{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:UAQ2IGCCO4IEX4J6ILTD7IX7GF","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":"3af10e5db3b23250c7e59819745304778863fa08685df4d4fdfaf359128e64d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-28T08:55:12Z","title_canon_sha256":"5765c0a0837547639a934ce2f943207db6bf22464d1f8661d0bcf2561a8c8d44"},"schema_version":"1.0","source":{"id":"2106.14485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.14485","created_at":"2026-07-05T02:52:51Z"},{"alias_kind":"arxiv_version","alias_value":"2106.14485v1","created_at":"2026-07-05T02:52:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.14485","created_at":"2026-07-05T02:52:51Z"},{"alias_kind":"pith_short_12","alias_value":"UAQ2IGCCO4IE","created_at":"2026-07-05T02:52:51Z"},{"alias_kind":"pith_short_16","alias_value":"UAQ2IGCCO4IEX4J6","created_at":"2026-07-05T02:52:51Z"},{"alias_kind":"pith_short_8","alias_value":"UAQ2IGCC","created_at":"2026-07-05T02:52:51Z"}],"graph_snapshots":[{"event_id":"sha256:db7869e3113a46bdbdb56cd661fc38876ba1d8eafa309f2383492e8f951a0c72","target":"graph","created_at":"2026-07-05T02:52:51Z","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/2106.14485/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport problem, where the cost function and the constraints on the marginals are associated with a graph structure. By exploiting these structures and building on recent advances in optimal transport theory, we develop an efficient method for such entropy-regularized optimal transport problems. In particular, the graph structure is utilized to efficiently compute ","authors_text":"Axel Ringh, Isabel Haasler, Johan Karlsson, Yongxin Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-28T08:55:12Z","title":"Scalable computation of dynamic flow problems via multi-marginal graph-structured optimal transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.14485","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":"sha256:89edf2db330960a6f8f5cd346219b248c7a99379c532fe6199076b45cf651fe5","target":"record","created_at":"2026-07-05T02:52:51Z","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":"3af10e5db3b23250c7e59819745304778863fa08685df4d4fdfaf359128e64d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-28T08:55:12Z","title_canon_sha256":"5765c0a0837547639a934ce2f943207db6bf22464d1f8661d0bcf2561a8c8d44"},"schema_version":"1.0","source":{"id":"2106.14485","kind":"arxiv","version":1}},"canonical_sha256":"a021a4184277104bf13e42e63fa2ff316a61be75d725c217b332f6cf319aecc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a021a4184277104bf13e42e63fa2ff316a61be75d725c217b332f6cf319aecc0","first_computed_at":"2026-07-05T02:52:51.306737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:52:51.306737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZNvrWoYPAEcwe5552PEi+1jleL9FiR0IJPo3lIyp7YTTMH0IamDv7oY28fJVFQM6TYutD87vYlgqMijEuIWAw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:52:51.307074Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.14485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89edf2db330960a6f8f5cd346219b248c7a99379c532fe6199076b45cf651fe5","sha256:db7869e3113a46bdbdb56cd661fc38876ba1d8eafa309f2383492e8f951a0c72"],"state_sha256":"7c3a30f45a8ed9777ac78d4862c4d611e167ef174fbf7c38488da47871ff61ec"}