{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OWNFOV3YUACOIIEQOZDCVPT2SY","short_pith_number":"pith:OWNFOV3Y","schema_version":"1.0","canonical_sha256":"759a575778a004e4209076462abe7a9630ebd97d1f80f04139db33bebaf3ac6d","source":{"kind":"arxiv","id":"1805.01577","version":1},"attestation_state":"computed","paper":{"title":"Local angles and dimension estimation from data on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Adolfo J. Quiroz, Mateo D\\'iaz, Mauricio Velasco","submitted_at":"2018-05-04T00:05:55Z","abstract_excerpt":"For data living in a manifold $M\\subseteq \\mathbb{R}^m$ and a point $p\\in M$ we consider a statistic $U_{k,n}$ which estimates the variance of the angle between pairs of vectors $X_i-p$ and $X_j-p$, for data points $X_i$, $X_j$, near $p$, and evaluate this statistic as a tool for estimation of the intrinsic dimension of $M$ at $p$. Consistency of the local dimension estimator is established and the asymptotic distribution of $U_{k,n}$ is found under minimal regularity assumptions. Performance of the proposed methodology is compared against state-of-the-art methods on simulated data."},"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":"1805.01577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-04T00:05:55Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"446f0c9e881ab0093086dc8803d937538b3537bea23803e5f53fdf6f43c3ebe6","abstract_canon_sha256":"d14b15b1d3b05f9028aaccbc9cc31dc2f4849119566e027b20eda9749d2bb66d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:47.429855Z","signature_b64":"lt5Rsf35P+RXwIsmyybCKjFWvjnrzv1jPqvaAHn2D4hBXC7Kf67j5O+DkaWrf1rcqLEdmp38dB23mw6kJOoQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"759a575778a004e4209076462abe7a9630ebd97d1f80f04139db33bebaf3ac6d","last_reissued_at":"2026-05-18T00:16:47.429211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:47.429211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local angles and dimension estimation from data on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Adolfo J. Quiroz, Mateo D\\'iaz, Mauricio Velasco","submitted_at":"2018-05-04T00:05:55Z","abstract_excerpt":"For data living in a manifold $M\\subseteq \\mathbb{R}^m$ and a point $p\\in M$ we consider a statistic $U_{k,n}$ which estimates the variance of the angle between pairs of vectors $X_i-p$ and $X_j-p$, for data points $X_i$, $X_j$, near $p$, and evaluate this statistic as a tool for estimation of the intrinsic dimension of $M$ at $p$. Consistency of the local dimension estimator is established and the asymptotic distribution of $U_{k,n}$ is found under minimal regularity assumptions. Performance of the proposed methodology is compared against state-of-the-art methods on simulated data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01577","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":"1805.01577","created_at":"2026-05-18T00:16:47.429310+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.01577v1","created_at":"2026-05-18T00:16:47.429310+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01577","created_at":"2026-05-18T00:16:47.429310+00:00"},{"alias_kind":"pith_short_12","alias_value":"OWNFOV3YUACO","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OWNFOV3YUACOIIEQ","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OWNFOV3Y","created_at":"2026-05-18T12:32:43.782077+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/OWNFOV3YUACOIIEQOZDCVPT2SY","json":"https://pith.science/pith/OWNFOV3YUACOIIEQOZDCVPT2SY.json","graph_json":"https://pith.science/api/pith-number/OWNFOV3YUACOIIEQOZDCVPT2SY/graph.json","events_json":"https://pith.science/api/pith-number/OWNFOV3YUACOIIEQOZDCVPT2SY/events.json","paper":"https://pith.science/paper/OWNFOV3Y"},"agent_actions":{"view_html":"https://pith.science/pith/OWNFOV3YUACOIIEQOZDCVPT2SY","download_json":"https://pith.science/pith/OWNFOV3YUACOIIEQOZDCVPT2SY.json","view_paper":"https://pith.science/paper/OWNFOV3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.01577&json=true","fetch_graph":"https://pith.science/api/pith-number/OWNFOV3YUACOIIEQOZDCVPT2SY/graph.json","fetch_events":"https://pith.science/api/pith-number/OWNFOV3YUACOIIEQOZDCVPT2SY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OWNFOV3YUACOIIEQOZDCVPT2SY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OWNFOV3YUACOIIEQOZDCVPT2SY/action/storage_attestation","attest_author":"https://pith.science/pith/OWNFOV3YUACOIIEQOZDCVPT2SY/action/author_attestation","sign_citation":"https://pith.science/pith/OWNFOV3YUACOIIEQOZDCVPT2SY/action/citation_signature","submit_replication":"https://pith.science/pith/OWNFOV3YUACOIIEQOZDCVPT2SY/action/replication_record"}},"created_at":"2026-05-18T00:16:47.429310+00:00","updated_at":"2026-05-18T00:16:47.429310+00:00"}