{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Y4B2M4XNLPLVEYDIBVLYFOH6SI","short_pith_number":"pith:Y4B2M4XN","canonical_record":{"source":{"id":"1209.1282","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-06T14:05:52Z","cross_cats_sorted":[],"title_canon_sha256":"d441b5a1b5f4625eb0c823730501df83cae177da71eb65e51dfa736047e5cc02","abstract_canon_sha256":"8627b36206c6c462343e687037d2caf09144b7f75624f960f7966da53bda0b73"},"schema_version":"1.0"},"canonical_sha256":"c703a672ed5bd75260680d5782b8fe920d723d26147bb5e2fe3d6df743c0153c","source":{"kind":"arxiv","id":"1209.1282","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Y4B2M4XNLPLVEYDIBVLYFOH6SI","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1282","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-06T14:05:52Z","cross_cats_sorted":[],"title_canon_sha256":"d441b5a1b5f4625eb0c823730501df83cae177da71eb65e51dfa736047e5cc02","abstract_canon_sha256":"8627b36206c6c462343e687037d2caf09144b7f75624f960f7966da53bda0b73"},"schema_version":"1.0"},"canonical_sha256":"c703a672ed5bd75260680d5782b8fe920d723d26147bb5e2fe3d6df743c0153c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:55.682493Z","signature_b64":"Rx2yEMt6pwtcDGaoMOs39BC7XVwRzQDZ1Gyb5o6cmV654ugYb3cxgvnx3wd5vBnpj2wCQqK3ZnhQC7Z11/PaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c703a672ed5bd75260680d5782b8fe920d723d26147bb5e2fe3d6df743c0153c","last_reissued_at":"2026-05-18T03:38:55.681861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:55.681861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1282","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jutzJwPNNL7cvQXR5kWgjygZEC9SRgM4cIy5klQ7+UCXWaYanag5OOa3dT/o/1w90DkNLinIyOcVJjV+bNGwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T10:36:27.915735Z"},"content_sha256":"cd0f5db9668e995e6c30524619ff081f60a9636ebe1320f7f4e6d6d44460e556","schema_version":"1.0","event_id":"sha256:cd0f5db9668e995e6c30524619ff081f60a9636ebe1320f7f4e6d6d44460e556"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Y4B2M4XNLPLVEYDIBVLYFOH6SI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A characterization of Whitney a-regular complex analytic stratifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Saurabh Trivedi","submitted_at":"2012-09-06T14:05:52Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1282","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0XA7qMiilkN8AxHBZx9EQy8M1+xTOdhfIGK2gWF0lNqihX3TUiyP2vsqExHOPIpfHv8vwgyZBbaQTebzjmi6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T10:36:27.916080Z"},"content_sha256":"5299cdd40e657baf052e57c6a3e15227e94b54cabb139a562fe71c43076d914e","schema_version":"1.0","event_id":"sha256:5299cdd40e657baf052e57c6a3e15227e94b54cabb139a562fe71c43076d914e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y4B2M4XNLPLVEYDIBVLYFOH6SI/bundle.json","state_url":"https://pith.science/pith/Y4B2M4XNLPLVEYDIBVLYFOH6SI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y4B2M4XNLPLVEYDIBVLYFOH6SI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T10:36:27Z","links":{"resolver":"https://pith.science/pith/Y4B2M4XNLPLVEYDIBVLYFOH6SI","bundle":"https://pith.science/pith/Y4B2M4XNLPLVEYDIBVLYFOH6SI/bundle.json","state":"https://pith.science/pith/Y4B2M4XNLPLVEYDIBVLYFOH6SI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y4B2M4XNLPLVEYDIBVLYFOH6SI/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cwqxiYc2UtQJeRnMLwZoVmLo6zxL6esh3dEfAsIiqhb77j0MYqgaJWjMyJ1eVsgKd8WobrNJUmYAByAHlglKBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T10:36:27.918053Z","bundle_sha256":"c0bc9dc825585bd7dccaffa7fc0e1f5146518e8b008b01bc338a20e8ff373cbd"}}