{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RILP2WFWYH5QAFQN76TAMDIQ52","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":"46d9b0b688bf3a13cd54af726c18e90f5fa0abdb8cf4c0b0aca16fea0b0c30f1","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-05-01T15:47:18Z","title_canon_sha256":"b7d0c5f730a0a41d6685d5af626d01247bb06c7c77a6052625e1b8b5e8c4b4d9"},"schema_version":"1.0","source":{"id":"1905.00350","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00350","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00350v2","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00350","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"RILP2WFWYH5Q","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RILP2WFWYH5QAFQN","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RILP2WFW","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:532215e599c57e1ea3f5877a8b668c79c9d6000e2c8918695666f08729f1cfa0","target":"graph","created_at":"2026-05-17T23:42:13Z","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 introduce here a framework to construct coordinates in \\emph{finite} Lens spaces for data with nontrivial 1-dimensional $\\mathbb{Z}_q$ persistent cohomology, $q\\geq 3$. Said coordinates are defined on an open neighborhood of the data, yet constructed with only a small subset of landmarks. We also introduce a dimensionality reduction scheme in $S^{2n-1}/\\mathbb{Z}_q$ (Lens-PCA: $\\mathsf{LPCA}$), and demonstrate the efficacy of the pipeline $PH^1(\\;\\cdot\\; ; \\mathbb{Z}_q)$ class $\\Rightarrow$ $S^{2n-1}/\\mathbb{Z}_q$ coordinates $\\Rightarrow$ $\\mathsf{LPCA}$, for nonlinear (topological) dimens","authors_text":"Jose A. Perea, Luis Polanco","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-05-01T15:47:18Z","title":"Coordinatizing Data With Lens Spaces and Persistent Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00350","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":"sha256:4a1c7240307999d769d6edd577edc2c322385c09aae5e8a1c9c4dbd4de6cf158","target":"record","created_at":"2026-05-17T23:42:13Z","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":"46d9b0b688bf3a13cd54af726c18e90f5fa0abdb8cf4c0b0aca16fea0b0c30f1","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-05-01T15:47:18Z","title_canon_sha256":"b7d0c5f730a0a41d6685d5af626d01247bb06c7c77a6052625e1b8b5e8c4b4d9"},"schema_version":"1.0","source":{"id":"1905.00350","kind":"arxiv","version":2}},"canonical_sha256":"8a16fd58b6c1fb00160dffa6060d10ee9c3fb064c42d9446fbebd82de6c7e9d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a16fd58b6c1fb00160dffa6060d10ee9c3fb064c42d9446fbebd82de6c7e9d1","first_computed_at":"2026-05-17T23:42:13.511481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:13.511481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4FgWZsctpcgFG5BA9Ka9Vx+upgOqsFzdYkTfL+CwRsKT8bS81nbK0Ez+dENzraYkftqtIrp0Y+o2gUJZV3b1BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:13.512024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.00350","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a1c7240307999d769d6edd577edc2c322385c09aae5e8a1c9c4dbd4de6cf158","sha256:532215e599c57e1ea3f5877a8b668c79c9d6000e2c8918695666f08729f1cfa0"],"state_sha256":"337303fe98e67ff81099a708ed49bb73a911ca179c2c9c05c90129bac2201194"}