{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:K6P45AODONYJHSVWUJDMSSZ2DT","short_pith_number":"pith:K6P45AOD","schema_version":"1.0","canonical_sha256":"579fce81c3737093cab6a246c94b3a1ce5606b544f6a5bbe66c232cc0ee5efbc","source":{"kind":"arxiv","id":"1701.02843","version":2},"attestation_state":"computed","paper":{"title":"Solving Partial Differential Equations on Manifolds From Incomplete Inter-Point Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.NA","authors_text":"Jia Li, Rongjie Lai","submitted_at":"2017-01-11T04:04:43Z","abstract_excerpt":"Solutions of partial differential equations (PDEs) on manifolds have provided important applications in different fields in science and engineering. Existing methods are majorly based on discretization of manifolds as implicit functions, triangle meshes, or point clouds, where the manifold structure is approximated by either zero level set of an implicit function or a set of points. In many applications, manifolds might be only provided as an inter-point distance matrix with possible missing values. This paper discusses a framework to discretize PDEs on manifolds represented as incomplete inte"},"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":"1701.02843","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-11T04:04:43Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"4729bfb52e2fdfeb05796c664cd537e9c766c8472882178bd1a79d14ea797123","abstract_canon_sha256":"66701a11e29036d170d67f7b08d22dc3f6bf067ece71354026a0c06516dbc600"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:46.281543Z","signature_b64":"ARik21ZL/pzCBtZ7SpXGv0vJ4rEM9SrVLPpYRS2GKuiSoyYSCvzl/i/tlDDbcWZYUXSscmHgE2TV05Cy+uXfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"579fce81c3737093cab6a246c94b3a1ce5606b544f6a5bbe66c232cc0ee5efbc","last_reissued_at":"2026-05-18T00:38:46.281001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:46.281001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solving Partial Differential Equations on Manifolds From Incomplete Inter-Point Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.NA","authors_text":"Jia Li, Rongjie Lai","submitted_at":"2017-01-11T04:04:43Z","abstract_excerpt":"Solutions of partial differential equations (PDEs) on manifolds have provided important applications in different fields in science and engineering. Existing methods are majorly based on discretization of manifolds as implicit functions, triangle meshes, or point clouds, where the manifold structure is approximated by either zero level set of an implicit function or a set of points. In many applications, manifolds might be only provided as an inter-point distance matrix with possible missing values. This paper discusses a framework to discretize PDEs on manifolds represented as incomplete inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02843","kind":"arxiv","version":2},"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":"1701.02843","created_at":"2026-05-18T00:38:46.281074+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.02843v2","created_at":"2026-05-18T00:38:46.281074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02843","created_at":"2026-05-18T00:38:46.281074+00:00"},{"alias_kind":"pith_short_12","alias_value":"K6P45AODONYJ","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"K6P45AODONYJHSVW","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"K6P45AOD","created_at":"2026-05-18T12:31:24.725408+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/K6P45AODONYJHSVWUJDMSSZ2DT","json":"https://pith.science/pith/K6P45AODONYJHSVWUJDMSSZ2DT.json","graph_json":"https://pith.science/api/pith-number/K6P45AODONYJHSVWUJDMSSZ2DT/graph.json","events_json":"https://pith.science/api/pith-number/K6P45AODONYJHSVWUJDMSSZ2DT/events.json","paper":"https://pith.science/paper/K6P45AOD"},"agent_actions":{"view_html":"https://pith.science/pith/K6P45AODONYJHSVWUJDMSSZ2DT","download_json":"https://pith.science/pith/K6P45AODONYJHSVWUJDMSSZ2DT.json","view_paper":"https://pith.science/paper/K6P45AOD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.02843&json=true","fetch_graph":"https://pith.science/api/pith-number/K6P45AODONYJHSVWUJDMSSZ2DT/graph.json","fetch_events":"https://pith.science/api/pith-number/K6P45AODONYJHSVWUJDMSSZ2DT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K6P45AODONYJHSVWUJDMSSZ2DT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K6P45AODONYJHSVWUJDMSSZ2DT/action/storage_attestation","attest_author":"https://pith.science/pith/K6P45AODONYJHSVWUJDMSSZ2DT/action/author_attestation","sign_citation":"https://pith.science/pith/K6P45AODONYJHSVWUJDMSSZ2DT/action/citation_signature","submit_replication":"https://pith.science/pith/K6P45AODONYJHSVWUJDMSSZ2DT/action/replication_record"}},"created_at":"2026-05-18T00:38:46.281074+00:00","updated_at":"2026-05-18T00:38:46.281074+00:00"}