{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KDM6B34S2ZHWXX334RQTBTNNNG","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":"e207d0010c39b529517c2474835e90fe19e62a593c541ec34d0be4e76fe798c3","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-01-24T20:44:40Z","title_canon_sha256":"e659de3594392faa6779d2a1b66f0fb770225f6f674b70d7c0cef590c775ccfc"},"schema_version":"1.0","source":{"id":"2301.10301","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.10301","created_at":"2026-07-05T05:35:49Z"},{"alias_kind":"arxiv_version","alias_value":"2301.10301v1","created_at":"2026-07-05T05:35:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.10301","created_at":"2026-07-05T05:35:49Z"},{"alias_kind":"pith_short_12","alias_value":"KDM6B34S2ZHW","created_at":"2026-07-05T05:35:49Z"},{"alias_kind":"pith_short_16","alias_value":"KDM6B34S2ZHWXX33","created_at":"2026-07-05T05:35:49Z"},{"alias_kind":"pith_short_8","alias_value":"KDM6B34S","created_at":"2026-07-05T05:35:49Z"}],"graph_snapshots":[{"event_id":"sha256:d9684655027bf0ec793d2e26be38c4a3d1c560d7d1ab8ec8c887447b8037c793","target":"graph","created_at":"2026-07-05T05:35:49Z","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/2301.10301/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a class of regularized proximal operators in Wasserstein-2 space. We derive their solutions by kernel integration formulas. We obtain the Wasserstein proximal operator using a pair of forward-backward partial differential equations consisting of a continuity equation and a Hamilton-Jacobi equation with a terminal time potential function and an initial time density function. We regularize the PDE pair by adding forward and backward Laplacian operators. We apply Hopf-Cole type transformations to rewrite these regularized PDE pairs into forward-backward heat equations. We then use the fu","authors_text":"Siting Liu, Stanley Osher, Wuchen Li","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-01-24T20:44:40Z","title":"A kernel formula for regularized Wasserstein proximal operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.10301","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:f7c47d37fae4112417a4e9194492f68f97b8a1752c3afe68f0a55fae03b276d1","target":"record","created_at":"2026-07-05T05:35:49Z","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":"e207d0010c39b529517c2474835e90fe19e62a593c541ec34d0be4e76fe798c3","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-01-24T20:44:40Z","title_canon_sha256":"e659de3594392faa6779d2a1b66f0fb770225f6f674b70d7c0cef590c775ccfc"},"schema_version":"1.0","source":{"id":"2301.10301","kind":"arxiv","version":1}},"canonical_sha256":"50d9e0ef92d64f6bdf7be46130cdad69bd69ad5b2dc08c658f373ba7603a1bce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50d9e0ef92d64f6bdf7be46130cdad69bd69ad5b2dc08c658f373ba7603a1bce","first_computed_at":"2026-07-05T05:35:49.601487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:35:49.601487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RAn+oAatv4mv83ix7DIMQgck8tprWM11iA5Yj4o3V3d8zt7RCjvM1enKx9awYRZ+aTCStpCptkaEQVrN0KXBBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:35:49.601953Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.10301","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7c47d37fae4112417a4e9194492f68f97b8a1752c3afe68f0a55fae03b276d1","sha256:d9684655027bf0ec793d2e26be38c4a3d1c560d7d1ab8ec8c887447b8037c793"],"state_sha256":"16a8875c4a2179f59bd85728c7588f65db352de56957baa841fbe980bfa2d6b7"}