{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:54FEGCCKBBYG73WI5HIWYBMGMJ","short_pith_number":"pith:54FEGCCK","canonical_record":{"source":{"id":"1708.05830","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-19T10:58:21Z","cross_cats_sorted":[],"title_canon_sha256":"9222196ba5a9d6bed01cd2f85f0e5c9dddbe0f812b43162a4130e40beec5a9ed","abstract_canon_sha256":"76660a2dd5359a7e0802f2338ce1d214da54ae03e46f8ecf79fbc57e5c16e54d"},"schema_version":"1.0"},"canonical_sha256":"ef0a43084a08706feec8e9d16c0586624548f7012d2bc37d4ebd7ace150225bf","source":{"kind":"arxiv","id":"1708.05830","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05830","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05830v4","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05830","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"54FEGCCKBBYG","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"54FEGCCKBBYG73WI","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"54FEGCCK","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:54FEGCCKBBYG73WI5HIWYBMGMJ","target":"record","payload":{"canonical_record":{"source":{"id":"1708.05830","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-19T10:58:21Z","cross_cats_sorted":[],"title_canon_sha256":"9222196ba5a9d6bed01cd2f85f0e5c9dddbe0f812b43162a4130e40beec5a9ed","abstract_canon_sha256":"76660a2dd5359a7e0802f2338ce1d214da54ae03e46f8ecf79fbc57e5c16e54d"},"schema_version":"1.0"},"canonical_sha256":"ef0a43084a08706feec8e9d16c0586624548f7012d2bc37d4ebd7ace150225bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:29.877288Z","signature_b64":"Z8JUsLl8OutxCQuXGTAf+sgwrXpbZ37mLTLD1Rk9wzHv9X3NHFzXhWHY924VE3LdySRv2pofG1a9b3o/XHZKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef0a43084a08706feec8e9d16c0586624548f7012d2bc37d4ebd7ace150225bf","last_reissued_at":"2026-05-17T23:55:29.876800Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:29.876800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.05830","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GPRs2H585D1bWod8bp/VkkMST0wIe/my14A81f1bhznOh9ky+ZiDHC/APX+XSP3YqxoMHwlLmH/sdH5mRQyMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:08:58.955852Z"},"content_sha256":"14eb9c0e31656bb63a6c2ee38db633f2b457b9942d2fda40283adb39cfd473bb","schema_version":"1.0","event_id":"sha256:14eb9c0e31656bb63a6c2ee38db633f2b457b9942d2fda40283adb39cfd473bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:54FEGCCKBBYG73WI5HIWYBMGMJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lusternik-Schnirelmann category of the configuration space of complex projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Cesar A. Ipanaque Zapata","submitted_at":"2017-08-19T10:58:21Z","abstract_excerpt":"The Lusternik-Schnirelmann category $cat(X)$ is a homotopy invariant which is a numerical bound on the number of critical points of a smooth function on a manifold. Another similar invariant is the topological complexity $TC(X)$ (a la Farber) which has interesting applications in Robotics, specifically, in the robot motion planning problem. In this paper we calculate the Lusternik-Schnirelmann category and as a consequence we calculate the topological complexity of the two-point ordered configuration space of $\\mathbb{CP}^n$ for every $n\\geq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05830","kind":"arxiv","version":4},"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":"2026-05-17T23:55:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w4/fxdNorecbZK/+/74TIGBkb1gEd4u4Rs4h0YHkTxNkhS9aA7eQyRBajLsDUe5oFtdkfiJUP9+gZNhTt6imBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:08:58.956511Z"},"content_sha256":"f6e0dd6188facf29c423e2828f85919c86f05439be7601c60a60bf7786d0f016","schema_version":"1.0","event_id":"sha256:f6e0dd6188facf29c423e2828f85919c86f05439be7601c60a60bf7786d0f016"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/54FEGCCKBBYG73WI5HIWYBMGMJ/bundle.json","state_url":"https://pith.science/pith/54FEGCCKBBYG73WI5HIWYBMGMJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/54FEGCCKBBYG73WI5HIWYBMGMJ/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":"2026-06-07T04:08:58Z","links":{"resolver":"https://pith.science/pith/54FEGCCKBBYG73WI5HIWYBMGMJ","bundle":"https://pith.science/pith/54FEGCCKBBYG73WI5HIWYBMGMJ/bundle.json","state":"https://pith.science/pith/54FEGCCKBBYG73WI5HIWYBMGMJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/54FEGCCKBBYG73WI5HIWYBMGMJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:54FEGCCKBBYG73WI5HIWYBMGMJ","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":"76660a2dd5359a7e0802f2338ce1d214da54ae03e46f8ecf79fbc57e5c16e54d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-19T10:58:21Z","title_canon_sha256":"9222196ba5a9d6bed01cd2f85f0e5c9dddbe0f812b43162a4130e40beec5a9ed"},"schema_version":"1.0","source":{"id":"1708.05830","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05830","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05830v4","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05830","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"54FEGCCKBBYG","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"54FEGCCKBBYG73WI","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"54FEGCCK","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:f6e0dd6188facf29c423e2828f85919c86f05439be7601c60a60bf7786d0f016","target":"graph","created_at":"2026-05-17T23:55:29Z","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":"The Lusternik-Schnirelmann category $cat(X)$ is a homotopy invariant which is a numerical bound on the number of critical points of a smooth function on a manifold. Another similar invariant is the topological complexity $TC(X)$ (a la Farber) which has interesting applications in Robotics, specifically, in the robot motion planning problem. In this paper we calculate the Lusternik-Schnirelmann category and as a consequence we calculate the topological complexity of the two-point ordered configuration space of $\\mathbb{CP}^n$ for every $n\\geq 1$.","authors_text":"Cesar A. Ipanaque Zapata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-19T10:58:21Z","title":"Lusternik-Schnirelmann category of the configuration space of complex projective space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05830","kind":"arxiv","version":4},"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":"sha256:14eb9c0e31656bb63a6c2ee38db633f2b457b9942d2fda40283adb39cfd473bb","target":"record","created_at":"2026-05-17T23:55:29Z","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":"76660a2dd5359a7e0802f2338ce1d214da54ae03e46f8ecf79fbc57e5c16e54d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-19T10:58:21Z","title_canon_sha256":"9222196ba5a9d6bed01cd2f85f0e5c9dddbe0f812b43162a4130e40beec5a9ed"},"schema_version":"1.0","source":{"id":"1708.05830","kind":"arxiv","version":4}},"canonical_sha256":"ef0a43084a08706feec8e9d16c0586624548f7012d2bc37d4ebd7ace150225bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef0a43084a08706feec8e9d16c0586624548f7012d2bc37d4ebd7ace150225bf","first_computed_at":"2026-05-17T23:55:29.876800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:29.876800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z8JUsLl8OutxCQuXGTAf+sgwrXpbZ37mLTLD1Rk9wzHv9X3NHFzXhWHY924VE3LdySRv2pofG1a9b3o/XHZKCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:29.877288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05830","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14eb9c0e31656bb63a6c2ee38db633f2b457b9942d2fda40283adb39cfd473bb","sha256:f6e0dd6188facf29c423e2828f85919c86f05439be7601c60a60bf7786d0f016"],"state_sha256":"eb2aa64315de9dad954e0ab6813d674f97174849ec136d7b770b69b8720658c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aNcDFrXedLA3ZvKUNz1fYra902OG3N3+NpQMSIVu8Z4jUKY452Kv6mPo3UquvnrCO38FkzhJV1uVS3QxOav5Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:08:58.959856Z","bundle_sha256":"ee013aba4ab3de6ac53f073bcd0713677e039db1d88b766fedfebd4e28f1447e"}}