{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PIBB462QP3T7BHHXISFAI7V32Q","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":"c748f6921d41440639b6deab4dbbe93a14da31e00c1951905cd5091f6627e608","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-25T18:35:37Z","title_canon_sha256":"ed7e7551382c080f5ed4b0a97b874a87c15ac19cf6c5e2918b644c53d9482fbd"},"schema_version":"1.0","source":{"id":"2411.16651","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16651","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16651v1","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16651","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"pith_short_12","alias_value":"PIBB462QP3T7","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"pith_short_16","alias_value":"PIBB462QP3T7BHHX","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"pith_short_8","alias_value":"PIBB462Q","created_at":"2026-07-05T09:40:12Z"}],"graph_snapshots":[{"event_id":"sha256:fd546830a45b637aa9590f59b2dbdf94fa98656d168de248eb40b491a6584305","target":"graph","created_at":"2026-07-05T09:40:12Z","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/2411.16651/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the simultaneous optimal transportation of measures, where the target marginal is not necessarily fixed. For this problem, we prove the existence of a solution for completely regular spaces and investigate the structure of the discrete problem. We establish a connection between the Monge problem and the Kantorovich problem by showing that their functionals are equal and that the solutions coincide in Euclidean space.","authors_text":"Kirill Sokolov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-25T18:35:37Z","title":"On a problem of optimal mixing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16651","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:e906c39f211d53b44e845bf29a9ed2792c4c43f1c23f064df729433da65bfb38","target":"record","created_at":"2026-07-05T09:40:12Z","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":"c748f6921d41440639b6deab4dbbe93a14da31e00c1951905cd5091f6627e608","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-25T18:35:37Z","title_canon_sha256":"ed7e7551382c080f5ed4b0a97b874a87c15ac19cf6c5e2918b644c53d9482fbd"},"schema_version":"1.0","source":{"id":"2411.16651","kind":"arxiv","version":1}},"canonical_sha256":"7a021e7b507ee7f09cf7448a047ebbd41f27f6615065bab8e716caf974fb04dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a021e7b507ee7f09cf7448a047ebbd41f27f6615065bab8e716caf974fb04dd","first_computed_at":"2026-07-05T09:40:12.406234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:12.406234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qkGhXpGpk7bTQzrhA7M0ocYbMePe36AC4T6SwBVtoNQVnTM9UIrTzGKrpOwpC4C+3gRBke8Gl06mCnYQOxpaAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:12.406680Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16651","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e906c39f211d53b44e845bf29a9ed2792c4c43f1c23f064df729433da65bfb38","sha256:fd546830a45b637aa9590f59b2dbdf94fa98656d168de248eb40b491a6584305"],"state_sha256":"38fb8f98dede9497a0867a9b2e47ded89c8a06b5fd511767301643b3a22c9c9e"}