{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YDZLH3WN3236RAQDICMSEFYBVF","short_pith_number":"pith:YDZLH3WN","schema_version":"1.0","canonical_sha256":"c0f2b3eecddeb7e882034099221701a951df6586540ee8ce30fe0c0762dbc02e","source":{"kind":"arxiv","id":"1709.07097","version":1},"attestation_state":"computed","paper":{"title":"Persistence Flamelets: multiscale Persistent Homology for kernel density exploration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Pierpaolo Brutti, Tullia Padellini","submitted_at":"2017-09-20T22:45:27Z","abstract_excerpt":"In recent years there has been noticeable interest in the study of the \"shape of data\". Among the many ways a \"shape\" could be defined, topology is the most general one, as it describes an object in terms of its connectivity structure: connected components (topological features of dimension 0), cycles (features of dimension 1) and so on. There is a growing number of techniques, generally denoted as Topological Data Analysis, aimed at estimating topological invariants of a fixed object; when we allow this object to change, however, little has been done to investigate the evolution in its topolo"},"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":"1709.07097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-09-20T22:45:27Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"2322485ba83176797079d206fc1bb4a732877d1bdffd2484586442b18a939c01","abstract_canon_sha256":"2fcbfd02d6c9e9b793add4b3922289e6862c5f7f9afc2c10cc910cf88ab9116f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:36.573635Z","signature_b64":"spzVPhwY9SDqkoeW4Spz8LDXrxPPMZwP4CNjew1xIGevtMoa/7vdmKGEDa9m2QWGLfvD/ndTo7AdWZjp4Q9qBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0f2b3eecddeb7e882034099221701a951df6586540ee8ce30fe0c0762dbc02e","last_reissued_at":"2026-05-18T00:34:36.573040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:36.573040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Persistence Flamelets: multiscale Persistent Homology for kernel density exploration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Pierpaolo Brutti, Tullia Padellini","submitted_at":"2017-09-20T22:45:27Z","abstract_excerpt":"In recent years there has been noticeable interest in the study of the \"shape of data\". Among the many ways a \"shape\" could be defined, topology is the most general one, as it describes an object in terms of its connectivity structure: connected components (topological features of dimension 0), cycles (features of dimension 1) and so on. There is a growing number of techniques, generally denoted as Topological Data Analysis, aimed at estimating topological invariants of a fixed object; when we allow this object to change, however, little has been done to investigate the evolution in its topolo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07097","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":""},"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":"1709.07097","created_at":"2026-05-18T00:34:36.573135+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.07097v1","created_at":"2026-05-18T00:34:36.573135+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07097","created_at":"2026-05-18T00:34:36.573135+00:00"},{"alias_kind":"pith_short_12","alias_value":"YDZLH3WN3236","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YDZLH3WN3236RAQD","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YDZLH3WN","created_at":"2026-05-18T12:31:56.362134+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/YDZLH3WN3236RAQDICMSEFYBVF","json":"https://pith.science/pith/YDZLH3WN3236RAQDICMSEFYBVF.json","graph_json":"https://pith.science/api/pith-number/YDZLH3WN3236RAQDICMSEFYBVF/graph.json","events_json":"https://pith.science/api/pith-number/YDZLH3WN3236RAQDICMSEFYBVF/events.json","paper":"https://pith.science/paper/YDZLH3WN"},"agent_actions":{"view_html":"https://pith.science/pith/YDZLH3WN3236RAQDICMSEFYBVF","download_json":"https://pith.science/pith/YDZLH3WN3236RAQDICMSEFYBVF.json","view_paper":"https://pith.science/paper/YDZLH3WN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.07097&json=true","fetch_graph":"https://pith.science/api/pith-number/YDZLH3WN3236RAQDICMSEFYBVF/graph.json","fetch_events":"https://pith.science/api/pith-number/YDZLH3WN3236RAQDICMSEFYBVF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YDZLH3WN3236RAQDICMSEFYBVF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YDZLH3WN3236RAQDICMSEFYBVF/action/storage_attestation","attest_author":"https://pith.science/pith/YDZLH3WN3236RAQDICMSEFYBVF/action/author_attestation","sign_citation":"https://pith.science/pith/YDZLH3WN3236RAQDICMSEFYBVF/action/citation_signature","submit_replication":"https://pith.science/pith/YDZLH3WN3236RAQDICMSEFYBVF/action/replication_record"}},"created_at":"2026-05-18T00:34:36.573135+00:00","updated_at":"2026-05-18T00:34:36.573135+00:00"}