{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QHOL4YXE6AIL6ZQTZTXE7RHYES","short_pith_number":"pith:QHOL4YXE","schema_version":"1.0","canonical_sha256":"81dcbe62e4f010bf6613ccee4fc4f8248c4483d73e91c2c9663aa017d868e023","source":{"kind":"arxiv","id":"1511.06812","version":1},"attestation_state":"computed","paper":{"title":"Vanishing polyhedron and collapsing map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Aur\\'elio Menegon Neto, L\\^e D\\~ung Tr\\'ang","submitted_at":"2015-11-21T01:42:57Z","abstract_excerpt":"In this paper we give a detailed proof that the Milnor fiber $X_t$ of an analytic complex isolated singularity function defined on a reduced $n$-equidimensional analytic complex space $X$ is a regular neighborhood of a polyhedron $P_t \\subset X_t$ of real dimension $n-1$. Moreover, we describe the degeneration of $X_t$ onto the special fiber $X_0$, by giving a continuous collapsing map $\\Psi_t: X_t \\to X_0$ which sends $P_t$ to $\\{0\\}$ and which restricts to a homeomorphism $X_t \\backslash P_t \\to X_0 \\backslash \\{0\\}$."},"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":"1511.06812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-11-21T01:42:57Z","cross_cats_sorted":[],"title_canon_sha256":"a6af7c65184942980a2c443ee6ddf8855795088466708ffd974a42dc6ecf580a","abstract_canon_sha256":"e9828bf69e7cc58af6be205d995a18a847dbe04d72091a2939ddd4bd1b244a3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:19.418131Z","signature_b64":"AWyG2QnhMhVH4HvCNQcXx9o2ebjHWv5drf0gZ7nX1Ffia92igP5rWq8E6OWWFClqellD+SK27jV5yV2jIbtzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81dcbe62e4f010bf6613ccee4fc4f8248c4483d73e91c2c9663aa017d868e023","last_reissued_at":"2026-05-18T01:26:19.417564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:19.417564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vanishing polyhedron and collapsing map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Aur\\'elio Menegon Neto, L\\^e D\\~ung Tr\\'ang","submitted_at":"2015-11-21T01:42:57Z","abstract_excerpt":"In this paper we give a detailed proof that the Milnor fiber $X_t$ of an analytic complex isolated singularity function defined on a reduced $n$-equidimensional analytic complex space $X$ is a regular neighborhood of a polyhedron $P_t \\subset X_t$ of real dimension $n-1$. Moreover, we describe the degeneration of $X_t$ onto the special fiber $X_0$, by giving a continuous collapsing map $\\Psi_t: X_t \\to X_0$ which sends $P_t$ to $\\{0\\}$ and which restricts to a homeomorphism $X_t \\backslash P_t \\to X_0 \\backslash \\{0\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06812","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":"1511.06812","created_at":"2026-05-18T01:26:19.417656+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.06812v1","created_at":"2026-05-18T01:26:19.417656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06812","created_at":"2026-05-18T01:26:19.417656+00:00"},{"alias_kind":"pith_short_12","alias_value":"QHOL4YXE6AIL","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"QHOL4YXE6AIL6ZQT","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"QHOL4YXE","created_at":"2026-05-18T12:29:37.295048+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/QHOL4YXE6AIL6ZQTZTXE7RHYES","json":"https://pith.science/pith/QHOL4YXE6AIL6ZQTZTXE7RHYES.json","graph_json":"https://pith.science/api/pith-number/QHOL4YXE6AIL6ZQTZTXE7RHYES/graph.json","events_json":"https://pith.science/api/pith-number/QHOL4YXE6AIL6ZQTZTXE7RHYES/events.json","paper":"https://pith.science/paper/QHOL4YXE"},"agent_actions":{"view_html":"https://pith.science/pith/QHOL4YXE6AIL6ZQTZTXE7RHYES","download_json":"https://pith.science/pith/QHOL4YXE6AIL6ZQTZTXE7RHYES.json","view_paper":"https://pith.science/paper/QHOL4YXE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.06812&json=true","fetch_graph":"https://pith.science/api/pith-number/QHOL4YXE6AIL6ZQTZTXE7RHYES/graph.json","fetch_events":"https://pith.science/api/pith-number/QHOL4YXE6AIL6ZQTZTXE7RHYES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QHOL4YXE6AIL6ZQTZTXE7RHYES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QHOL4YXE6AIL6ZQTZTXE7RHYES/action/storage_attestation","attest_author":"https://pith.science/pith/QHOL4YXE6AIL6ZQTZTXE7RHYES/action/author_attestation","sign_citation":"https://pith.science/pith/QHOL4YXE6AIL6ZQTZTXE7RHYES/action/citation_signature","submit_replication":"https://pith.science/pith/QHOL4YXE6AIL6ZQTZTXE7RHYES/action/replication_record"}},"created_at":"2026-05-18T01:26:19.417656+00:00","updated_at":"2026-05-18T01:26:19.417656+00:00"}