{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:W2DSZSWJYWBJ53T237B6WQLFSX","short_pith_number":"pith:W2DSZSWJ","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"},"canonical_sha256":"b6872ccac9c5829eee7adfc3eb416595dff3984daf6e775bab4d5a41e0eb38d6","source":{"kind":"arxiv","id":"1103.4408","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4408","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4408v1","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4408","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"W2DSZSWJYWBJ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"W2DSZSWJYWBJ53T2","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"W2DSZSWJ","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:W2DSZSWJYWBJ53T237B6WQLFSX","target":"record","payload":{"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"},"canonical_sha256":"b6872ccac9c5829eee7adfc3eb416595dff3984daf6e775bab4d5a41e0eb38d6","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"},"source_kind":"arxiv","source_id":"1103.4408","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1YX8iuz0JsbEFXUk0TT+mY32IicX9+Aeu+6gPvkMsbcTxQfqqdYwJEjSg4o2R/Kov07eFHKzv+Cvmyiv9c9NBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T23:23:44.924864Z"},"content_sha256":"3a918d9cac7c28dd3170f800f129f0fa742472d8886d58cdd84aed12094acaba","schema_version":"1.0","event_id":"sha256:3a918d9cac7c28dd3170f800f129f0fa742472d8886d58cdd84aed12094acaba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:W2DSZSWJYWBJ53T237B6WQLFSX","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JgGr3/ze+AFQY3lLx7+XxOyhZF1CMQ8WrNUcwyhKnCo4LyTiDTzAD5YvmopW1uD61lQWCcvwnfNqIwycxknNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T23:23:44.925663Z"},"content_sha256":"e0631dc3c847233cd3f2b3c349af4ee3a5aa5f9101c54555f24ab8404456ca74","schema_version":"1.0","event_id":"sha256:e0631dc3c847233cd3f2b3c349af4ee3a5aa5f9101c54555f24ab8404456ca74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX/bundle.json","state_url":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2DSZSWJYWBJ53T237B6WQLFSX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T23:23:44Z","links":{"resolver":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX","bundle":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX/bundle.json","state":"https://pith.science/pith/W2DSZSWJYWBJ53T237B6WQLFSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2DSZSWJYWBJ53T237B6WQLFSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:W2DSZSWJYWBJ53T237B6WQLFSX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2755a9cac1cfd465cc13a5632621c6400019981a428c02a830d4e2d78d29b2e3","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-22T23:08:09Z","title_canon_sha256":"5ae1838f9741a8fc49bb083a0988f96d8310adddcdf282d6a906630d06a95c39"},"schema_version":"1.0","source":{"id":"1103.4408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4408","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4408v1","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4408","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"W2DSZSWJYWBJ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"W2DSZSWJYWBJ53T2","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"W2DSZSWJ","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:e0631dc3c847233cd3f2b3c349af4ee3a5aa5f9101c54555f24ab8404456ca74","target":"graph","created_at":"2026-05-18T04:10:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Ingrid Daubechies, Yaron Lipman","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-22T23:08:09Z","title":"Conformal Wasserstein distances: comparing surfaces in polynomial time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4408","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3a918d9cac7c28dd3170f800f129f0fa742472d8886d58cdd84aed12094acaba","target":"record","created_at":"2026-05-18T04:10:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2755a9cac1cfd465cc13a5632621c6400019981a428c02a830d4e2d78d29b2e3","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-22T23:08:09Z","title_canon_sha256":"5ae1838f9741a8fc49bb083a0988f96d8310adddcdf282d6a906630d06a95c39"},"schema_version":"1.0","source":{"id":"1103.4408","kind":"arxiv","version":1}},"canonical_sha256":"b6872ccac9c5829eee7adfc3eb416595dff3984daf6e775bab4d5a41e0eb38d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6872ccac9c5829eee7adfc3eb416595dff3984daf6e775bab4d5a41e0eb38d6","first_computed_at":"2026-05-18T04:10:34.320906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:34.320906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bDQaWa3X29SyWblO0PBXmXLqXOnyOAESQcLv93pw/pjyHNk6ifnexRkJslYv13rTjVBfcuZiGpJpjs2YKtpXCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:34.321646Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a918d9cac7c28dd3170f800f129f0fa742472d8886d58cdd84aed12094acaba","sha256:e0631dc3c847233cd3f2b3c349af4ee3a5aa5f9101c54555f24ab8404456ca74"],"state_sha256":"9b12e950a215376df2a0573c6e895ace3e90a1cfd6460ca0cb516e700d4c1bef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YVr7cPP0+C29wcUnkxm8rT5l8zVZqCnCQ1b2y0T8NjYACYx5C3heg/4MoJAVKMCStOa+Bdq08zFqnsIQ8S0FDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T23:23:44.930040Z","bundle_sha256":"ab57a6b4bbfaa08d1e4fdf23f8c43cb92020232142470df1108974d13698e8b3"}}