{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ELEKUSPMWEESVZOZXIEN4WGDZI","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":"b94a0cdae0715599ec5b19433de70389460a949c909e5d3fea49ae7ed782ff0a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-29T06:39:50Z","title_canon_sha256":"39bb461f3e2ad241a10f4d8463d5f46034d5457bec37cab0575d2952635bed7a"},"schema_version":"1.0","source":{"id":"1206.6950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6950","created_at":"2026-05-18T03:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6950v1","created_at":"2026-05-18T03:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6950","created_at":"2026-05-18T03:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"ELEKUSPMWEES","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ELEKUSPMWEESVZOZ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ELEKUSPM","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:2a83d5885cd82961264efb2e1ac494717532f7cf6591c201a2b3611969675849","target":"graph","created_at":"2026-05-18T03:52:13Z","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 study Thom Transversality Theorem using a point of view, suggested by Gromov, which allows to avoid the use of Sard Theorem and gives finer informations on the structure of the set of non-transverse maps.","authors_text":"Patrick Bernard (CEREMADE), Vito Mandorino (CEREMADE)","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-29T06:39:50Z","title":"Some remarks on Thom's Transversality Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6950","kind":"arxiv","version":1},"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":"sha256:6eeb073a575879fa217b1f9f959620f1d4bb58fbc9b55581dcfb1f9b813cbbbd","target":"record","created_at":"2026-05-18T03:52:13Z","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":"b94a0cdae0715599ec5b19433de70389460a949c909e5d3fea49ae7ed782ff0a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-29T06:39:50Z","title_canon_sha256":"39bb461f3e2ad241a10f4d8463d5f46034d5457bec37cab0575d2952635bed7a"},"schema_version":"1.0","source":{"id":"1206.6950","kind":"arxiv","version":1}},"canonical_sha256":"22c8aa49ecb1092ae5d9ba08de58c3ca1888af4ec30dabdbfe6ef94f7705be2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22c8aa49ecb1092ae5d9ba08de58c3ca1888af4ec30dabdbfe6ef94f7705be2f","first_computed_at":"2026-05-18T03:52:13.429267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:13.429267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rlrNE+6MIfruGNhP/1moTSbZe/TPjsB71teRCIComAOqsBfHSPH6gZTUwJf1rTE1GjJlhRf2CKmhBOT8kOMdDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:13.430153Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6eeb073a575879fa217b1f9f959620f1d4bb58fbc9b55581dcfb1f9b813cbbbd","sha256:2a83d5885cd82961264efb2e1ac494717532f7cf6591c201a2b3611969675849"],"state_sha256":"8a7f28bde55bd39e2a29e490a4992c762111f74022d3156a4da5afcaf1d8c5a1"}