{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XSQOXNKBVXIBWLYJLADXPFMMKP","short_pith_number":"pith:XSQOXNKB","canonical_record":{"source":{"id":"1807.10971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-28T19:21:10Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"9b7f1ad053bf64e3ddf50fa64ee2c728409daf5904ec9145b46265fee1993f30","abstract_canon_sha256":"8b16c6e46fb0ae8439e70bdc14da4a1c1fe191e754f3b87b7e9013b6d1efc135"},"schema_version":"1.0"},"canonical_sha256":"bca0ebb541add01b2f09580777958c53d51b57ba174ff7f6de36ceb5c01fe48a","source":{"kind":"arxiv","id":"1807.10971","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XSQOXNKBVXIBWLYJLADXPFMMKP","target":"record","payload":{"canonical_record":{"source":{"id":"1807.10971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-28T19:21:10Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"9b7f1ad053bf64e3ddf50fa64ee2c728409daf5904ec9145b46265fee1993f30","abstract_canon_sha256":"8b16c6e46fb0ae8439e70bdc14da4a1c1fe191e754f3b87b7e9013b6d1efc135"},"schema_version":"1.0"},"canonical_sha256":"bca0ebb541add01b2f09580777958c53d51b57ba174ff7f6de36ceb5c01fe48a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:34.865252Z","signature_b64":"dDpkw67slIX/Ji887xiKBofV5jbUO/fYlcBb0j9ImnVm+xzdG8YhxAw4CvBhw97khkE5AZyISc4H1D5yITigDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bca0ebb541add01b2f09580777958c53d51b57ba174ff7f6de36ceb5c01fe48a","last_reissued_at":"2026-05-18T00:09:34.864822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:34.864822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.10971","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:09:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CMub1imECJhsvUG8/8bHj5jO4KMk67Yd59vce2Z8BnMt8ry1tjabISQcUNndsW8ceJBIfPHoAupRxT2NaNtsAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:27:37.501255Z"},"content_sha256":"bf1e926b87931a381e46a8d012596d556a6117338094274d0f665d883adefddd","schema_version":"1.0","event_id":"sha256:bf1e926b87931a381e46a8d012596d556a6117338094274d0f665d883adefddd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XSQOXNKBVXIBWLYJLADXPFMMKP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vietoris-Rips Complexes of Regular Polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Adam Quinn Jaffe, Bonginkosi Sibanda, Henry Adams, Samir Chowdhury","submitted_at":"2018-07-28T19:21:10Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10971","kind":"arxiv","version":1},"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":"2026-05-18T00:09:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QqihHHeMaOpRtfjoxOpZp+DqGnIxIk2M3thLNPAHMghj5a5qgoAlBEiaZGTYwgGnPHjkq9TSfd9PZfXcxHyxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:27:37.501618Z"},"content_sha256":"f8fcc921089d488aa4b067919a2fe092a8af00a1b4254a028a10a27fed68b9af","schema_version":"1.0","event_id":"sha256:f8fcc921089d488aa4b067919a2fe092a8af00a1b4254a028a10a27fed68b9af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSQOXNKBVXIBWLYJLADXPFMMKP/bundle.json","state_url":"https://pith.science/pith/XSQOXNKBVXIBWLYJLADXPFMMKP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSQOXNKBVXIBWLYJLADXPFMMKP/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":"2026-06-04T20:27:37Z","links":{"resolver":"https://pith.science/pith/XSQOXNKBVXIBWLYJLADXPFMMKP","bundle":"https://pith.science/pith/XSQOXNKBVXIBWLYJLADXPFMMKP/bundle.json","state":"https://pith.science/pith/XSQOXNKBVXIBWLYJLADXPFMMKP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSQOXNKBVXIBWLYJLADXPFMMKP/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wYGG2taZ8ZR7A/q9K5QiOPf+++VwqDpyXgIfVoM70uPKBDqeo6FUPsl7jJoFerD1gJEczb8Qo+LU9jdCksy+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:27:37.503584Z","bundle_sha256":"af5a7a3c9ff522bfd7e5bb994ccb7c87593af3d32f4feb871c1a36d99da37636"}}