{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:D63MMBNDNQY2XQ6I5HUATXQWO2","short_pith_number":"pith:D63MMBND","canonical_record":{"source":{"id":"2311.02172","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2023-11-03T18:02:15Z","cross_cats_sorted":[],"title_canon_sha256":"4820ae2ee13f28ed888b516f56ad974399756dff0eda3a694a4c97e418ea9f8f","abstract_canon_sha256":"f0fc17b2f4176ea8e713b4d883b813780afb5c316f3cc06326e6001453dce60d"},"schema_version":"1.0"},"canonical_sha256":"1fb6c605a36c31abc3c8e9e809de167689bea6b950bb43899b56b7971afd5824","source":{"kind":"arxiv","id":"2311.02172","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.02172","created_at":"2026-07-05T07:09:06Z"},{"alias_kind":"arxiv_version","alias_value":"2311.02172v1","created_at":"2026-07-05T07:09:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.02172","created_at":"2026-07-05T07:09:06Z"},{"alias_kind":"pith_short_12","alias_value":"D63MMBNDNQY2","created_at":"2026-07-05T07:09:06Z"},{"alias_kind":"pith_short_16","alias_value":"D63MMBNDNQY2XQ6I","created_at":"2026-07-05T07:09:06Z"},{"alias_kind":"pith_short_8","alias_value":"D63MMBND","created_at":"2026-07-05T07:09:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:D63MMBNDNQY2XQ6I5HUATXQWO2","target":"record","payload":{"canonical_record":{"source":{"id":"2311.02172","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2023-11-03T18:02:15Z","cross_cats_sorted":[],"title_canon_sha256":"4820ae2ee13f28ed888b516f56ad974399756dff0eda3a694a4c97e418ea9f8f","abstract_canon_sha256":"f0fc17b2f4176ea8e713b4d883b813780afb5c316f3cc06326e6001453dce60d"},"schema_version":"1.0"},"canonical_sha256":"1fb6c605a36c31abc3c8e9e809de167689bea6b950bb43899b56b7971afd5824","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:09:06.399683Z","signature_b64":"hFTFsq0yh1o/kYmICX6cZgLjuN79N6bgXrfL8aruhX5GrK3ke9SheOMDHUGlecXIYRKEcybkA04u/rmE8KaCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fb6c605a36c31abc3c8e9e809de167689bea6b950bb43899b56b7971afd5824","last_reissued_at":"2026-07-05T07:09:06.399232Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:09:06.399232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.02172","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":"2026-07-05T07:09:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qy0PWKjFMTND3/FXEKZUSKnM9sluT/xYvH6QqYPc1h1Ub/W8v8p8eRavmtSxaBmVh5gT2u/p4fVfgEJ/U9V/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T23:43:00.577740Z"},"content_sha256":"fe3b8c994fc7fd0342d090a835ac354e3e4d317b4414ecdfb85f4949b823ba60","schema_version":"1.0","event_id":"sha256:fe3b8c994fc7fd0342d090a835ac354e3e4d317b4414ecdfb85f4949b823ba60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:D63MMBNDNQY2XQ6I5HUATXQWO2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast and Accurate Approximations of the Optimal Transport in Semi-Discrete and Discrete Settings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Keegan Yao, Pankaj K. Agarwal, Pouyan Shirzadian, Sharath Raghvendra","submitted_at":"2023-11-03T18:02:15Z","abstract_excerpt":"Given a $d$-dimensional continuous (resp. discrete) probability distribution $\\mu$ and a discrete distribution $\\nu$, the semi-discrete (resp. discrete) Optimal Transport (OT) problem asks for computing a minimum-cost plan to transport mass from $\\mu$ to $\\nu$; we assume $n$ to be the size of the support of the discrete distributions, and we assume we have access to an oracle outputting the mass of $\\mu$ inside a constant-complexity region in $O(1)$ time. In this paper, we present three approximation algorithms for the OT problem.\n  (i) Semi-discrete additive approximation: For any $\\epsilon>0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02172","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.02172/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:09:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EVeMCyVO4pCxouDV4GHxhWO2geTARjlY4dqe4N66/Rr3n/aHfs4RVKlwj4xenHR9wfthk4+i+Hn7jpEGgjrbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T23:43:00.578308Z"},"content_sha256":"e4755e298ffb6d8113fbdfb6cbb37a1376914fa51b0929af8be49f05c3ea497c","schema_version":"1.0","event_id":"sha256:e4755e298ffb6d8113fbdfb6cbb37a1376914fa51b0929af8be49f05c3ea497c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/bundle.json","state_url":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/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":"2026-08-03T23:43:00Z","links":{"resolver":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2","bundle":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/bundle.json","state":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:D63MMBNDNQY2XQ6I5HUATXQWO2","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":"f0fc17b2f4176ea8e713b4d883b813780afb5c316f3cc06326e6001453dce60d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2023-11-03T18:02:15Z","title_canon_sha256":"4820ae2ee13f28ed888b516f56ad974399756dff0eda3a694a4c97e418ea9f8f"},"schema_version":"1.0","source":{"id":"2311.02172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.02172","created_at":"2026-07-05T07:09:06Z"},{"alias_kind":"arxiv_version","alias_value":"2311.02172v1","created_at":"2026-07-05T07:09:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.02172","created_at":"2026-07-05T07:09:06Z"},{"alias_kind":"pith_short_12","alias_value":"D63MMBNDNQY2","created_at":"2026-07-05T07:09:06Z"},{"alias_kind":"pith_short_16","alias_value":"D63MMBNDNQY2XQ6I","created_at":"2026-07-05T07:09:06Z"},{"alias_kind":"pith_short_8","alias_value":"D63MMBND","created_at":"2026-07-05T07:09:06Z"}],"graph_snapshots":[{"event_id":"sha256:e4755e298ffb6d8113fbdfb6cbb37a1376914fa51b0929af8be49f05c3ea497c","target":"graph","created_at":"2026-07-05T07:09:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.02172/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a $d$-dimensional continuous (resp. discrete) probability distribution $\\mu$ and a discrete distribution $\\nu$, the semi-discrete (resp. discrete) Optimal Transport (OT) problem asks for computing a minimum-cost plan to transport mass from $\\mu$ to $\\nu$; we assume $n$ to be the size of the support of the discrete distributions, and we assume we have access to an oracle outputting the mass of $\\mu$ inside a constant-complexity region in $O(1)$ time. In this paper, we present three approximation algorithms for the OT problem.\n  (i) Semi-discrete additive approximation: For any $\\epsilon>0","authors_text":"Keegan Yao, Pankaj K. Agarwal, Pouyan Shirzadian, Sharath Raghvendra","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2023-11-03T18:02:15Z","title":"Fast and Accurate Approximations of the Optimal Transport in Semi-Discrete and Discrete Settings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02172","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:fe3b8c994fc7fd0342d090a835ac354e3e4d317b4414ecdfb85f4949b823ba60","target":"record","created_at":"2026-07-05T07:09:06Z","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":"f0fc17b2f4176ea8e713b4d883b813780afb5c316f3cc06326e6001453dce60d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2023-11-03T18:02:15Z","title_canon_sha256":"4820ae2ee13f28ed888b516f56ad974399756dff0eda3a694a4c97e418ea9f8f"},"schema_version":"1.0","source":{"id":"2311.02172","kind":"arxiv","version":1}},"canonical_sha256":"1fb6c605a36c31abc3c8e9e809de167689bea6b950bb43899b56b7971afd5824","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fb6c605a36c31abc3c8e9e809de167689bea6b950bb43899b56b7971afd5824","first_computed_at":"2026-07-05T07:09:06.399232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:09:06.399232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hFTFsq0yh1o/kYmICX6cZgLjuN79N6bgXrfL8aruhX5GrK3ke9SheOMDHUGlecXIYRKEcybkA04u/rmE8KaCDg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:09:06.399683Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.02172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe3b8c994fc7fd0342d090a835ac354e3e4d317b4414ecdfb85f4949b823ba60","sha256:e4755e298ffb6d8113fbdfb6cbb37a1376914fa51b0929af8be49f05c3ea497c"],"state_sha256":"5277d54a59f74e03fbdb7e736f17f56e02771b11b922f980e2a6a7b8b7f0790f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZRSaMGysIjIOqZ0r8ACDvDLOG59MjP7WBAYt8sGPBzM7OIU/HvaARL3KEzRdHXOiDj84bT4M5SUVEGqpBOLPAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T23:43:00.582311Z","bundle_sha256":"587b3d66fc081eb22d199b68f940cefe192a65b8f5c40cd81e24284c41e5d886"}}