{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KBCAODM74DGLHVQUB5ZSQ6ICRI","short_pith_number":"pith:KBCAODM7","schema_version":"1.0","canonical_sha256":"5044070d9fe0ccb3d6140f732879028a1cd4d7b41317acbb59daf1338b638b10","source":{"kind":"arxiv","id":"2411.09960","version":1},"attestation_state":"computed","paper":{"title":"Stable Similarity Comparison of Persistent Homology Groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Bingzhe Hou, Jiaxing He, Tieru Wu, Yang Cao","submitted_at":"2024-11-15T05:29:25Z","abstract_excerpt":"Classification in the sense of similarity is an important issue. In this paper, we study similarity classification in Topological Data Analysis. We define a pseudometric $d_{S}^{(p)}$ to measure the distance between barcodes generated by persistent homology groups of topological spaces, and we provide that our pseudometric $d_{S}^{(2)}$ is a similarity invariant. Thereby, we establish a connection between Operator Theory and Topological Data Analysis. We give the calculation formula of the pseudometric $d_{S}^{(2)}$ $(d_{S}^{(1)})$ by arranging all eigenvalues of matrices determined by barcode"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.09960","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-11-15T05:29:25Z","cross_cats_sorted":[],"title_canon_sha256":"cec7134db2ee74eac45f6203d53170f2c7fdfcd27acb03bffffb408f449cd329","abstract_canon_sha256":"dfcb02aca49201afc1c441e5048dc8485a5015388e905ece31d1dbdbaae5ed30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:35:56.348928Z","signature_b64":"E/U85w0l3LQUZ5v3Y0R9MU9y4gQD/dEngbJQDdLXWEoKBE5Sn+DLsFSnDsQkQsLD+y+tnDwWpOB5vl4fB0ErCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5044070d9fe0ccb3d6140f732879028a1cd4d7b41317acbb59daf1338b638b10","last_reissued_at":"2026-07-05T09:35:56.348019Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:35:56.348019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable Similarity Comparison of Persistent Homology Groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Bingzhe Hou, Jiaxing He, Tieru Wu, Yang Cao","submitted_at":"2024-11-15T05:29:25Z","abstract_excerpt":"Classification in the sense of similarity is an important issue. In this paper, we study similarity classification in Topological Data Analysis. We define a pseudometric $d_{S}^{(p)}$ to measure the distance between barcodes generated by persistent homology groups of topological spaces, and we provide that our pseudometric $d_{S}^{(2)}$ is a similarity invariant. Thereby, we establish a connection between Operator Theory and Topological Data Analysis. We give the calculation formula of the pseudometric $d_{S}^{(2)}$ $(d_{S}^{(1)})$ by arranging all eigenvalues of matrices determined by barcode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09960","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/2411.09960/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2411.09960","created_at":"2026-07-05T09:35:56.348358+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.09960v1","created_at":"2026-07-05T09:35:56.348358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09960","created_at":"2026-07-05T09:35:56.348358+00:00"},{"alias_kind":"pith_short_12","alias_value":"KBCAODM74DGL","created_at":"2026-07-05T09:35:56.348358+00:00"},{"alias_kind":"pith_short_16","alias_value":"KBCAODM74DGLHVQU","created_at":"2026-07-05T09:35:56.348358+00:00"},{"alias_kind":"pith_short_8","alias_value":"KBCAODM7","created_at":"2026-07-05T09:35:56.348358+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KBCAODM74DGLHVQUB5ZSQ6ICRI","json":"https://pith.science/pith/KBCAODM74DGLHVQUB5ZSQ6ICRI.json","graph_json":"https://pith.science/api/pith-number/KBCAODM74DGLHVQUB5ZSQ6ICRI/graph.json","events_json":"https://pith.science/api/pith-number/KBCAODM74DGLHVQUB5ZSQ6ICRI/events.json","paper":"https://pith.science/paper/KBCAODM7"},"agent_actions":{"view_html":"https://pith.science/pith/KBCAODM74DGLHVQUB5ZSQ6ICRI","download_json":"https://pith.science/pith/KBCAODM74DGLHVQUB5ZSQ6ICRI.json","view_paper":"https://pith.science/paper/KBCAODM7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.09960&json=true","fetch_graph":"https://pith.science/api/pith-number/KBCAODM74DGLHVQUB5ZSQ6ICRI/graph.json","fetch_events":"https://pith.science/api/pith-number/KBCAODM74DGLHVQUB5ZSQ6ICRI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KBCAODM74DGLHVQUB5ZSQ6ICRI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KBCAODM74DGLHVQUB5ZSQ6ICRI/action/storage_attestation","attest_author":"https://pith.science/pith/KBCAODM74DGLHVQUB5ZSQ6ICRI/action/author_attestation","sign_citation":"https://pith.science/pith/KBCAODM74DGLHVQUB5ZSQ6ICRI/action/citation_signature","submit_replication":"https://pith.science/pith/KBCAODM74DGLHVQUB5ZSQ6ICRI/action/replication_record"}},"created_at":"2026-07-05T09:35:56.348358+00:00","updated_at":"2026-07-05T09:35:56.348358+00:00"}