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This leads to a practical Sinkhorn-type algorithm for the Schrödinger potentials and, as the noise level vanishes, a recovery of the deterministic sub-Riemannian optimal transport problem.","weakest_assumption":"The added noise is aligned with the control directions and the manifold satisfies bracket-generating hypotheses, which are invoked to guarantee smooth strictly positive transition densities for the degenerate diffusion."}},"verdict_id":"6a0330ca-0e57-4907-aef4-335e517b6b2b"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b0e7eb2abef8dbd755a4202a0d2a96b5607149dc133593e6cd4b1478f2d45b05","target":"record","created_at":"2026-05-20T00:01:43Z","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":"2a27a4ae0d5326f1ef20cdd2f5dda7581ddf9c780e9cb00b50d4fb0d85d6b713","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-12T02:30:08Z","title_canon_sha256":"3a19822fac5f15f28ab6acf653adce1107c3dd2a9f912fea9abc375430567f5e"},"schema_version":"1.0","source":{"id":"2605.11429","kind":"arxiv","version":2}},"canonical_sha256":"d6b26c738d6862295d1718a1d4f2216326f2d6f33bae5b0d5c73fb6be6d7bc18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6b26c738d6862295d1718a1d4f2216326f2d6f33bae5b0d5c73fb6be6d7bc18","first_computed_at":"2026-05-20T00:01:43.921977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:43.921977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H/dKCXrsXCrx1atLt2XLd4yD4y4zm//qpB6LxNecWANFKd52O24xIg4zpo2omenrYtbSpohAKpGCUjjNZjTWCw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:43.922440Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.11429","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0e7eb2abef8dbd755a4202a0d2a96b5607149dc133593e6cd4b1478f2d45b05","sha256:0b5dad727345eab48a181da30892dfac9488ad72670183c1a836415fb1411b4e"],"state_sha256":"714181e094e33e11fee8980b7871aedd7f72c8afa9728ae75585fadcb2aa9984"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"drrHnI80Z7mo1mCpX5MYFP5ArJSJX2gAcMBg50+PfDQfMx8Ju4Z5o2dMOHiyua/0Cr7kba3Hn9ilVdiBYaDeCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:38:19.983893Z","bundle_sha256":"957c5f698c5bf598e87598ba3878b68ebff2249cde3a335caf73d3c0d1107390"}}