{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GZG37UURNR5N4CTBL5CMAQ7DBZ","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":"419ed33e1913c830dde33459f78442218226d19da965af732117337fccfeeeec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-06-24T11:41:20Z","title_canon_sha256":"36a4f11b52afa071c3eae8f5be30e7d57cd4c110b98f01b7326da328cc894c40"},"schema_version":"1.0","source":{"id":"1106.4943","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4943","created_at":"2026-05-18T04:01:49Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4943v2","created_at":"2026-05-18T04:01:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4943","created_at":"2026-05-18T04:01:49Z"},{"alias_kind":"pith_short_12","alias_value":"GZG37UURNR5N","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GZG37UURNR5N4CTB","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GZG37UUR","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:e0e79479a548608427eab198d5746430916414b8df9c46784b1b6e702ddd87d8","target":"graph","created_at":"2026-05-18T04:01:49Z","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 analyze some relationships between the topological complexity of a space $X$ and the category of $C_{\\Delta_X},$ the homotopy cofibre of the diagonal map $\\Delta_X:X\\rightarrow X\\times X.$ We establish the equality of the two invariants for several classes of spaces including the spheres, the H-spaces, the real and complex projective spaces and almost all the (standard) lens spaces.","authors_text":"J. Calcines, L. Vandembroucq","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-06-24T11:41:20Z","title":"Topological complexity and the homotopy cofibre of the diagonal map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4943","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":"sha256:3c14e147e220e95960e3c1929cd3292a76bfd12af40fc41f99ae6f9867c01f79","target":"record","created_at":"2026-05-18T04:01:49Z","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":"419ed33e1913c830dde33459f78442218226d19da965af732117337fccfeeeec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-06-24T11:41:20Z","title_canon_sha256":"36a4f11b52afa071c3eae8f5be30e7d57cd4c110b98f01b7326da328cc894c40"},"schema_version":"1.0","source":{"id":"1106.4943","kind":"arxiv","version":2}},"canonical_sha256":"364dbfd2916c7ade0a615f44c043e30e7f8cb06d2579e53947adeef758bd8234","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"364dbfd2916c7ade0a615f44c043e30e7f8cb06d2579e53947adeef758bd8234","first_computed_at":"2026-05-18T04:01:49.682725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:49.682725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+H8OxFzH4L/LBN1vfu2/ApZm4KCb/HKuPAt+x2oSIISP4IarTylhxaYFDc3F6PpYDcE1pRTOw6cVgjUfv1bMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:49.683203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4943","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c14e147e220e95960e3c1929cd3292a76bfd12af40fc41f99ae6f9867c01f79","sha256:e0e79479a548608427eab198d5746430916414b8df9c46784b1b6e702ddd87d8"],"state_sha256":"0e6973bc83b0b7e6abf0bf966e0e7a988b82d2c8dd8860bc8e8eed4424fd86e3"}