{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M3HCGCS7ELGFXTCLU7WLAHWBDJ","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":"a76fa7d46764fc897d4e7245ef4508cd34e66a4c6737114a02d15764c950741c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-07-19T16:23:11Z","title_canon_sha256":"ea83f6a2c700bf8796a778d88a7479bcb8a657e251153666719039d27b4a44f9"},"schema_version":"1.0","source":{"id":"1207.4725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4725","created_at":"2026-05-18T03:50:35Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4725v1","created_at":"2026-05-18T03:50:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4725","created_at":"2026-05-18T03:50:35Z"},{"alias_kind":"pith_short_12","alias_value":"M3HCGCS7ELGF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M3HCGCS7ELGFXTCL","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M3HCGCS7","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:9fb0abcb052115de849d4985f3b2e91d49ed3c2520d115173bebb44fa056865a","target":"graph","created_at":"2026-05-18T03:50:35Z","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 prove that a space whose topological complexity equals 1 is homotopy equivalent to some odd-dimensional sphere. We prove a similar result, although not in complete generality, for spaces X whose higher topological complexity TC_n(X) is as low as possible, namely n-1.","authors_text":"Gregory Lupton, John Oprea, Mark Grant","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-07-19T16:23:11Z","title":"Spaces of Topological Complexity One"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4725","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":"sha256:8661cc719c09aa04f2a067a3dfba33e9a3b1cdba6803c7bbe77990de87ce745d","target":"record","created_at":"2026-05-18T03:50:35Z","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":"a76fa7d46764fc897d4e7245ef4508cd34e66a4c6737114a02d15764c950741c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-07-19T16:23:11Z","title_canon_sha256":"ea83f6a2c700bf8796a778d88a7479bcb8a657e251153666719039d27b4a44f9"},"schema_version":"1.0","source":{"id":"1207.4725","kind":"arxiv","version":1}},"canonical_sha256":"66ce230a5f22cc5bcc4ba7ecb01ec11a45bb51b74070e7fcfd21d3cfcb31595a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66ce230a5f22cc5bcc4ba7ecb01ec11a45bb51b74070e7fcfd21d3cfcb31595a","first_computed_at":"2026-05-18T03:50:35.953126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:35.953126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p/uA4rQidBAzjiJovhvMN9DCG/JD5i2aflw2MSZPPwetD9XO2/UvBn6Qgz5QORa+SYu2djrDPdHvPDtU129lCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:35.953793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8661cc719c09aa04f2a067a3dfba33e9a3b1cdba6803c7bbe77990de87ce745d","sha256:9fb0abcb052115de849d4985f3b2e91d49ed3c2520d115173bebb44fa056865a"],"state_sha256":"7db44639fdd4795490605b4c33f3b394a230dbb46c077c45471c0be624bef54a"}