{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:H5ZDE5RCBQ4JCPUY6P34ZAWJND","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":"d9fc381ec271d1dbe701ceaeb294064b8682c911e77cc1da4d05738d0827638b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.CG","submitted_at":"2014-12-04T14:41:56Z","title_canon_sha256":"c5ac36d68616e30a224deba7697fce1c4cdaed466f02e28ba65901cfbffa82d7"},"schema_version":"1.0","source":{"id":"1412.1680","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1680","created_at":"2026-05-18T02:19:27Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1680v3","created_at":"2026-05-18T02:19:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1680","created_at":"2026-05-18T02:19:27Z"},{"alias_kind":"pith_short_12","alias_value":"H5ZDE5RCBQ4J","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"H5ZDE5RCBQ4JCPUY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"H5ZDE5RC","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:e4ffb2b8d933e46e0c7fdaf854889bde7db4c3a3efddb8dd519ada1567661a92","target":"graph","created_at":"2026-05-18T02:19:27Z","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":"Given a real-valued function $f$ defined over a manifold $M$ embedded in $\\mathbb{R}^d$, we are interested in recovering structural information about $f$ from the sole information of its values on a finite sample $P$. Existing methods provide approximation to the persistence diagram of $f$ when geometric noise and functional noise are bounded. However, they fail in the presence of aberrant values, also called outliers, both in theory and practice.\n  We propose a new algorithm that deals with outliers. We handle aberrant functional values with a method inspired from the k-nearest neighbors regr","authors_text":"Fengtao Fan, Fr\\'ed\\'eric Chazal, Micka\\\"el Buchet, Steve Y. Oudot, Tamal K. Dey, Yusu Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.CG","submitted_at":"2014-12-04T14:41:56Z","title":"Topological analysis of scalar fields with outliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1680","kind":"arxiv","version":3},"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":"sha256:9a326cc6e3efc9a7bd3c38d6cd1937ed1a3ef1db7863bf563897b66c278fccb6","target":"record","created_at":"2026-05-18T02:19:27Z","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":"d9fc381ec271d1dbe701ceaeb294064b8682c911e77cc1da4d05738d0827638b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.CG","submitted_at":"2014-12-04T14:41:56Z","title_canon_sha256":"c5ac36d68616e30a224deba7697fce1c4cdaed466f02e28ba65901cfbffa82d7"},"schema_version":"1.0","source":{"id":"1412.1680","kind":"arxiv","version":3}},"canonical_sha256":"3f723276220c38913e98f3f7cc82c968c54d3e8f2eac449efdf839435105fff2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f723276220c38913e98f3f7cc82c968c54d3e8f2eac449efdf839435105fff2","first_computed_at":"2026-05-18T02:19:27.986508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:27.986508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TkZYF1aMO0rMHHKNl8egWXNvomKgkzs6WOhNjqeWvDzNJWNyZb1OrgdR5qS1D0LX2u572PA1bBJTquavcA3gBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:27.986992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1680","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a326cc6e3efc9a7bd3c38d6cd1937ed1a3ef1db7863bf563897b66c278fccb6","sha256:e4ffb2b8d933e46e0c7fdaf854889bde7db4c3a3efddb8dd519ada1567661a92"],"state_sha256":"b92b785963f2817e57d0611682010b174ac13059a724fe1bcd84aef060c837cc"}