{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KK6HVLGD42K7T7Q6SZWXJ7U5YG","short_pith_number":"pith:KK6HVLGD","canonical_record":{"source":{"id":"1206.4581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-06-20T19:09:17Z","cross_cats_sorted":[],"title_canon_sha256":"a9ee3bdb396fa077fd781954f4b446c39794ae1385ffe7be15bd5a45ad82467c","abstract_canon_sha256":"2a464ca09c4e3782ed42a1aeda9812e0491aeedec5ab00cf5d8b803c4c6a5a34"},"schema_version":"1.0"},"canonical_sha256":"52bc7aacc3e695f9fe1e966d74fe9dc1a701ccd65426f299160cbaa50146022f","source":{"kind":"arxiv","id":"1206.4581","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KK6HVLGD42K7T7Q6SZWXJ7U5YG","target":"record","payload":{"canonical_record":{"source":{"id":"1206.4581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-06-20T19:09:17Z","cross_cats_sorted":[],"title_canon_sha256":"a9ee3bdb396fa077fd781954f4b446c39794ae1385ffe7be15bd5a45ad82467c","abstract_canon_sha256":"2a464ca09c4e3782ed42a1aeda9812e0491aeedec5ab00cf5d8b803c4c6a5a34"},"schema_version":"1.0"},"canonical_sha256":"52bc7aacc3e695f9fe1e966d74fe9dc1a701ccd65426f299160cbaa50146022f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:56.592302Z","signature_b64":"Qis10C6EXFWUTr2kX+T/KY/iItAN9lhQoDyfXxhqCb3GQf2zMS/UIkrfnuAarHwLBWDjOsK0E4veGFGkfXpGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52bc7aacc3e695f9fe1e966d74fe9dc1a701ccd65426f299160cbaa50146022f","last_reissued_at":"2026-05-18T03:01:56.591728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:56.591728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.4581","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"seCCalzTBk6/KnNRD/8XcSGrCWrk2ao8uZauNyOe8UpBRak0AN16lrEOWIJn6zsoMwzTjhMnFtbQhO2FNPp9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:25:59.856206Z"},"content_sha256":"4d9ce5a267c1f78bcd5db23891b09b69ea6f8d2a94757d5510bd7122562ecac5","schema_version":"1.0","event_id":"sha256:4d9ce5a267c1f78bcd5db23891b09b69ea6f8d2a94757d5510bd7122562ecac5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KK6HVLGD42K7T7Q6SZWXJ7U5YG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Andrew J. Blumberg, Itamar Gal, Matthew Pancia, Michael A. Mandell","submitted_at":"2012-06-20T19:09:17Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4581","kind":"arxiv","version":2},"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":"2026-05-18T03:01:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vL4Ox+Gj+vZi4Ak5hWo+yjs1FG2SkePl9McRTVY4OLr8L4jxVz+U1X0NSsOiLCwi0eqIJdi8v+NmZAxz+wNADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:25:59.856781Z"},"content_sha256":"b5cd5f7708aed167660f86c2cbd8372d9edddcf2c28471c5894b240e01d39fc2","schema_version":"1.0","event_id":"sha256:b5cd5f7708aed167660f86c2cbd8372d9edddcf2c28471c5894b240e01d39fc2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KK6HVLGD42K7T7Q6SZWXJ7U5YG/bundle.json","state_url":"https://pith.science/pith/KK6HVLGD42K7T7Q6SZWXJ7U5YG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KK6HVLGD42K7T7Q6SZWXJ7U5YG/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":"2026-06-23T16:25:59Z","links":{"resolver":"https://pith.science/pith/KK6HVLGD42K7T7Q6SZWXJ7U5YG","bundle":"https://pith.science/pith/KK6HVLGD42K7T7Q6SZWXJ7U5YG/bundle.json","state":"https://pith.science/pith/KK6HVLGD42K7T7Q6SZWXJ7U5YG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KK6HVLGD42K7T7Q6SZWXJ7U5YG/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NJIRUEwsihqPuGve0NaPtFcYp7biihed0DX7IqsFtKH/N/x01KWX+UpNpVAnIZ9pyYcQ8JDNBeAINwEVVYfLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:25:59.859692Z","bundle_sha256":"f77170e42fbb1ac120f94d610569e8d34352a39f3d976fcf66e4c12c048ad3e2"}}