{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZIY23DAPWYAWEOGNCYZ6FNORHS","short_pith_number":"pith:ZIY23DAP","schema_version":"1.0","canonical_sha256":"ca31ad8c0fb6016238cd1633e2b5d13c806a075eaffad98af75a7b581d9f4f52","source":{"kind":"arxiv","id":"1505.06462","version":1},"attestation_state":"computed","paper":{"title":"Parameter-free Topology Inference and Sparsification for Data on Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"cs.CG","authors_text":"Tamal K. Dey, Yusu Wang, Zhe Dong","submitted_at":"2015-05-24T17:44:06Z","abstract_excerpt":"In topology inference from data, current approaches face two major problems. One concerns the selection of a correct parameter to build an appropriate complex on top of the data points; the other involves with the typical `large' size of this complex. We address these two issues in the context of inferring homology from sample points of a smooth manifold of known dimension sitting in an Euclidean space $\\mathbb{R}^k$. We show that, for a sample size of $n$ points, we can identify a set of $O(n^2)$ points (as opposed to $O(n^{\\lceil \\frac{k}{2}\\rceil})$ Voronoi vertices) approximating a subset "},"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":"1505.06462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-05-24T17:44:06Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"e45af0c20cb529afce8ced3f88640a7e8820b3721717640e1b01f8f7464f2eec","abstract_canon_sha256":"9f39e4acbecf80963a93e1ef760a9c8df44709fe448d06e803ca47a2fbbfa49f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:45.664902Z","signature_b64":"1sFvv8m4O2jUN53UmrSZ3NnMmMny2G64Jkyr3vpyJqOJ43aXJMkdar/m65L4HMMeMbHiGCA0990R3m2ixJgsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca31ad8c0fb6016238cd1633e2b5d13c806a075eaffad98af75a7b581d9f4f52","last_reissued_at":"2026-05-18T02:03:45.664294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:45.664294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parameter-free Topology Inference and Sparsification for Data on Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"cs.CG","authors_text":"Tamal K. Dey, Yusu Wang, Zhe Dong","submitted_at":"2015-05-24T17:44:06Z","abstract_excerpt":"In topology inference from data, current approaches face two major problems. One concerns the selection of a correct parameter to build an appropriate complex on top of the data points; the other involves with the typical `large' size of this complex. We address these two issues in the context of inferring homology from sample points of a smooth manifold of known dimension sitting in an Euclidean space $\\mathbb{R}^k$. We show that, for a sample size of $n$ points, we can identify a set of $O(n^2)$ points (as opposed to $O(n^{\\lceil \\frac{k}{2}\\rceil})$ Voronoi vertices) approximating a subset "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06462","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":"1505.06462","created_at":"2026-05-18T02:03:45.664408+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06462v1","created_at":"2026-05-18T02:03:45.664408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06462","created_at":"2026-05-18T02:03:45.664408+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZIY23DAPWYAW","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZIY23DAPWYAWEOGN","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZIY23DAP","created_at":"2026-05-18T12:29:52.810259+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/ZIY23DAPWYAWEOGNCYZ6FNORHS","json":"https://pith.science/pith/ZIY23DAPWYAWEOGNCYZ6FNORHS.json","graph_json":"https://pith.science/api/pith-number/ZIY23DAPWYAWEOGNCYZ6FNORHS/graph.json","events_json":"https://pith.science/api/pith-number/ZIY23DAPWYAWEOGNCYZ6FNORHS/events.json","paper":"https://pith.science/paper/ZIY23DAP"},"agent_actions":{"view_html":"https://pith.science/pith/ZIY23DAPWYAWEOGNCYZ6FNORHS","download_json":"https://pith.science/pith/ZIY23DAPWYAWEOGNCYZ6FNORHS.json","view_paper":"https://pith.science/paper/ZIY23DAP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06462&json=true","fetch_graph":"https://pith.science/api/pith-number/ZIY23DAPWYAWEOGNCYZ6FNORHS/graph.json","fetch_events":"https://pith.science/api/pith-number/ZIY23DAPWYAWEOGNCYZ6FNORHS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZIY23DAPWYAWEOGNCYZ6FNORHS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZIY23DAPWYAWEOGNCYZ6FNORHS/action/storage_attestation","attest_author":"https://pith.science/pith/ZIY23DAPWYAWEOGNCYZ6FNORHS/action/author_attestation","sign_citation":"https://pith.science/pith/ZIY23DAPWYAWEOGNCYZ6FNORHS/action/citation_signature","submit_replication":"https://pith.science/pith/ZIY23DAPWYAWEOGNCYZ6FNORHS/action/replication_record"}},"created_at":"2026-05-18T02:03:45.664408+00:00","updated_at":"2026-05-18T02:03:45.664408+00:00"}