{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2QSJPPR3VLIOHUDFX264I7E45Y","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":"f02f48b58b911d35b07aece192a7e8914f00c452bf506da176a894b0a55a8244","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-16T20:27:36Z","title_canon_sha256":"36e7998b20b1b7c2b44189ec7a3ac61f031260b88ddad980e4553e7ca274f4cd"},"schema_version":"1.0","source":{"id":"1412.5154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5154","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5154v1","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5154","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"pith_short_12","alias_value":"2QSJPPR3VLIO","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2QSJPPR3VLIOHUDF","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2QSJPPR3","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:7f66fca3fce5a0f8f5ede0b62acfc25d762ff261e69b57e19152b61b5ae9cd45","target":"graph","created_at":"2026-05-18T02:31:09Z","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":"This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized problem corresponds to a Kullback-Leibler Bregman di-vergence projection of a vector (representing some initial joint distribu-tion) on the polytope of constraints. We show that for many problems related to optimal transport, the set of linear constraints can be split in an intersection of a few simple constraints, for which the projections can be computed in clos","authors_text":"Gabriel Peyr\\'e (CEREMADE), Guillaume Carlier (CEREMADE), Jean-David Benamou (INRIA Paris-Rocquencourt), Luca Nenna (INRIA Paris-Rocquencourt), Marco Cuturi","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-16T20:27:36Z","title":"Iterative Bregman Projections for Regularized Transportation Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5154","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":"sha256:4a2e612eea3bd833b1fcf2673e0fcb9177e35a7f85d8c3b0f970cfe7ab9f1b50","target":"record","created_at":"2026-05-18T02:31:09Z","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":"f02f48b58b911d35b07aece192a7e8914f00c452bf506da176a894b0a55a8244","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-16T20:27:36Z","title_canon_sha256":"36e7998b20b1b7c2b44189ec7a3ac61f031260b88ddad980e4553e7ca274f4cd"},"schema_version":"1.0","source":{"id":"1412.5154","kind":"arxiv","version":1}},"canonical_sha256":"d42497be3baad0e3d065bebdc47c9cee19c3f9bdc2458531cc41dbc8d3717407","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d42497be3baad0e3d065bebdc47c9cee19c3f9bdc2458531cc41dbc8d3717407","first_computed_at":"2026-05-18T02:31:09.542088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:09.542088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"13tLlu9p3063MpwgPVS9VAGQds6XqILN1eBKKcx9fM3Oum6+sqTHKHwd5AQYTScphs4seXMjLO3XEYgc8vObBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:09.542758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a2e612eea3bd833b1fcf2673e0fcb9177e35a7f85d8c3b0f970cfe7ab9f1b50","sha256:7f66fca3fce5a0f8f5ede0b62acfc25d762ff261e69b57e19152b61b5ae9cd45"],"state_sha256":"1d41fee8084325944d2329dadcedefbc40610c20ace1e3a32f3ce0cc5e487007"}