{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UB4QGUQRGWFQEVDRQQNF7WFK4G","short_pith_number":"pith:UB4QGUQR","schema_version":"1.0","canonical_sha256":"a079035211358b025471841a5fd8aae18c30c2cd0ddf146c622687e5cb477626","source":{"kind":"arxiv","id":"1902.07190","version":3},"attestation_state":"computed","paper":{"title":"Approximating Continuous Functions on Persistence Diagrams Using Template Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.CG","authors_text":"Elizabeth Munch, Firas A. Khasawneh, Jose A. Perea","submitted_at":"2019-02-19T18:43:14Z","abstract_excerpt":"The persistence diagram is an increasingly useful tool from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. The most success to date has come from methods that map persistence diagrams into vector spaces, in a way which maximizes the structure preserved. This process is commonly referred to as featurization. In this paper, we describe a mathematical framework for featurization called \\emph{template functions}, and we show that it addresses the problem of approximating continuous functions on compact subsets of the space of per"},"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":"1902.07190","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-02-19T18:43:14Z","cross_cats_sorted":["math.AT","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"519f7ad56983d20a26b9c5d622faa3be3291585288cb0df9fc184ed006398503","abstract_canon_sha256":"3cf128e361b91f30023267e0439accc0d4f40c3afbacf92cc97a20f57fb4c5a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:50:35.730414Z","signature_b64":"LkxwtGp0zDPE1R0WGFqP5sHGal/j2iD4qGiJdxSiltFJ0dpjR7qJOdxMIRZ9m2FZ/OqKfNyjQA9FHmD+E1bXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a079035211358b025471841a5fd8aae18c30c2cd0ddf146c622687e5cb477626","last_reissued_at":"2026-07-05T05:50:35.730043Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:50:35.730043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating Continuous Functions on Persistence Diagrams Using Template Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.CG","authors_text":"Elizabeth Munch, Firas A. Khasawneh, Jose A. Perea","submitted_at":"2019-02-19T18:43:14Z","abstract_excerpt":"The persistence diagram is an increasingly useful tool from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. The most success to date has come from methods that map persistence diagrams into vector spaces, in a way which maximizes the structure preserved. This process is commonly referred to as featurization. In this paper, we describe a mathematical framework for featurization called \\emph{template functions}, and we show that it addresses the problem of approximating continuous functions on compact subsets of the space of per"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07190","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/1902.07190/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":"1902.07190","created_at":"2026-07-05T05:50:35.730100+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.07190v3","created_at":"2026-07-05T05:50:35.730100+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07190","created_at":"2026-07-05T05:50:35.730100+00:00"},{"alias_kind":"pith_short_12","alias_value":"UB4QGUQRGWFQ","created_at":"2026-07-05T05:50:35.730100+00:00"},{"alias_kind":"pith_short_16","alias_value":"UB4QGUQRGWFQEVDR","created_at":"2026-07-05T05:50:35.730100+00:00"},{"alias_kind":"pith_short_8","alias_value":"UB4QGUQR","created_at":"2026-07-05T05:50:35.730100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.01678","citing_title":"Chatter Detection in Turning Using Machine Learning and Similarity Measures of Time Series via Dynamic Time Warping","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UB4QGUQRGWFQEVDRQQNF7WFK4G","json":"https://pith.science/pith/UB4QGUQRGWFQEVDRQQNF7WFK4G.json","graph_json":"https://pith.science/api/pith-number/UB4QGUQRGWFQEVDRQQNF7WFK4G/graph.json","events_json":"https://pith.science/api/pith-number/UB4QGUQRGWFQEVDRQQNF7WFK4G/events.json","paper":"https://pith.science/paper/UB4QGUQR"},"agent_actions":{"view_html":"https://pith.science/pith/UB4QGUQRGWFQEVDRQQNF7WFK4G","download_json":"https://pith.science/pith/UB4QGUQRGWFQEVDRQQNF7WFK4G.json","view_paper":"https://pith.science/paper/UB4QGUQR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.07190&json=true","fetch_graph":"https://pith.science/api/pith-number/UB4QGUQRGWFQEVDRQQNF7WFK4G/graph.json","fetch_events":"https://pith.science/api/pith-number/UB4QGUQRGWFQEVDRQQNF7WFK4G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UB4QGUQRGWFQEVDRQQNF7WFK4G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UB4QGUQRGWFQEVDRQQNF7WFK4G/action/storage_attestation","attest_author":"https://pith.science/pith/UB4QGUQRGWFQEVDRQQNF7WFK4G/action/author_attestation","sign_citation":"https://pith.science/pith/UB4QGUQRGWFQEVDRQQNF7WFK4G/action/citation_signature","submit_replication":"https://pith.science/pith/UB4QGUQRGWFQEVDRQQNF7WFK4G/action/replication_record"}},"created_at":"2026-07-05T05:50:35.730100+00:00","updated_at":"2026-07-05T05:50:35.730100+00:00"}