{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:2BY4BVE2HHOCB52RXGBU5QF3HM","short_pith_number":"pith:2BY4BVE2","schema_version":"1.0","canonical_sha256":"d071c0d49a39dc20f751b9834ec0bb3b1027cf4a813bfb8f81c9acb8d793e4ae","source":{"kind":"arxiv","id":"1604.08489","version":1},"attestation_state":"computed","paper":{"title":"On the L\\^e-Milnor fibration for real analytic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aurelio Menegon Neto, Jos\\'e Seade","submitted_at":"2016-04-28T16:09:03Z","abstract_excerpt":"In this paper, we study the topology of real analytic map-germs with isolated critical value $f: (\\mathbb{R}^m,0) \\to (\\mathbb{R}^n,0)$, with $1 <n <m$. We compare the topology of $f$ with the topology of the compositions $\\pi_i^* \\circ f$, where $\\pi_i^*: \\mathbb{R}^n \\to \\mathbb{R}^{n-1}$ are the projections $(t_1, \\dots, t_n) \\mapsto (t_1, \\dots, t_{i-1}, t_{i+1}, \\dots, t_n)$, for $i=1, \\dots, n$. As a main result, we give necessary and sufficient conditions for $f$ to have a L\\^e-Milnor fibration in the tube."},"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":"1604.08489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-28T16:09:03Z","cross_cats_sorted":[],"title_canon_sha256":"6851bdfa16b9767218fc9522f497f1ab243cf4f448e027ccaf6e84e4d597e7eb","abstract_canon_sha256":"3dc66e5759fcff0cdd46bc06875308102e1a30913234834cecc76d8ebc9f03e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:03.826388Z","signature_b64":"9ZUOwf0n1W7yxzsuhIQPuTFHaNdxigsWHeecjmT8W4oB/yu6ETYq/iUPont7UFGCvWKG3AzXTn0lLggMxSMeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d071c0d49a39dc20f751b9834ec0bb3b1027cf4a813bfb8f81c9acb8d793e4ae","last_reissued_at":"2026-05-18T01:16:03.825677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:03.825677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the L\\^e-Milnor fibration for real analytic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aurelio Menegon Neto, Jos\\'e Seade","submitted_at":"2016-04-28T16:09:03Z","abstract_excerpt":"In this paper, we study the topology of real analytic map-germs with isolated critical value $f: (\\mathbb{R}^m,0) \\to (\\mathbb{R}^n,0)$, with $1 <n <m$. We compare the topology of $f$ with the topology of the compositions $\\pi_i^* \\circ f$, where $\\pi_i^*: \\mathbb{R}^n \\to \\mathbb{R}^{n-1}$ are the projections $(t_1, \\dots, t_n) \\mapsto (t_1, \\dots, t_{i-1}, t_{i+1}, \\dots, t_n)$, for $i=1, \\dots, n$. As a main result, we give necessary and sufficient conditions for $f$ to have a L\\^e-Milnor fibration in the tube."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08489","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":"1604.08489","created_at":"2026-05-18T01:16:03.825789+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.08489v1","created_at":"2026-05-18T01:16:03.825789+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08489","created_at":"2026-05-18T01:16:03.825789+00:00"},{"alias_kind":"pith_short_12","alias_value":"2BY4BVE2HHOC","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"2BY4BVE2HHOCB52R","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"2BY4BVE2","created_at":"2026-05-18T12:29:52.810259+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/2BY4BVE2HHOCB52RXGBU5QF3HM","json":"https://pith.science/pith/2BY4BVE2HHOCB52RXGBU5QF3HM.json","graph_json":"https://pith.science/api/pith-number/2BY4BVE2HHOCB52RXGBU5QF3HM/graph.json","events_json":"https://pith.science/api/pith-number/2BY4BVE2HHOCB52RXGBU5QF3HM/events.json","paper":"https://pith.science/paper/2BY4BVE2"},"agent_actions":{"view_html":"https://pith.science/pith/2BY4BVE2HHOCB52RXGBU5QF3HM","download_json":"https://pith.science/pith/2BY4BVE2HHOCB52RXGBU5QF3HM.json","view_paper":"https://pith.science/paper/2BY4BVE2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.08489&json=true","fetch_graph":"https://pith.science/api/pith-number/2BY4BVE2HHOCB52RXGBU5QF3HM/graph.json","fetch_events":"https://pith.science/api/pith-number/2BY4BVE2HHOCB52RXGBU5QF3HM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2BY4BVE2HHOCB52RXGBU5QF3HM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2BY4BVE2HHOCB52RXGBU5QF3HM/action/storage_attestation","attest_author":"https://pith.science/pith/2BY4BVE2HHOCB52RXGBU5QF3HM/action/author_attestation","sign_citation":"https://pith.science/pith/2BY4BVE2HHOCB52RXGBU5QF3HM/action/citation_signature","submit_replication":"https://pith.science/pith/2BY4BVE2HHOCB52RXGBU5QF3HM/action/replication_record"}},"created_at":"2026-05-18T01:16:03.825789+00:00","updated_at":"2026-05-18T01:16:03.825789+00:00"}