{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:RRQFDBGFU5DLNK26VLEZHLQQMG","short_pith_number":"pith:RRQFDBGF","canonical_record":{"source":{"id":"2006.16824","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-06-30T14:01:05Z","cross_cats_sorted":[],"title_canon_sha256":"a0f3cfdd61fbe4708367e529693778fad7800f8fbfce0c44caa01a80005d2bff","abstract_canon_sha256":"84f3afa33e2b9b99af8a35fba8ed8dd23cafa8f762b5baa008677d2ec65ec4d4"},"schema_version":"1.0"},"canonical_sha256":"8c605184c5a746b6ab5eaac993ae1061a53e1c361dc8ef763a578710537a7bb1","source":{"kind":"arxiv","id":"2006.16824","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.16824","created_at":"2026-07-05T11:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"2006.16824v7","created_at":"2026-07-05T11:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.16824","created_at":"2026-07-05T11:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"RRQFDBGFU5DL","created_at":"2026-07-05T11:34:38Z"},{"alias_kind":"pith_short_16","alias_value":"RRQFDBGFU5DLNK26","created_at":"2026-07-05T11:34:38Z"},{"alias_kind":"pith_short_8","alias_value":"RRQFDBGF","created_at":"2026-07-05T11:34:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:RRQFDBGFU5DLNK26VLEZHLQQMG","target":"record","payload":{"canonical_record":{"source":{"id":"2006.16824","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-06-30T14:01:05Z","cross_cats_sorted":[],"title_canon_sha256":"a0f3cfdd61fbe4708367e529693778fad7800f8fbfce0c44caa01a80005d2bff","abstract_canon_sha256":"84f3afa33e2b9b99af8a35fba8ed8dd23cafa8f762b5baa008677d2ec65ec4d4"},"schema_version":"1.0"},"canonical_sha256":"8c605184c5a746b6ab5eaac993ae1061a53e1c361dc8ef763a578710537a7bb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:38.739513Z","signature_b64":"WNwiC3U/L9lQvES1CAGFMcq81krRwHq/zc9EIPqTu1KRUuajPaf7x/Og5QGWfRYLb2MBRlXZuNPESXhxgfwYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c605184c5a746b6ab5eaac993ae1061a53e1c361dc8ef763a578710537a7bb1","last_reissued_at":"2026-07-05T11:34:38.739011Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:38.739011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.16824","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kW+hWXTFae4+7zelHXFLSvpvAy1ALVnTlDwg4bQJaLd2wNd5MF3AYxi8O5eTb5JP7LLImaSS+awGFzWGWbLCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T07:55:54.611410Z"},"content_sha256":"6b0c394be88c3ae6717c3f1abc0e64141929001c68ef807ca2b2b51028344a57","schema_version":"1.0","event_id":"sha256:6b0c394be88c3ae6717c3f1abc0e64141929001c68ef807ca2b2b51028344a57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:RRQFDBGFU5DLNK26VLEZHLQQMG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wasserstein Stability for Persistence Diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Katharine Turner, Primoz Skraba","submitted_at":"2020-06-30T14:01:05Z","abstract_excerpt":"The stability of persistence diagrams is among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bottleneck distance between diagrams and the $\\infty$-norm of perturbations. This has two main implications: it makes the space of persistence diagrams rather pathological and it is often provides very pessimistic bounds with respect to outliers. In this paper, we provide new stability results with respect to the $p$-Wasserstein distance between persistence diagrams. This includes an elementary proof for the setting of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16824","kind":"arxiv","version":7},"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/2006.16824/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":"2026-07-05T11:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PtvUIlccvAzw4L0uOMl6krmXz3aUbEPv+urmLQSmwKrxHmCGkuzHPMGfjghdGHKXYFYL+Ot7N1BuFhFmHUKiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T07:55:54.612547Z"},"content_sha256":"f31732c913936e90c9964e3a00a77c8c07c12f17535db05fb7f86448ff358002","schema_version":"1.0","event_id":"sha256:f31732c913936e90c9964e3a00a77c8c07c12f17535db05fb7f86448ff358002"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RRQFDBGFU5DLNK26VLEZHLQQMG/bundle.json","state_url":"https://pith.science/pith/RRQFDBGFU5DLNK26VLEZHLQQMG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RRQFDBGFU5DLNK26VLEZHLQQMG/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":"2026-08-14T07:55:54Z","links":{"resolver":"https://pith.science/pith/RRQFDBGFU5DLNK26VLEZHLQQMG","bundle":"https://pith.science/pith/RRQFDBGFU5DLNK26VLEZHLQQMG/bundle.json","state":"https://pith.science/pith/RRQFDBGFU5DLNK26VLEZHLQQMG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RRQFDBGFU5DLNK26VLEZHLQQMG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:RRQFDBGFU5DLNK26VLEZHLQQMG","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":"84f3afa33e2b9b99af8a35fba8ed8dd23cafa8f762b5baa008677d2ec65ec4d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-06-30T14:01:05Z","title_canon_sha256":"a0f3cfdd61fbe4708367e529693778fad7800f8fbfce0c44caa01a80005d2bff"},"schema_version":"1.0","source":{"id":"2006.16824","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.16824","created_at":"2026-07-05T11:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"2006.16824v7","created_at":"2026-07-05T11:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.16824","created_at":"2026-07-05T11:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"RRQFDBGFU5DL","created_at":"2026-07-05T11:34:38Z"},{"alias_kind":"pith_short_16","alias_value":"RRQFDBGFU5DLNK26","created_at":"2026-07-05T11:34:38Z"},{"alias_kind":"pith_short_8","alias_value":"RRQFDBGF","created_at":"2026-07-05T11:34:38Z"}],"graph_snapshots":[{"event_id":"sha256:f31732c913936e90c9964e3a00a77c8c07c12f17535db05fb7f86448ff358002","target":"graph","created_at":"2026-07-05T11:34:38Z","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/2006.16824/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The stability of persistence diagrams is among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bottleneck distance between diagrams and the $\\infty$-norm of perturbations. This has two main implications: it makes the space of persistence diagrams rather pathological and it is often provides very pessimistic bounds with respect to outliers. In this paper, we provide new stability results with respect to the $p$-Wasserstein distance between persistence diagrams. This includes an elementary proof for the setting of ","authors_text":"Katharine Turner, Primoz Skraba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-06-30T14:01:05Z","title":"Wasserstein Stability for Persistence Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16824","kind":"arxiv","version":7},"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":"sha256:6b0c394be88c3ae6717c3f1abc0e64141929001c68ef807ca2b2b51028344a57","target":"record","created_at":"2026-07-05T11:34:38Z","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":"84f3afa33e2b9b99af8a35fba8ed8dd23cafa8f762b5baa008677d2ec65ec4d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-06-30T14:01:05Z","title_canon_sha256":"a0f3cfdd61fbe4708367e529693778fad7800f8fbfce0c44caa01a80005d2bff"},"schema_version":"1.0","source":{"id":"2006.16824","kind":"arxiv","version":7}},"canonical_sha256":"8c605184c5a746b6ab5eaac993ae1061a53e1c361dc8ef763a578710537a7bb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c605184c5a746b6ab5eaac993ae1061a53e1c361dc8ef763a578710537a7bb1","first_computed_at":"2026-07-05T11:34:38.739011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:38.739011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WNwiC3U/L9lQvES1CAGFMcq81krRwHq/zc9EIPqTu1KRUuajPaf7x/Og5QGWfRYLb2MBRlXZuNPESXhxgfwYDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:38.739513Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.16824","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b0c394be88c3ae6717c3f1abc0e64141929001c68ef807ca2b2b51028344a57","sha256:f31732c913936e90c9964e3a00a77c8c07c12f17535db05fb7f86448ff358002"],"state_sha256":"2a427b1958288f9d28bd82b38c75635e260c0b23fa118c74b79c7f1d74625be4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2siHPBbESwL+RuoIBVgfcRoNjxI4DYDPMon1rp8B24O1q/uP8vdUOE4sRsZ9aSb0SW3LL8zYbv9J9H86HguMAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T07:55:54.619083Z","bundle_sha256":"7b836362504ceaee592cf5dca2f286a96acebab9347f7de2b78416d2aad69fed"}}