{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:5UXWWS3RN3DW5EP4GSO7JSCQ2E","short_pith_number":"pith:5UXWWS3R","canonical_record":{"source":{"id":"2606.06310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-06-04T15:51:27Z","cross_cats_sorted":["cs.MS","math.AT"],"title_canon_sha256":"901cce5591668dd2423bf7c54749ef4e272fbf38441fb18db03f336dc06d4bda","abstract_canon_sha256":"e23523875734494f447b578e930165aa172298ae995fd657921a3f164acffc90"},"schema_version":"1.0"},"canonical_sha256":"ed2f6b4b716ec76e91fc349df4c850d103835f2501de474a9c8da5e5cd8885c5","source":{"kind":"arxiv","id":"2606.06310","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06310","created_at":"2026-06-05T01:15:41Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06310v1","created_at":"2026-06-05T01:15:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06310","created_at":"2026-06-05T01:15:41Z"},{"alias_kind":"pith_short_12","alias_value":"5UXWWS3RN3DW","created_at":"2026-06-05T01:15:41Z"},{"alias_kind":"pith_short_16","alias_value":"5UXWWS3RN3DW5EP4","created_at":"2026-06-05T01:15:41Z"},{"alias_kind":"pith_short_8","alias_value":"5UXWWS3R","created_at":"2026-06-05T01:15:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:5UXWWS3RN3DW5EP4GSO7JSCQ2E","target":"record","payload":{"canonical_record":{"source":{"id":"2606.06310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-06-04T15:51:27Z","cross_cats_sorted":["cs.MS","math.AT"],"title_canon_sha256":"901cce5591668dd2423bf7c54749ef4e272fbf38441fb18db03f336dc06d4bda","abstract_canon_sha256":"e23523875734494f447b578e930165aa172298ae995fd657921a3f164acffc90"},"schema_version":"1.0"},"canonical_sha256":"ed2f6b4b716ec76e91fc349df4c850d103835f2501de474a9c8da5e5cd8885c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:41.527587Z","signature_b64":"P4rEDu5jLVpveaVNRGJ4Y5bzHmndXpF79WoEdHTP1jPrcTtvcWfmtEvNrrRo4eFoXuXuqqIPtwqTxKRnUd+tDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed2f6b4b716ec76e91fc349df4c850d103835f2501de474a9c8da5e5cd8885c5","last_reissued_at":"2026-06-05T01:15:41.527167Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:41.527167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.06310","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":"2026-06-05T01:15:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u0UvU3ZOjqId6DZm5XnKCqaS84H0mSm7+f6nzu22hwtGiQ8mobhNT6VRrksG8bRSx89pGeqUh2QmAUFGohMXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:15:28.163080Z"},"content_sha256":"9bf4267d0ba1d12405a82b7d4e84945b54ef2f69f41e92e598e3a3900a4d1a1f","schema_version":"1.0","event_id":"sha256:9bf4267d0ba1d12405a82b7d4e84945b54ef2f69f41e92e598e3a3900a4d1a1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:5UXWWS3RN3DW5EP4GSO7JSCQ2E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"RedZeD: Computing persistent homology by Reduction to Zero Differentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS","math.AT"],"primary_cat":"cs.CG","authors_text":"Chris Kapulkin, Nathan Kershaw","submitted_at":"2026-06-04T15:51:27Z","abstract_excerpt":"We introduce a new algorithm for computing persistent homology of Vietoris--Rips filtrations, which in many cases offers a considerable speedup over the existing implementation of the persistence pairing algorithm. The key innovation, called active enumeration, is made possible by a new theoretical framework of Reduction to Zero Differentials (hence RedZeD) in which to view persistent homology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06310","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06310/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-05T01:15:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SiTFtj5jgpJKKn1MS/FqArURjeyb+OSAYTD3dKBdFDS4k0vuy0r4Y+7dyq8tYKtn5lQcVuDPw2IQ6PeGfdBlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:15:28.163470Z"},"content_sha256":"adb661bc9815b5343478e510e302fd8526e946f4eb1892c3dd4ef2515050b00a","schema_version":"1.0","event_id":"sha256:adb661bc9815b5343478e510e302fd8526e946f4eb1892c3dd4ef2515050b00a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5UXWWS3RN3DW5EP4GSO7JSCQ2E/bundle.json","state_url":"https://pith.science/pith/5UXWWS3RN3DW5EP4GSO7JSCQ2E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5UXWWS3RN3DW5EP4GSO7JSCQ2E/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":"2026-06-23T13:15:28Z","links":{"resolver":"https://pith.science/pith/5UXWWS3RN3DW5EP4GSO7JSCQ2E","bundle":"https://pith.science/pith/5UXWWS3RN3DW5EP4GSO7JSCQ2E/bundle.json","state":"https://pith.science/pith/5UXWWS3RN3DW5EP4GSO7JSCQ2E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5UXWWS3RN3DW5EP4GSO7JSCQ2E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5UXWWS3RN3DW5EP4GSO7JSCQ2E","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":"e23523875734494f447b578e930165aa172298ae995fd657921a3f164acffc90","cross_cats_sorted":["cs.MS","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-06-04T15:51:27Z","title_canon_sha256":"901cce5591668dd2423bf7c54749ef4e272fbf38441fb18db03f336dc06d4bda"},"schema_version":"1.0","source":{"id":"2606.06310","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06310","created_at":"2026-06-05T01:15:41Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06310v1","created_at":"2026-06-05T01:15:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06310","created_at":"2026-06-05T01:15:41Z"},{"alias_kind":"pith_short_12","alias_value":"5UXWWS3RN3DW","created_at":"2026-06-05T01:15:41Z"},{"alias_kind":"pith_short_16","alias_value":"5UXWWS3RN3DW5EP4","created_at":"2026-06-05T01:15:41Z"},{"alias_kind":"pith_short_8","alias_value":"5UXWWS3R","created_at":"2026-06-05T01:15:41Z"}],"graph_snapshots":[{"event_id":"sha256:adb661bc9815b5343478e510e302fd8526e946f4eb1892c3dd4ef2515050b00a","target":"graph","created_at":"2026-06-05T01:15:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.06310/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a new algorithm for computing persistent homology of Vietoris--Rips filtrations, which in many cases offers a considerable speedup over the existing implementation of the persistence pairing algorithm. The key innovation, called active enumeration, is made possible by a new theoretical framework of Reduction to Zero Differentials (hence RedZeD) in which to view persistent homology.","authors_text":"Chris Kapulkin, Nathan Kershaw","cross_cats":["cs.MS","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-06-04T15:51:27Z","title":"RedZeD: Computing persistent homology by Reduction to Zero Differentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06310","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":"sha256:9bf4267d0ba1d12405a82b7d4e84945b54ef2f69f41e92e598e3a3900a4d1a1f","target":"record","created_at":"2026-06-05T01:15:41Z","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":"e23523875734494f447b578e930165aa172298ae995fd657921a3f164acffc90","cross_cats_sorted":["cs.MS","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-06-04T15:51:27Z","title_canon_sha256":"901cce5591668dd2423bf7c54749ef4e272fbf38441fb18db03f336dc06d4bda"},"schema_version":"1.0","source":{"id":"2606.06310","kind":"arxiv","version":1}},"canonical_sha256":"ed2f6b4b716ec76e91fc349df4c850d103835f2501de474a9c8da5e5cd8885c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed2f6b4b716ec76e91fc349df4c850d103835f2501de474a9c8da5e5cd8885c5","first_computed_at":"2026-06-05T01:15:41.527167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:41.527167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P4rEDu5jLVpveaVNRGJ4Y5bzHmndXpF79WoEdHTP1jPrcTtvcWfmtEvNrrRo4eFoXuXuqqIPtwqTxKRnUd+tDg==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:41.527587Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06310","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bf4267d0ba1d12405a82b7d4e84945b54ef2f69f41e92e598e3a3900a4d1a1f","sha256:adb661bc9815b5343478e510e302fd8526e946f4eb1892c3dd4ef2515050b00a"],"state_sha256":"1024c259544887bebc4a80bedad7c950f918cefa91a1e68b9cf4e59ce25bf80f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5FVMhN9wB3MB5qlQi/ow/R7xs4XeSOMZrp/md3DGWuYf7R7LVO+CslSzIdanzAehufbnsbF40V50+ehkuztFBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:15:28.165464Z","bundle_sha256":"5ebe51a098a063c57e8c501a34518b0039a8d88078c59433813a2caaaae8337c"}}