{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y4B2M4XNLPLVEYDIBVLYFOH6SI","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":"8627b36206c6c462343e687037d2caf09144b7f75624f960f7966da53bda0b73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-06T14:05:52Z","title_canon_sha256":"d441b5a1b5f4625eb0c823730501df83cae177da71eb65e51dfa736047e5cc02"},"schema_version":"1.0","source":{"id":"1209.1282","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1282","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1282v2","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1282","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"pith_short_12","alias_value":"Y4B2M4XNLPLV","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y4B2M4XNLPLVEYDI","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y4B2M4XN","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:5299cdd40e657baf052e57c6a3e15227e94b54cabb139a562fe71c43076d914e","target":"graph","created_at":"2026-05-18T03:38:55Z","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":"We prove that the openness of the set of maps, between a Stein manifold and an Oka manifold, transverse to a stratification of a complex analytic subvariety in the target implies that the stratification is Whitney $a$-regular. Our result can be seen as a complex version of Trotman's theorem.","authors_text":"Saurabh Trivedi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-06T14:05:52Z","title":"A characterization of Whitney a-regular complex analytic stratifications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1282","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:cd0f5db9668e995e6c30524619ff081f60a9636ebe1320f7f4e6d6d44460e556","target":"record","created_at":"2026-05-18T03:38:55Z","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":"8627b36206c6c462343e687037d2caf09144b7f75624f960f7966da53bda0b73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-06T14:05:52Z","title_canon_sha256":"d441b5a1b5f4625eb0c823730501df83cae177da71eb65e51dfa736047e5cc02"},"schema_version":"1.0","source":{"id":"1209.1282","kind":"arxiv","version":2}},"canonical_sha256":"c703a672ed5bd75260680d5782b8fe920d723d26147bb5e2fe3d6df743c0153c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c703a672ed5bd75260680d5782b8fe920d723d26147bb5e2fe3d6df743c0153c","first_computed_at":"2026-05-18T03:38:55.681861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:55.681861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rx2yEMt6pwtcDGaoMOs39BC7XVwRzQDZ1Gyb5o6cmV654ugYb3cxgvnx3wd5vBnpj2wCQqK3ZnhQC7Z11/PaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:55.682493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1282","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd0f5db9668e995e6c30524619ff081f60a9636ebe1320f7f4e6d6d44460e556","sha256:5299cdd40e657baf052e57c6a3e15227e94b54cabb139a562fe71c43076d914e"],"state_sha256":"d6e81e8638ba99e9867e3a0013b1b71ba78df71eaad990fc974eaa7fbdb456ed"}