{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:D2CYAH7EJJS7Z2E74TVVI4K2KU","short_pith_number":"pith:D2CYAH7E","canonical_record":{"source":{"id":"1410.1689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-10-07T11:31:41Z","cross_cats_sorted":[],"title_canon_sha256":"3ce3237028ea7b226ddd39b68c04a2c932f6d8c497508ae3794632ed3a8536b8","abstract_canon_sha256":"1a77fedff26cc511e0e2ae039a593cc31c656e2aaa955dbf715aeba0c4e922c9"},"schema_version":"1.0"},"canonical_sha256":"1e85801fe44a65fce89fe4eb54715a551251c441a61c7e9ca441bbd58920d940","source":{"kind":"arxiv","id":"1410.1689","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1689","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1689v1","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1689","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"D2CYAH7EJJS7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D2CYAH7EJJS7Z2E7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D2CYAH7E","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:D2CYAH7EJJS7Z2E74TVVI4K2KU","target":"record","payload":{"canonical_record":{"source":{"id":"1410.1689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-10-07T11:31:41Z","cross_cats_sorted":[],"title_canon_sha256":"3ce3237028ea7b226ddd39b68c04a2c932f6d8c497508ae3794632ed3a8536b8","abstract_canon_sha256":"1a77fedff26cc511e0e2ae039a593cc31c656e2aaa955dbf715aeba0c4e922c9"},"schema_version":"1.0"},"canonical_sha256":"1e85801fe44a65fce89fe4eb54715a551251c441a61c7e9ca441bbd58920d940","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:55.051681Z","signature_b64":"/t6cKN8ePt72a+sJKYxm8Xbrfk8QSmJvSZrZTE8Z9p4dMRGR/wVhkZsV80P//cm6FX0jJfo2ki+lP5G8oQBdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e85801fe44a65fce89fe4eb54715a551251c441a61c7e9ca441bbd58920d940","last_reissued_at":"2026-05-18T02:40:55.051236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:55.051236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.1689","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":"2026-05-18T02:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TrKexmbLZmJNbYFXKV8iJXwcjnvuJ+JwV7+phpwh0LJy9OLFcHS3DaDTdGhuhwg+wJnm8XaFXflihAZCGl8ABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:13:39.240472Z"},"content_sha256":"176899e14d77358a93b0b1b65435cf5dbe221828a4b7276deebeb65e124d756e","schema_version":"1.0","event_id":"sha256:176899e14d77358a93b0b1b65435cf5dbe221828a4b7276deebeb65e124d756e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:D2CYAH7EJJS7Z2E74TVVI4K2KU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational approximations of sectional category and Poincar\\'e duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jos\\'e Gabriel Carrasquel-Vera, Lucile Vandembroucq, Thomas Kahl","submitted_at":"2014-10-07T11:31:41Z","abstract_excerpt":"F\\'elix, Halperin, and Lemaire have shown that the rational module category Mcat and the rational Toomer invariant $e_0$ coincide for simply connected Poincar\\'e duality complexes. We establish an analogue of this result for the sectional category of a fibration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1689","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":"2026-05-18T02:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l7p73v58z6HqMxHSxiI4tkKnxeUVL4UxNp2IjfD07gtxAT10N73/PNnXIOPEBXzQN6bJv4C1nTqEpBZHmvlPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:13:39.240809Z"},"content_sha256":"b7a5ed287c0e9e4b1e52c4d29a71c8e2b9545bf7bc4bc0200197fdb285357164","schema_version":"1.0","event_id":"sha256:b7a5ed287c0e9e4b1e52c4d29a71c8e2b9545bf7bc4bc0200197fdb285357164"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2CYAH7EJJS7Z2E74TVVI4K2KU/bundle.json","state_url":"https://pith.science/pith/D2CYAH7EJJS7Z2E74TVVI4K2KU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2CYAH7EJJS7Z2E74TVVI4K2KU/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":"2026-06-24T23:13:39Z","links":{"resolver":"https://pith.science/pith/D2CYAH7EJJS7Z2E74TVVI4K2KU","bundle":"https://pith.science/pith/D2CYAH7EJJS7Z2E74TVVI4K2KU/bundle.json","state":"https://pith.science/pith/D2CYAH7EJJS7Z2E74TVVI4K2KU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2CYAH7EJJS7Z2E74TVVI4K2KU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D2CYAH7EJJS7Z2E74TVVI4K2KU","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":"1a77fedff26cc511e0e2ae039a593cc31c656e2aaa955dbf715aeba0c4e922c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-10-07T11:31:41Z","title_canon_sha256":"3ce3237028ea7b226ddd39b68c04a2c932f6d8c497508ae3794632ed3a8536b8"},"schema_version":"1.0","source":{"id":"1410.1689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1689","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1689v1","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1689","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"D2CYAH7EJJS7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D2CYAH7EJJS7Z2E7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D2CYAH7E","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:b7a5ed287c0e9e4b1e52c4d29a71c8e2b9545bf7bc4bc0200197fdb285357164","target":"graph","created_at":"2026-05-18T02:40:55Z","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":"F\\'elix, Halperin, and Lemaire have shown that the rational module category Mcat and the rational Toomer invariant $e_0$ coincide for simply connected Poincar\\'e duality complexes. We establish an analogue of this result for the sectional category of a fibration.","authors_text":"Jos\\'e Gabriel Carrasquel-Vera, Lucile Vandembroucq, Thomas Kahl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-10-07T11:31:41Z","title":"Rational approximations of sectional category and Poincar\\'e duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1689","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":"sha256:176899e14d77358a93b0b1b65435cf5dbe221828a4b7276deebeb65e124d756e","target":"record","created_at":"2026-05-18T02:40:55Z","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":"1a77fedff26cc511e0e2ae039a593cc31c656e2aaa955dbf715aeba0c4e922c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-10-07T11:31:41Z","title_canon_sha256":"3ce3237028ea7b226ddd39b68c04a2c932f6d8c497508ae3794632ed3a8536b8"},"schema_version":"1.0","source":{"id":"1410.1689","kind":"arxiv","version":1}},"canonical_sha256":"1e85801fe44a65fce89fe4eb54715a551251c441a61c7e9ca441bbd58920d940","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e85801fe44a65fce89fe4eb54715a551251c441a61c7e9ca441bbd58920d940","first_computed_at":"2026-05-18T02:40:55.051236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:55.051236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/t6cKN8ePt72a+sJKYxm8Xbrfk8QSmJvSZrZTE8Z9p4dMRGR/wVhkZsV80P//cm6FX0jJfo2ki+lP5G8oQBdBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:55.051681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:176899e14d77358a93b0b1b65435cf5dbe221828a4b7276deebeb65e124d756e","sha256:b7a5ed287c0e9e4b1e52c4d29a71c8e2b9545bf7bc4bc0200197fdb285357164"],"state_sha256":"7a4345e221f72e35faf417f543b3db7c7e415eda9b7c206c97bb8e8b325f5f26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7GxeStf6qc18Mkvrga5kIumRujVli7S89KGEnF45ps/iXYId81MwYqlO+6A04r4FVROO6MSq7nGXNMD7ueZAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:13:39.242724Z","bundle_sha256":"758fcb69b36d55ed16e096c9a21dd3ca448962a63b6a3e2778d8c5c86bbbe0d8"}}