","submitted_at":"2014-09-17T16:21:53Z","abstract_excerpt":"In this survey, we remind some fibrations structure theorems (also called Milnor's fibrations) recently proved in the real and complex case, in the local and global settings. We give several Poincar\\'e-Hopf type formulae which relates the Euler-Poincar\\'e characteristic of these fibers (also called Milnor's fibers) and indices (topological degree) of appropriated vector fields defined on spheres of radii small or big enough."},"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":"1409.5053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-17T16:21:53Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"65f278482f80212186ee5e2e69ababe34b1b0aeff5f785fc9e7e1860b0bff742","abstract_canon_sha256":"c129334ddf7e0097c5eb9de1b4393b43492a73f6afa0a96b0d1ef6debf605b0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:37.965805Z","signature_b64":"iJpvLaDjNb7cCzQCzu0wwVVk5S0NImOJmD62n01ZcyAOFgweU8WpEBSWptJBqOYwyyDKCkDSC9bjDAoSpBKtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"808a7868ffcdb9add90a6e89561a00bdf4cb4e7038b6f9fdb982ffaf7e5037a9","last_reissued_at":"2026-05-18T02:42:37.965278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:37.965278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fibrations structure and degree formulae for Milnor fibers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Antonio Andrade (ICMC), Nicolas Dutertre (I2M), Raimundo N. Ara\\'ujo Dos Santos (ICMC), Ying Chen (ICMC)","submitted_at":"2014-09-17T16:21:53Z","abstract_excerpt":"In this survey, we remind some fibrations structure theorems (also called Milnor's fibrations) recently proved in the real and complex case, in the local and global settings. We give several Poincar\\'e-Hopf type formulae which relates the Euler-Poincar\\'e characteristic of these fibers (also called Milnor's fibers) and indices (topological degree) of appropriated vector fields defined on spheres of radii small or big enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5053","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":"1409.5053","created_at":"2026-05-18T02:42:37.965375+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.5053v1","created_at":"2026-05-18T02:42:37.965375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5053","created_at":"2026-05-18T02:42:37.965375+00:00"},{"alias_kind":"pith_short_12","alias_value":"QCFHQ2H7ZW42","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"QCFHQ2H7ZW423WIK","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"QCFHQ2H7","created_at":"2026-05-18T12:28:43.426989+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/QCFHQ2H7ZW423WIKN2EVMGQAXX","json":"https://pith.science/pith/QCFHQ2H7ZW423WIKN2EVMGQAXX.json","graph_json":"https://pith.science/api/pith-number/QCFHQ2H7ZW423WIKN2EVMGQAXX/graph.json","events_json":"https://pith.science/api/pith-number/QCFHQ2H7ZW423WIKN2EVMGQAXX/events.json","paper":"https://pith.science/paper/QCFHQ2H7"},"agent_actions":{"view_html":"https://pith.science/pith/QCFHQ2H7ZW423WIKN2EVMGQAXX","download_json":"https://pith.science/pith/QCFHQ2H7ZW423WIKN2EVMGQAXX.json","view_paper":"https://pith.science/paper/QCFHQ2H7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.5053&json=true","fetch_graph":"https://pith.science/api/pith-number/QCFHQ2H7ZW423WIKN2EVMGQAXX/graph.json","fetch_events":"https://pith.science/api/pith-number/QCFHQ2H7ZW423WIKN2EVMGQAXX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QCFHQ2H7ZW423WIKN2EVMGQAXX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QCFHQ2H7ZW423WIKN2EVMGQAXX/action/storage_attestation","attest_author":"https://pith.science/pith/QCFHQ2H7ZW423WIKN2EVMGQAXX/action/author_attestation","sign_citation":"https://pith.science/pith/QCFHQ2H7ZW423WIKN2EVMGQAXX/action/citation_signature","submit_replication":"https://pith.science/pith/QCFHQ2H7ZW423WIKN2EVMGQAXX/action/replication_record"}},"created_at":"2026-05-18T02:42:37.965375+00:00","updated_at":"2026-05-18T02:42:37.965375+00:00"}