{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XSQOXNKBVXIBWLYJLADXPFMMKP","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":"8b16c6e46fb0ae8439e70bdc14da4a1c1fe191e754f3b87b7e9013b6d1efc135","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-28T19:21:10Z","title_canon_sha256":"9b7f1ad053bf64e3ddf50fa64ee2c728409daf5904ec9145b46265fee1993f30"},"schema_version":"1.0","source":{"id":"1807.10971","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10971","created_at":"2026-05-18T00:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10971v1","created_at":"2026-05-18T00:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10971","created_at":"2026-05-18T00:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"XSQOXNKBVXIB","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XSQOXNKBVXIBWLYJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XSQOXNKB","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:f8fcc921089d488aa4b067919a2fe092a8af00a1b4254a028a10a27fed68b9af","target":"graph","created_at":"2026-05-18T00:09:34Z","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":"Persistent homology has emerged as a novel tool for data analysis in the past two decades. However, there are still very few shapes or even manifolds whose persistent homology barcodes (say of the Vietoris-Rips complex) are fully known. Towards this direction, let $P_n$ be the boundary of a regular polygon in the plane with $n$ sides; we describe the homotopy types of Vietoris-Rips complexes of $P_n$. Indeed, when $n=(k+1)!!$ is an odd double factorial, we provide a complete characterization of the homotopy types and persistent homology of the Vietoris-Rips complexes of $P_n$ up to a scale par","authors_text":"Adam Quinn Jaffe, Bonginkosi Sibanda, Henry Adams, Samir Chowdhury","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-28T19:21:10Z","title":"Vietoris-Rips Complexes of Regular Polygons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10971","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:bf1e926b87931a381e46a8d012596d556a6117338094274d0f665d883adefddd","target":"record","created_at":"2026-05-18T00:09:34Z","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":"8b16c6e46fb0ae8439e70bdc14da4a1c1fe191e754f3b87b7e9013b6d1efc135","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-28T19:21:10Z","title_canon_sha256":"9b7f1ad053bf64e3ddf50fa64ee2c728409daf5904ec9145b46265fee1993f30"},"schema_version":"1.0","source":{"id":"1807.10971","kind":"arxiv","version":1}},"canonical_sha256":"bca0ebb541add01b2f09580777958c53d51b57ba174ff7f6de36ceb5c01fe48a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bca0ebb541add01b2f09580777958c53d51b57ba174ff7f6de36ceb5c01fe48a","first_computed_at":"2026-05-18T00:09:34.864822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:34.864822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dDpkw67slIX/Ji887xiKBofV5jbUO/fYlcBb0j9ImnVm+xzdG8YhxAw4CvBhw97khkE5AZyISc4H1D5yITigDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:34.865252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.10971","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf1e926b87931a381e46a8d012596d556a6117338094274d0f665d883adefddd","sha256:f8fcc921089d488aa4b067919a2fe092a8af00a1b4254a028a10a27fed68b9af"],"state_sha256":"ab31fe2604d64f9b804d7e9e6631c24aaa1daff9ea084f454ddc324a87ae2851"}