{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ODVT6KUWVDJNY6QOS7BXLTU4G6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b24820664f8ed25e20715c375ebf059184bcaf7e691b987aa57a0c3c771f1904","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-07T18:19:01Z","title_canon_sha256":"7fde3710f10374e9ff92f019be39accb38f92c53ac6b026f234cbf394417a84f"},"schema_version":"1.0","source":{"id":"1805.02681","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02681","created_at":"2026-05-18T00:11:27Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02681v2","created_at":"2026-05-18T00:11:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02681","created_at":"2026-05-18T00:11:27Z"},{"alias_kind":"pith_short_12","alias_value":"ODVT6KUWVDJN","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"ODVT6KUWVDJNY6QO","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"ODVT6KUW","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:3fc75bcaf370b2e6d0fc017bc24578dd56cb97931fe7fea3ef6060659202ff9e","target":"graph","created_at":"2026-05-18T00:11:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $X\\subset\\Bbb C^n$ be an affine variety and $f:X\\to\\Bbb C^m$ be the restriction to $X$ of a polynomial map $\\Bbb C^n\\to\\Bbb C^m$. In this paper, we construct an affine Whitney stratification of $X$. The set $K(f)$ of stratified generalized critical values of $f$ can be also computed. We show that $K(f)$ is a nowhere dense subset of $\\Bbb C^m$, which contains the set $B(f)$ of bifurcation values of $f$ by proving a version of the isotopy lemma for non-proper polynomial maps on singular varieties.","authors_text":"Si Tiep Dinh, Zbigniew Jelonek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-07T18:19:01Z","title":"Thom isotopy theorem for non proper maps and computation of sets of stratified generalized critical values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02681","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:939dcd8c674d4d2789fb25a63e16f48d4ab40357151131f81a3fc67797ead547","target":"record","created_at":"2026-05-18T00:11:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b24820664f8ed25e20715c375ebf059184bcaf7e691b987aa57a0c3c771f1904","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-07T18:19:01Z","title_canon_sha256":"7fde3710f10374e9ff92f019be39accb38f92c53ac6b026f234cbf394417a84f"},"schema_version":"1.0","source":{"id":"1805.02681","kind":"arxiv","version":2}},"canonical_sha256":"70eb3f2a96a8d2dc7a0e97c375ce9c378f919d6a5f54e515e53099577b7468b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70eb3f2a96a8d2dc7a0e97c375ce9c378f919d6a5f54e515e53099577b7468b5","first_computed_at":"2026-05-18T00:11:27.948518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:27.948518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ZWLrwwzMHjradsuR7wIqpsR4UcbuDp9tiPj0UTBMKRTgd1y5grXh1hV+fIotH4gryoON7FRy1/7gNaqM5ejBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:27.948932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02681","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:939dcd8c674d4d2789fb25a63e16f48d4ab40357151131f81a3fc67797ead547","sha256:3fc75bcaf370b2e6d0fc017bc24578dd56cb97931fe7fea3ef6060659202ff9e"],"state_sha256":"e211a13af2b1f2ba8667c8735c6f5afdc0247251e61da4dba49f76a254ab142d"}