{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:W2DSZSWJYWBJ53T237B6WQLFSX","short_pith_number":"pith:W2DSZSWJ","schema_version":"1.0","canonical_sha256":"b6872ccac9c5829eee7adfc3eb416595dff3984daf6e775bab4d5a41e0eb38d6","source":{"kind":"arxiv","id":"1103.4408","version":1},"attestation_state":"computed","paper":{"title":"Conformal Wasserstein distances: comparing surfaces in polynomial time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Ingrid Daubechies, Yaron Lipman","submitted_at":"2011-03-22T23:08:09Z","abstract_excerpt":"We present a constructive approach to surface comparison realizable by a polynomial-time algorithm. We determine the \"similarity\" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solution to be invariant under global M\\\"{o}bius transformations. We present in detail the case where the surfaces to compare are disk-like; we also sketch how the approach can be generalized to other types of surfaces."},"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":"1103.4408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-22T23:08:09Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"5ae1838f9741a8fc49bb083a0988f96d8310adddcdf282d6a906630d06a95c39","abstract_canon_sha256":"2755a9cac1cfd465cc13a5632621c6400019981a428c02a830d4e2d78d29b2e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:34.321646Z","signature_b64":"bDQaWa3X29SyWblO0PBXmXLqXOnyOAESQcLv93pw/pjyHNk6ifnexRkJslYv13rTjVBfcuZiGpJpjs2YKtpXCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6872ccac9c5829eee7adfc3eb416595dff3984daf6e775bab4d5a41e0eb38d6","last_reissued_at":"2026-05-18T04:10:34.320906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:34.320906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conformal Wasserstein distances: comparing surfaces in polynomial time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Ingrid Daubechies, Yaron Lipman","submitted_at":"2011-03-22T23:08:09Z","abstract_excerpt":"We present a constructive approach to surface comparison realizable by a polynomial-time algorithm. We determine the \"similarity\" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solution to be invariant under global M\\\"{o}bius transformations. We present in detail the case where the surfaces to compare are disk-like; we also sketch how the approach can be generalized to other types of surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4408","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":"1103.4408","created_at":"2026-05-18T04:10:34.321019+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.4408v1","created_at":"2026-05-18T04:10:34.321019+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4408","created_at":"2026-05-18T04:10:34.321019+00:00"},{"alias_kind":"pith_short_12","alias_value":"W2DSZSWJYWBJ","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"W2DSZSWJYWBJ53T2","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"W2DSZSWJ","created_at":"2026-05-18T12:26:44.992195+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/W2DSZSWJYWBJ53T237B6WQLFSX","json":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX.json","graph_json":"https://pith.science/api/pith-number/W2DSZSWJYWBJ53T237B6WQLFSX/graph.json","events_json":"https://pith.science/api/pith-number/W2DSZSWJYWBJ53T237B6WQLFSX/events.json","paper":"https://pith.science/paper/W2DSZSWJ"},"agent_actions":{"view_html":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX","download_json":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX.json","view_paper":"https://pith.science/paper/W2DSZSWJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.4408&json=true","fetch_graph":"https://pith.science/api/pith-number/W2DSZSWJYWBJ53T237B6WQLFSX/graph.json","fetch_events":"https://pith.science/api/pith-number/W2DSZSWJYWBJ53T237B6WQLFSX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX/action/storage_attestation","attest_author":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX/action/author_attestation","sign_citation":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX/action/citation_signature","submit_replication":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX/action/replication_record"}},"created_at":"2026-05-18T04:10:34.321019+00:00","updated_at":"2026-05-18T04:10:34.321019+00:00"}