{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AU2BQFDIRA4HCJA7PMMPJIWXOG","short_pith_number":"pith:AU2BQFDI","canonical_record":{"source":{"id":"1610.06447","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-20T14:49:36Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"e1fa6a2de57a66e05d45bac0cd1db022c4fea9b313eee6d29ee54727ad3195d5","abstract_canon_sha256":"c8812f3daa0cff0ceff24ce3a1ac14637ff3571a5efd764a23424bbb5ad35efe"},"schema_version":"1.0"},"canonical_sha256":"0534181468883871241f7b18f4a2d7719d81b011169e67a29f48cf29ab5316c4","source":{"kind":"arxiv","id":"1610.06447","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06447","created_at":"2026-05-18T00:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06447v4","created_at":"2026-05-18T00:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06447","created_at":"2026-05-18T00:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"AU2BQFDIRA4H","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AU2BQFDIRA4HCJA7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AU2BQFDI","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AU2BQFDIRA4HCJA7PMMPJIWXOG","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06447","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-20T14:49:36Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"e1fa6a2de57a66e05d45bac0cd1db022c4fea9b313eee6d29ee54727ad3195d5","abstract_canon_sha256":"c8812f3daa0cff0ceff24ce3a1ac14637ff3571a5efd764a23424bbb5ad35efe"},"schema_version":"1.0"},"canonical_sha256":"0534181468883871241f7b18f4a2d7719d81b011169e67a29f48cf29ab5316c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:48.030770Z","signature_b64":"HlfaKndxVAwo9ErPaj3reL8ziTlqXOkPTyQaDFATvacIWwq6j81PzLBjDwa5RxHpswtOpu1IsuS6V+VCBO0fDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0534181468883871241f7b18f4a2d7719d81b011169e67a29f48cf29ab5316c4","last_reissued_at":"2026-05-18T00:10:48.030182Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:48.030182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06447","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZQgR1KLk10WccJ82zA2iwJDNTiET9viM94o/66GS6dWijOeKlA9mGWxyz659WS+nDYL30xgxJOyZ+iRBJ2iDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:10:54.006279Z"},"content_sha256":"41ab829994b2bb2cb5d5e16cef4e4a68f3383075c53ac6ed42e0b1bdffa35f6f","schema_version":"1.0","event_id":"sha256:41ab829994b2bb2cb5d5e16cef4e4a68f3383075c53ac6ed42e0b1bdffa35f6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AU2BQFDIRA4HCJA7PMMPJIWXOG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularized Optimal Transport and the Rot Mover's Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Arnaud Dessein, Jean-Luc Rouas, Nicolas Papadakis","submitted_at":"2016-10-20T14:49:36Z","abstract_excerpt":"This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed regularization based on the Boltzmann-Shannon entropy related to the Kullback-Leibler divergence, and solved with the Sinkhorn-Knopp algorithm. We call the regularized optimal transport distance the rot mover's distance in reference to the classical earth mover's distance. We dev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06447","kind":"arxiv","version":4},"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":"2026-05-18T00:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Twb9O7gSx5w3uNJmp3j2+f16+tMjlZj+3s9S+DZZwV+3Drv/yeFErGiSGThSpLVN6fWHMlQ/l72Z0RvYq0KDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:10:54.006638Z"},"content_sha256":"55cd07dc428dd50d75b713cf02b71fc74a06b00cf2deb5dc1b4aed4dee4ab1c9","schema_version":"1.0","event_id":"sha256:55cd07dc428dd50d75b713cf02b71fc74a06b00cf2deb5dc1b4aed4dee4ab1c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AU2BQFDIRA4HCJA7PMMPJIWXOG/bundle.json","state_url":"https://pith.science/pith/AU2BQFDIRA4HCJA7PMMPJIWXOG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AU2BQFDIRA4HCJA7PMMPJIWXOG/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":"2026-06-01T15:10:54Z","links":{"resolver":"https://pith.science/pith/AU2BQFDIRA4HCJA7PMMPJIWXOG","bundle":"https://pith.science/pith/AU2BQFDIRA4HCJA7PMMPJIWXOG/bundle.json","state":"https://pith.science/pith/AU2BQFDIRA4HCJA7PMMPJIWXOG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AU2BQFDIRA4HCJA7PMMPJIWXOG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AU2BQFDIRA4HCJA7PMMPJIWXOG","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":"c8812f3daa0cff0ceff24ce3a1ac14637ff3571a5efd764a23424bbb5ad35efe","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-20T14:49:36Z","title_canon_sha256":"e1fa6a2de57a66e05d45bac0cd1db022c4fea9b313eee6d29ee54727ad3195d5"},"schema_version":"1.0","source":{"id":"1610.06447","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06447","created_at":"2026-05-18T00:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06447v4","created_at":"2026-05-18T00:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06447","created_at":"2026-05-18T00:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"AU2BQFDIRA4H","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AU2BQFDIRA4HCJA7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AU2BQFDI","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:55cd07dc428dd50d75b713cf02b71fc74a06b00cf2deb5dc1b4aed4dee4ab1c9","target":"graph","created_at":"2026-05-18T00:10:48Z","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 paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed regularization based on the Boltzmann-Shannon entropy related to the Kullback-Leibler divergence, and solved with the Sinkhorn-Knopp algorithm. We call the regularized optimal transport distance the rot mover's distance in reference to the classical earth mover's distance. We dev","authors_text":"Arnaud Dessein, Jean-Luc Rouas, Nicolas Papadakis","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-20T14:49:36Z","title":"Regularized Optimal Transport and the Rot Mover's Distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06447","kind":"arxiv","version":4},"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":"sha256:41ab829994b2bb2cb5d5e16cef4e4a68f3383075c53ac6ed42e0b1bdffa35f6f","target":"record","created_at":"2026-05-18T00:10:48Z","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":"c8812f3daa0cff0ceff24ce3a1ac14637ff3571a5efd764a23424bbb5ad35efe","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-20T14:49:36Z","title_canon_sha256":"e1fa6a2de57a66e05d45bac0cd1db022c4fea9b313eee6d29ee54727ad3195d5"},"schema_version":"1.0","source":{"id":"1610.06447","kind":"arxiv","version":4}},"canonical_sha256":"0534181468883871241f7b18f4a2d7719d81b011169e67a29f48cf29ab5316c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0534181468883871241f7b18f4a2d7719d81b011169e67a29f48cf29ab5316c4","first_computed_at":"2026-05-18T00:10:48.030182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:48.030182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HlfaKndxVAwo9ErPaj3reL8ziTlqXOkPTyQaDFATvacIWwq6j81PzLBjDwa5RxHpswtOpu1IsuS6V+VCBO0fDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:48.030770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06447","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41ab829994b2bb2cb5d5e16cef4e4a68f3383075c53ac6ed42e0b1bdffa35f6f","sha256:55cd07dc428dd50d75b713cf02b71fc74a06b00cf2deb5dc1b4aed4dee4ab1c9"],"state_sha256":"81f71aff80d67285fc7888e4365793b7a02d7c0cb3b3f1c06b71c1d9ccf01723"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EKEEWDNMuoJAB8AaO1n4jj08fbgw5QAtGI3lnKSrHtBpZ2H2zeAh+4f+KtnFftG/ScrD+f69oS1euWJ6YfurAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:10:54.008492Z","bundle_sha256":"34d65d43818d09b718fb08a67f98ed17290da0db177223f6258ed7f2d19038f1"}}