{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:YWBBWERZXYG6G6LVS45VDXEWL2","short_pith_number":"pith:YWBBWERZ","canonical_record":{"source":{"id":"2101.12288","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2021-01-28T21:36:45Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"844bee6850d7feac59ddfe11768914866a2e98a8f705a8ac642817c46cc6aee7","abstract_canon_sha256":"d0f0a8c97543a1199e7b2354fa343e88b6f05f61bcc84b8f1b003074b5cc84c6"},"schema_version":"1.0"},"canonical_sha256":"c5821b1239be0de37975973b51dc965eaef6d24a552d8bd028423e7b7105b662","source":{"kind":"arxiv","id":"2101.12288","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.12288","created_at":"2026-07-05T03:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"2101.12288v3","created_at":"2026-07-05T03:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.12288","created_at":"2026-07-05T03:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"YWBBWERZXYG6","created_at":"2026-07-05T03:57:52Z"},{"alias_kind":"pith_short_16","alias_value":"YWBBWERZXYG6G6LV","created_at":"2026-07-05T03:57:52Z"},{"alias_kind":"pith_short_8","alias_value":"YWBBWERZ","created_at":"2026-07-05T03:57:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:YWBBWERZXYG6G6LVS45VDXEWL2","target":"record","payload":{"canonical_record":{"source":{"id":"2101.12288","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2021-01-28T21:36:45Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"844bee6850d7feac59ddfe11768914866a2e98a8f705a8ac642817c46cc6aee7","abstract_canon_sha256":"d0f0a8c97543a1199e7b2354fa343e88b6f05f61bcc84b8f1b003074b5cc84c6"},"schema_version":"1.0"},"canonical_sha256":"c5821b1239be0de37975973b51dc965eaef6d24a552d8bd028423e7b7105b662","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:57:52.935918Z","signature_b64":"IJlVyMROc9j0/wbEyXBF0IIBOETTgUmBt8hVulghpfve9smbe2/BMJ1xu+FZEHBsu9/YlHGjf6FS/QELjaFwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5821b1239be0de37975973b51dc965eaef6d24a552d8bd028423e7b7105b662","last_reissued_at":"2026-07-05T03:57:52.935424Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:57:52.935424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2101.12288","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:57:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QYprRJXTw5pbPORSpByj9MKQUHSmPLtHKyDnW6MAC+gnIPqw+U1LewHmUA8uQX7ZTJZl1VpKcAT5IkwIPeRfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T23:23:55.026692Z"},"content_sha256":"83d7d6bef3aaeb52469f69180ee89c676c1fe09d604c16252b99bb869a66e51e","schema_version":"1.0","event_id":"sha256:83d7d6bef3aaeb52469f69180ee89c676c1fe09d604c16252b99bb869a66e51e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:YWBBWERZXYG6G6LVS45VDXEWL2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Geometry to Topology: Inverse Theorems for Distributed Persistence","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.AT","authors_text":"Alexander Wagner, Elchanan Solomon, Paul Bendich","submitted_at":"2021-01-28T21:36:45Z","abstract_excerpt":"What is the \"right\" topological invariant of a large point cloud X? Prior research has focused on estimating the full persistence diagram of X, a quantity that is very expensive to compute, unstable to outliers, and far from a sufficient statistic. We therefore propose that the correct invariant is not the persistence diagram of X, but rather the collection of persistence diagrams of many small subsets. This invariant, which we call \"distributed persistence,\" is perfectly parallelizable, more stable to outliers, and has a rich inverse theory. The map from the space of point clouds (with the qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.12288","kind":"arxiv","version":3},"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/2101.12288/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":"2026-07-05T03:57:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shu6HKD5RDrHtVvaMsx4cbObi0eVdFhRwZ5cA/GRgtaI5O/0UFfbfRhC99hMUgPaQGGcxnEOVoPXldNwXgJ0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T23:23:55.027750Z"},"content_sha256":"d5a68972a0df882959f7033890cd29fb52eb589624c1ca4315b27bacdd88399b","schema_version":"1.0","event_id":"sha256:d5a68972a0df882959f7033890cd29fb52eb589624c1ca4315b27bacdd88399b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWBBWERZXYG6G6LVS45VDXEWL2/bundle.json","state_url":"https://pith.science/pith/YWBBWERZXYG6G6LVS45VDXEWL2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWBBWERZXYG6G6LVS45VDXEWL2/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":"2026-08-13T23:23:55Z","links":{"resolver":"https://pith.science/pith/YWBBWERZXYG6G6LVS45VDXEWL2","bundle":"https://pith.science/pith/YWBBWERZXYG6G6LVS45VDXEWL2/bundle.json","state":"https://pith.science/pith/YWBBWERZXYG6G6LVS45VDXEWL2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWBBWERZXYG6G6LVS45VDXEWL2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YWBBWERZXYG6G6LVS45VDXEWL2","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":"d0f0a8c97543a1199e7b2354fa343e88b6f05f61bcc84b8f1b003074b5cc84c6","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2021-01-28T21:36:45Z","title_canon_sha256":"844bee6850d7feac59ddfe11768914866a2e98a8f705a8ac642817c46cc6aee7"},"schema_version":"1.0","source":{"id":"2101.12288","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.12288","created_at":"2026-07-05T03:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"2101.12288v3","created_at":"2026-07-05T03:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.12288","created_at":"2026-07-05T03:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"YWBBWERZXYG6","created_at":"2026-07-05T03:57:52Z"},{"alias_kind":"pith_short_16","alias_value":"YWBBWERZXYG6G6LV","created_at":"2026-07-05T03:57:52Z"},{"alias_kind":"pith_short_8","alias_value":"YWBBWERZ","created_at":"2026-07-05T03:57:52Z"}],"graph_snapshots":[{"event_id":"sha256:d5a68972a0df882959f7033890cd29fb52eb589624c1ca4315b27bacdd88399b","target":"graph","created_at":"2026-07-05T03:57:52Z","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/2101.12288/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"What is the \"right\" topological invariant of a large point cloud X? Prior research has focused on estimating the full persistence diagram of X, a quantity that is very expensive to compute, unstable to outliers, and far from a sufficient statistic. We therefore propose that the correct invariant is not the persistence diagram of X, but rather the collection of persistence diagrams of many small subsets. This invariant, which we call \"distributed persistence,\" is perfectly parallelizable, more stable to outliers, and has a rich inverse theory. The map from the space of point clouds (with the qu","authors_text":"Alexander Wagner, Elchanan Solomon, Paul Bendich","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2021-01-28T21:36:45Z","title":"From Geometry to Topology: Inverse Theorems for Distributed Persistence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.12288","kind":"arxiv","version":3},"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":"sha256:83d7d6bef3aaeb52469f69180ee89c676c1fe09d604c16252b99bb869a66e51e","target":"record","created_at":"2026-07-05T03:57:52Z","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":"d0f0a8c97543a1199e7b2354fa343e88b6f05f61bcc84b8f1b003074b5cc84c6","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2021-01-28T21:36:45Z","title_canon_sha256":"844bee6850d7feac59ddfe11768914866a2e98a8f705a8ac642817c46cc6aee7"},"schema_version":"1.0","source":{"id":"2101.12288","kind":"arxiv","version":3}},"canonical_sha256":"c5821b1239be0de37975973b51dc965eaef6d24a552d8bd028423e7b7105b662","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5821b1239be0de37975973b51dc965eaef6d24a552d8bd028423e7b7105b662","first_computed_at":"2026-07-05T03:57:52.935424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:57:52.935424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IJlVyMROc9j0/wbEyXBF0IIBOETTgUmBt8hVulghpfve9smbe2/BMJ1xu+FZEHBsu9/YlHGjf6FS/QELjaFwCg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:57:52.935918Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.12288","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83d7d6bef3aaeb52469f69180ee89c676c1fe09d604c16252b99bb869a66e51e","sha256:d5a68972a0df882959f7033890cd29fb52eb589624c1ca4315b27bacdd88399b"],"state_sha256":"11e8a86a1127878b76e1565b0e18229f71c6389e4c3b80be0ef6a3c3294ccdc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d/Aejm6jV+VCxBhWX4NKcsQ/M0LY9ICPFuy8iB2fcRHNCB5z62A9V3oinZ9qMdjyB2xsH7t/gP+Jvjv+yx5zBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T23:23:55.044056Z","bundle_sha256":"ad3f4b3cb7ced7afa362200d66e59273cd427ecc02fee439f5fb96ac92dbbd36"}}