{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QXSEFHXYNAOY3MRZT7QHZYBW7S","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":"7c9e0e7b31a704945cefc4ab3519005d72cb6da92a9b198af9ccaa478a228991","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-20T18:44:38Z","title_canon_sha256":"1ed0a235b3ecc64fffc8a2e9373d4baf4f449d7c1518090332757803bb893e36"},"schema_version":"1.0","source":{"id":"1608.05862","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05862","created_at":"2026-05-18T00:23:40Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05862v2","created_at":"2026-05-18T00:23:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05862","created_at":"2026-05-18T00:23:40Z"},{"alias_kind":"pith_short_12","alias_value":"QXSEFHXYNAOY","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QXSEFHXYNAOY3MRZ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QXSEFHXY","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:7859eba2d028b61eb302e900cd3476a7a2719a87bddc7c2b5fcc7f5b2683121e","target":"graph","created_at":"2026-05-18T00:23:40Z","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":"In the first part of this paper we generalize the result of Georgiou-Pavon that a positive square matrix can be scaled uniquely to a column stochastic matrix which maps a given positive probability vector to another given positive probability vector. In the second part of this paper we prove that a positive quantum channel can be scaled to another positive quantum channel which maps a given positive definite density matrix to another given positive definite density matrix using Brower's fixed point theorem. This result proves the Georgiou-Pavon conjecture for two positive definite density matr","authors_text":"Shmuel Friedland","cross_cats":["math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-20T18:44:38Z","title":"On Schrodinger's bridge problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05862","kind":"arxiv","version":2},"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":"sha256:0530ca21e90f36b1acc21295f4b118a6510c30cc17ee6c77c56aad4aad5fbae8","target":"record","created_at":"2026-05-18T00:23:40Z","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":"7c9e0e7b31a704945cefc4ab3519005d72cb6da92a9b198af9ccaa478a228991","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-20T18:44:38Z","title_canon_sha256":"1ed0a235b3ecc64fffc8a2e9373d4baf4f449d7c1518090332757803bb893e36"},"schema_version":"1.0","source":{"id":"1608.05862","kind":"arxiv","version":2}},"canonical_sha256":"85e4429ef8681d8db2399fe07ce036fc825d3c5b36bad3df46cc06425d50b74c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85e4429ef8681d8db2399fe07ce036fc825d3c5b36bad3df46cc06425d50b74c","first_computed_at":"2026-05-18T00:23:40.665420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:40.665420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RS0qy1Mc9AnjdZ0WsoRfC/evjwfH/cCvLvRnkvZOBfE42vn3k3LxtjjjRCMFrnI7yZByeTrbdxCDmKMEuJC2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:40.666132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05862","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0530ca21e90f36b1acc21295f4b118a6510c30cc17ee6c77c56aad4aad5fbae8","sha256:7859eba2d028b61eb302e900cd3476a7a2719a87bddc7c2b5fcc7f5b2683121e"],"state_sha256":"867e88ce16700640ed9dda09a5e4836b041268cfd15190a2c5eb5595d5d8ff9e"}