{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:POD3WS6CC7FFMQAWTMZ62BSN6J","short_pith_number":"pith:POD3WS6C","canonical_record":{"source":{"id":"1503.02533","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-03-09T15:49:21Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"174b584396e9919b3362962d5eab3b6b3522e52058c96139f42dd6f6112269bb","abstract_canon_sha256":"a0b1a32154073f7ff8488bac48a76fb2b88c7d58faf854ac32af47965e07305b"},"schema_version":"1.0"},"canonical_sha256":"7b87bb4bc217ca5640169b33ed064df247e1a02f612abd4289a998b62808ad1e","source":{"kind":"arxiv","id":"1503.02533","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02533","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02533v2","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02533","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"pith_short_12","alias_value":"POD3WS6CC7FF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"POD3WS6CC7FFMQAW","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"POD3WS6C","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:POD3WS6CC7FFMQAWTMZ62BSN6J","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02533","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-03-09T15:49:21Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"174b584396e9919b3362962d5eab3b6b3522e52058c96139f42dd6f6112269bb","abstract_canon_sha256":"a0b1a32154073f7ff8488bac48a76fb2b88c7d58faf854ac32af47965e07305b"},"schema_version":"1.0"},"canonical_sha256":"7b87bb4bc217ca5640169b33ed064df247e1a02f612abd4289a998b62808ad1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:50.363632Z","signature_b64":"jPFHaNWqwT/6uBxzsetI2/rRxS1+K7EI3dBEO0sJBkmq44keFg9puZggomA7Z8oaGy0IST975HU3SBJl2e3aAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b87bb4bc217ca5640169b33ed064df247e1a02f612abd4289a998b62808ad1e","last_reissued_at":"2026-05-18T01:34:50.363095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:50.363095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02533","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BtzLYY76cilVKzT1o1qSXL8rK5qsxf9JkcdTVukgJXn/LpfdeVvsoPwQgJapu5a1iKkSs7v1m1cozpjntq+dBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:04:37.896117Z"},"content_sha256":"d3f4c2f235f4d9f78dafb49e643b4f19bd8a16fc36b09a1fa7ba13033a08d396","schema_version":"1.0","event_id":"sha256:d3f4c2f235f4d9f78dafb49e643b4f19bd8a16fc36b09a1fa7ba13033a08d396"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:POD3WS6CC7FFMQAWTMZ62BSN6J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Smoothed Dual Approach for Variational Wasserstein Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"stat.ML","authors_text":"Gabriel Peyr\\'e, Marco Cuturi","submitted_at":"2015-03-09T15:49:21Z","abstract_excerpt":"Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities (Wasserstein distances) that are themselves hard to compute. We show that the dual formulation of Wasserstein variational problems introduced recently by Carlier et al. (2014) can be regularized using an entropic smoothing, which leads to smooth, differentiable, convex optimization problems that are simpler to implement and numerically"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02533","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z5NHjJ8fxsTnqsDPJLmAs3YrDcQCgpQ7ACtsJ8DPfokboadTgZa6zV3bqUEr94yvH/wKbGYxiM+Na23RZ8OzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:04:37.896796Z"},"content_sha256":"7779c3a8da46c057ee3abcdb2c017d2fd9702b5b441ef048a007c282b8660268","schema_version":"1.0","event_id":"sha256:7779c3a8da46c057ee3abcdb2c017d2fd9702b5b441ef048a007c282b8660268"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/POD3WS6CC7FFMQAWTMZ62BSN6J/bundle.json","state_url":"https://pith.science/pith/POD3WS6CC7FFMQAWTMZ62BSN6J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/POD3WS6CC7FFMQAWTMZ62BSN6J/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":"2026-05-25T16:04:37Z","links":{"resolver":"https://pith.science/pith/POD3WS6CC7FFMQAWTMZ62BSN6J","bundle":"https://pith.science/pith/POD3WS6CC7FFMQAWTMZ62BSN6J/bundle.json","state":"https://pith.science/pith/POD3WS6CC7FFMQAWTMZ62BSN6J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/POD3WS6CC7FFMQAWTMZ62BSN6J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:POD3WS6CC7FFMQAWTMZ62BSN6J","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":"a0b1a32154073f7ff8488bac48a76fb2b88c7d58faf854ac32af47965e07305b","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-03-09T15:49:21Z","title_canon_sha256":"174b584396e9919b3362962d5eab3b6b3522e52058c96139f42dd6f6112269bb"},"schema_version":"1.0","source":{"id":"1503.02533","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02533","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02533v2","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02533","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"pith_short_12","alias_value":"POD3WS6CC7FF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"POD3WS6CC7FFMQAW","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"POD3WS6C","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:7779c3a8da46c057ee3abcdb2c017d2fd9702b5b441ef048a007c282b8660268","target":"graph","created_at":"2026-05-18T01:34:50Z","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":"Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities (Wasserstein distances) that are themselves hard to compute. We show that the dual formulation of Wasserstein variational problems introduced recently by Carlier et al. (2014) can be regularized using an entropic smoothing, which leads to smooth, differentiable, convex optimization problems that are simpler to implement and numerically","authors_text":"Gabriel Peyr\\'e, Marco Cuturi","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-03-09T15:49:21Z","title":"A Smoothed Dual Approach for Variational Wasserstein Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02533","kind":"arxiv","version":2},"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:d3f4c2f235f4d9f78dafb49e643b4f19bd8a16fc36b09a1fa7ba13033a08d396","target":"record","created_at":"2026-05-18T01:34:50Z","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":"a0b1a32154073f7ff8488bac48a76fb2b88c7d58faf854ac32af47965e07305b","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-03-09T15:49:21Z","title_canon_sha256":"174b584396e9919b3362962d5eab3b6b3522e52058c96139f42dd6f6112269bb"},"schema_version":"1.0","source":{"id":"1503.02533","kind":"arxiv","version":2}},"canonical_sha256":"7b87bb4bc217ca5640169b33ed064df247e1a02f612abd4289a998b62808ad1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b87bb4bc217ca5640169b33ed064df247e1a02f612abd4289a998b62808ad1e","first_computed_at":"2026-05-18T01:34:50.363095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:50.363095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jPFHaNWqwT/6uBxzsetI2/rRxS1+K7EI3dBEO0sJBkmq44keFg9puZggomA7Z8oaGy0IST975HU3SBJl2e3aAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:50.363632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02533","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3f4c2f235f4d9f78dafb49e643b4f19bd8a16fc36b09a1fa7ba13033a08d396","sha256:7779c3a8da46c057ee3abcdb2c017d2fd9702b5b441ef048a007c282b8660268"],"state_sha256":"3a0a71aaf3fbedc825217bffa6927535fc49b53cedda1eea33574edf48edfa9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Vfib0/QVTQcunLpBkGWEn2E/jVvLePN0lkHlKLA+3x+y7P6nzNd7pWsJDi9hJ8gpfac4tpD/1VmBA5y8dtqBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:04:37.900487Z","bundle_sha256":"e217074374a0ef0516361dea607238dc3b4c6671ac48ebd75cd4ba767805051c"}}