{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RC3HWPZOWJJ5BKVPGWMAS25XWC","short_pith_number":"pith:RC3HWPZO","schema_version":"1.0","canonical_sha256":"88b67b3f2eb253d0aaaf3598096bb7b0a560e6554d117dc0a8ce5b4f90f0dd8d","source":{"kind":"arxiv","id":"1509.07707","version":1},"attestation_state":"computed","paper":{"title":"Iterated Diffusion Maps for Feature Identification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"John Harlim, Tyrus Berry","submitted_at":"2015-09-25T13:16:13Z","abstract_excerpt":"Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data set sampled from a manifold embedded in Euclidean space. Moreover, local kernels were used to represent a diffeomorphism, H, between a data set and a feature of interest using an anisotropic kernel function, defined by a covariance matrix based on the local derivatives, DH. In this paper, we generalize the theory of local kernels to represent degenerate mappings where the intrinsic dimension of the data set is higher "},"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":"1509.07707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-25T13:16:13Z","cross_cats_sorted":[],"title_canon_sha256":"b6b3583a8f81abab05f50ad5ec448e7bfc3028590c136ad936d9a59c07c3f990","abstract_canon_sha256":"6519dca4227e1a34fdc003b61afd6f63dce2093777e7da7fb7cb4a293fc2d2cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:02.128467Z","signature_b64":"BZXqMZGUzlZmdclTIUY4bpENF0kY8k86IIFGkVhz95yZWI++3hHEFnJfOmk2fU8rXVyJooRONZsG3fP9dEBeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88b67b3f2eb253d0aaaf3598096bb7b0a560e6554d117dc0a8ce5b4f90f0dd8d","last_reissued_at":"2026-05-18T01:32:02.128026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:02.128026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iterated Diffusion Maps for Feature Identification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"John Harlim, Tyrus Berry","submitted_at":"2015-09-25T13:16:13Z","abstract_excerpt":"Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data set sampled from a manifold embedded in Euclidean space. Moreover, local kernels were used to represent a diffeomorphism, H, between a data set and a feature of interest using an anisotropic kernel function, defined by a covariance matrix based on the local derivatives, DH. In this paper, we generalize the theory of local kernels to represent degenerate mappings where the intrinsic dimension of the data set is higher "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07707","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":"1509.07707","created_at":"2026-05-18T01:32:02.128097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07707v1","created_at":"2026-05-18T01:32:02.128097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07707","created_at":"2026-05-18T01:32:02.128097+00:00"},{"alias_kind":"pith_short_12","alias_value":"RC3HWPZOWJJ5","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RC3HWPZOWJJ5BKVP","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RC3HWPZO","created_at":"2026-05-18T12:29:39.896362+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/RC3HWPZOWJJ5BKVPGWMAS25XWC","json":"https://pith.science/pith/RC3HWPZOWJJ5BKVPGWMAS25XWC.json","graph_json":"https://pith.science/api/pith-number/RC3HWPZOWJJ5BKVPGWMAS25XWC/graph.json","events_json":"https://pith.science/api/pith-number/RC3HWPZOWJJ5BKVPGWMAS25XWC/events.json","paper":"https://pith.science/paper/RC3HWPZO"},"agent_actions":{"view_html":"https://pith.science/pith/RC3HWPZOWJJ5BKVPGWMAS25XWC","download_json":"https://pith.science/pith/RC3HWPZOWJJ5BKVPGWMAS25XWC.json","view_paper":"https://pith.science/paper/RC3HWPZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07707&json=true","fetch_graph":"https://pith.science/api/pith-number/RC3HWPZOWJJ5BKVPGWMAS25XWC/graph.json","fetch_events":"https://pith.science/api/pith-number/RC3HWPZOWJJ5BKVPGWMAS25XWC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RC3HWPZOWJJ5BKVPGWMAS25XWC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RC3HWPZOWJJ5BKVPGWMAS25XWC/action/storage_attestation","attest_author":"https://pith.science/pith/RC3HWPZOWJJ5BKVPGWMAS25XWC/action/author_attestation","sign_citation":"https://pith.science/pith/RC3HWPZOWJJ5BKVPGWMAS25XWC/action/citation_signature","submit_replication":"https://pith.science/pith/RC3HWPZOWJJ5BKVPGWMAS25XWC/action/replication_record"}},"created_at":"2026-05-18T01:32:02.128097+00:00","updated_at":"2026-05-18T01:32:02.128097+00:00"}