{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KK6HVLGD42K7T7Q6SZWXJ7U5YG","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":"2a464ca09c4e3782ed42a1aeda9812e0491aeedec5ab00cf5d8b803c4c6a5a34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-06-20T19:09:17Z","title_canon_sha256":"a9ee3bdb396fa077fd781954f4b446c39794ae1385ffe7be15bd5a45ad82467c"},"schema_version":"1.0","source":{"id":"1206.4581","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4581","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4581v2","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4581","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"pith_short_12","alias_value":"KK6HVLGD42K7","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KK6HVLGD42K7T7Q6","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KK6HVLGD","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:b5cd5f7708aed167660f86c2cbd8372d9edddcf2c28471c5894b240e01d39fc2","target":"graph","created_at":"2026-05-18T03:01:56Z","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 study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use in hypothesis testing and providing confidence intervals for topological data analysis.","authors_text":"Andrew J. Blumberg, Itamar Gal, Matthew Pancia, Michael A. Mandell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-06-20T19:09:17Z","title":"Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4581","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":"sha256:4d9ce5a267c1f78bcd5db23891b09b69ea6f8d2a94757d5510bd7122562ecac5","target":"record","created_at":"2026-05-18T03:01:56Z","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":"2a464ca09c4e3782ed42a1aeda9812e0491aeedec5ab00cf5d8b803c4c6a5a34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-06-20T19:09:17Z","title_canon_sha256":"a9ee3bdb396fa077fd781954f4b446c39794ae1385ffe7be15bd5a45ad82467c"},"schema_version":"1.0","source":{"id":"1206.4581","kind":"arxiv","version":2}},"canonical_sha256":"52bc7aacc3e695f9fe1e966d74fe9dc1a701ccd65426f299160cbaa50146022f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52bc7aacc3e695f9fe1e966d74fe9dc1a701ccd65426f299160cbaa50146022f","first_computed_at":"2026-05-18T03:01:56.591728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:56.591728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qis10C6EXFWUTr2kX+T/KY/iItAN9lhQoDyfXxhqCb3GQf2zMS/UIkrfnuAarHwLBWDjOsK0E4veGFGkfXpGBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:56.592302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4581","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d9ce5a267c1f78bcd5db23891b09b69ea6f8d2a94757d5510bd7122562ecac5","sha256:b5cd5f7708aed167660f86c2cbd8372d9edddcf2c28471c5894b240e01d39fc2"],"state_sha256":"aa7d544de752a860c87a707964f896a4d7512e4d838c484f1e5ded6927b67b73"}