{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DVYBQWANEFPMNH4IMJ7JYOO5GZ","short_pith_number":"pith:DVYBQWAN","canonical_record":{"source":{"id":"1403.1627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-07T00:49:34Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"8a665e26012c17b47a5bb1227d41668be1a70890b085ffb41bd87047d1a8fc89","abstract_canon_sha256":"b47f443acf6e52b1161efda6a3621a19f90e5a53d88ccddd1cf4a49073c53303"},"schema_version":"1.0"},"canonical_sha256":"1d7018580d215ec69f88627e9c39dd3660ddf9050e4a1cde3d16e0412592b5ec","source":{"kind":"arxiv","id":"1403.1627","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1627","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1627v1","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1627","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"DVYBQWANEFPM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DVYBQWANEFPMNH4I","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DVYBQWAN","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DVYBQWANEFPMNH4IMJ7JYOO5GZ","target":"record","payload":{"canonical_record":{"source":{"id":"1403.1627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-07T00:49:34Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"8a665e26012c17b47a5bb1227d41668be1a70890b085ffb41bd87047d1a8fc89","abstract_canon_sha256":"b47f443acf6e52b1161efda6a3621a19f90e5a53d88ccddd1cf4a49073c53303"},"schema_version":"1.0"},"canonical_sha256":"1d7018580d215ec69f88627e9c39dd3660ddf9050e4a1cde3d16e0412592b5ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:52.945683Z","signature_b64":"HdEmeh8daOWY7w9tJh2ri8+ElTmW9gHDxb+cmTsEtFICHS6uIxHeFkgio+nYJJZucm8Px9UnD7yeALw7OtQKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d7018580d215ec69f88627e9c39dd3660ddf9050e4a1cde3d16e0412592b5ec","last_reissued_at":"2026-05-18T02:56:52.945233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:52.945233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.1627","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNCw5rwRBqTqBZ4KqhyCTZYNywv9TlPPMSknGkUYyXWeaCtVOm33/d1YlapxKwijuimzCkxfRusf/JAyV76iBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:37:51.980880Z"},"content_sha256":"c4b9e38a1ecd9992dfda93c45c97d411e4c74c2db2590625d81b1f8704878e7c","schema_version":"1.0","event_id":"sha256:c4b9e38a1ecd9992dfda93c45c97d411e4c74c2db2590625d81b1f8704878e7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DVYBQWANEFPMNH4IMJ7JYOO5GZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Whitney functions determine the real homotopy type of a semi-analytic set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AT","authors_text":"Bryce Chriestenson, Markus J. Pflaum","submitted_at":"2014-03-07T00:49:34Z","abstract_excerpt":"In this paper, we investigate the Whitney--de Rham complex $\\Omega^\\bullet_\\text{W} (X)$ associated to a semi-analytic subset $X$ of an analytic manifold $M$. This complex is a commutative differential graded algebra, that is defined to be the quotient of the de Rham complex of smooth differential forms on $M$ by the differential graded ideal generated by all smooth functions which are flat on $X$. We use Hironaka's desingularization theorem to prove a Poincar\\'e Lemma for $\\Omega^\\bullet_\\text{W} (X)$ holds true, which entails that its cohomology is isomorphic to the real cohomology of $X$. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1627","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tZf9wahylFNMpv9fhQqvYNNJqiG/UJg+j1fNhEaIAcXwlcdvxiMGJ5rC5bciVHQDeWZDaXcvVWa5U6oEai9sCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:37:51.981343Z"},"content_sha256":"8055318c9e996fbdf6bee6b252b4dfe4068ffe727bd5d0067be150facb6a205f","schema_version":"1.0","event_id":"sha256:8055318c9e996fbdf6bee6b252b4dfe4068ffe727bd5d0067be150facb6a205f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DVYBQWANEFPMNH4IMJ7JYOO5GZ/bundle.json","state_url":"https://pith.science/pith/DVYBQWANEFPMNH4IMJ7JYOO5GZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DVYBQWANEFPMNH4IMJ7JYOO5GZ/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":"2026-06-23T17:37:51Z","links":{"resolver":"https://pith.science/pith/DVYBQWANEFPMNH4IMJ7JYOO5GZ","bundle":"https://pith.science/pith/DVYBQWANEFPMNH4IMJ7JYOO5GZ/bundle.json","state":"https://pith.science/pith/DVYBQWANEFPMNH4IMJ7JYOO5GZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DVYBQWANEFPMNH4IMJ7JYOO5GZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DVYBQWANEFPMNH4IMJ7JYOO5GZ","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":"b47f443acf6e52b1161efda6a3621a19f90e5a53d88ccddd1cf4a49073c53303","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-07T00:49:34Z","title_canon_sha256":"8a665e26012c17b47a5bb1227d41668be1a70890b085ffb41bd87047d1a8fc89"},"schema_version":"1.0","source":{"id":"1403.1627","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1627","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1627v1","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1627","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"DVYBQWANEFPM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DVYBQWANEFPMNH4I","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DVYBQWAN","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:8055318c9e996fbdf6bee6b252b4dfe4068ffe727bd5d0067be150facb6a205f","target":"graph","created_at":"2026-05-18T02:56:52Z","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":"In this paper, we investigate the Whitney--de Rham complex $\\Omega^\\bullet_\\text{W} (X)$ associated to a semi-analytic subset $X$ of an analytic manifold $M$. This complex is a commutative differential graded algebra, that is defined to be the quotient of the de Rham complex of smooth differential forms on $M$ by the differential graded ideal generated by all smooth functions which are flat on $X$. We use Hironaka's desingularization theorem to prove a Poincar\\'e Lemma for $\\Omega^\\bullet_\\text{W} (X)$ holds true, which entails that its cohomology is isomorphic to the real cohomology of $X$. F","authors_text":"Bryce Chriestenson, Markus J. Pflaum","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-07T00:49:34Z","title":"Whitney functions determine the real homotopy type of a semi-analytic set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1627","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:c4b9e38a1ecd9992dfda93c45c97d411e4c74c2db2590625d81b1f8704878e7c","target":"record","created_at":"2026-05-18T02:56:52Z","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":"b47f443acf6e52b1161efda6a3621a19f90e5a53d88ccddd1cf4a49073c53303","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-07T00:49:34Z","title_canon_sha256":"8a665e26012c17b47a5bb1227d41668be1a70890b085ffb41bd87047d1a8fc89"},"schema_version":"1.0","source":{"id":"1403.1627","kind":"arxiv","version":1}},"canonical_sha256":"1d7018580d215ec69f88627e9c39dd3660ddf9050e4a1cde3d16e0412592b5ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d7018580d215ec69f88627e9c39dd3660ddf9050e4a1cde3d16e0412592b5ec","first_computed_at":"2026-05-18T02:56:52.945233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:52.945233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HdEmeh8daOWY7w9tJh2ri8+ElTmW9gHDxb+cmTsEtFICHS6uIxHeFkgio+nYJJZucm8Px9UnD7yeALw7OtQKCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:52.945683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1627","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4b9e38a1ecd9992dfda93c45c97d411e4c74c2db2590625d81b1f8704878e7c","sha256:8055318c9e996fbdf6bee6b252b4dfe4068ffe727bd5d0067be150facb6a205f"],"state_sha256":"7d35999cdd46e2947a027e1146f580bf1ff1cedcac103727d539914cc4fa5f33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yHSBl1yctCRW/QXef5Vi3yXSdO9+IIo8DTVZVzNIF7NH6dm/4oigaYl7j4mpvFAaXLqoYD+K0CEK3eCD3iVqAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:37:51.983635Z","bundle_sha256":"08d28bcc8d3837fe200b5d0a6397716598718dda3c69b42bbf824125c7a6b0f5"}}