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The deterministic limit is obtained pathwise, without having to take averages with respect to different realizations of the random flow.","weakest_assumption":"The suitable scaling assumption on the turbulent model (dominant space-scale ℓ∼N^{-1}, time-scale τ, white in time) together with the choice of weighted spaces that handle the FENE force singularity near the boundary and the no-flux boundary condition; if these do not hold the convergence to the claimed deterministic limit with the second-order operator may fail."}},"verdict_id":"2a18bb73-367d-4f63-8530-29d255951486"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0886a1a71f3906ceedcb97134b92e52e7747cac018e78299681fcf3ef84dfc11","target":"record","created_at":"2026-05-20T00:01:15Z","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":"141c21ee6762559075c61ccdf6f4bc588e7d063e2fb8273a8473e2aef4d0772f","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-15T08:52:04Z","title_canon_sha256":"1c8cf1d3b6d3aebfb90462b6df482e7146f3c9e6ae2dfeedbfccd63f6de6e951"},"schema_version":"1.0","source":{"id":"2605.15742","kind":"arxiv","version":1}},"canonical_sha256":"2b400794ef1b8a5c68903fff193aca842a049bbca495ce10f3ee3083847ae959","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b400794ef1b8a5c68903fff193aca842a049bbca495ce10f3ee3083847ae959","first_computed_at":"2026-05-20T00:01:15.824436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:15.824436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OosGlM9cpEd5Nekmt/hhh09INM3JuwQ6h0jQy3YtjlC0q6EkEBfobJE1Fmb96k+mh02qV5WIjgONY9pqHV4PBw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:15.825305Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15742","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0886a1a71f3906ceedcb97134b92e52e7747cac018e78299681fcf3ef84dfc11","sha256:6fe2fe909c553c7fe855173518073e705f5eee2ac239ddb8c735b79b8e6030a1"],"state_sha256":"8f59da3a63a2a01c4783a6b4a3af6c8cd725f4a699341bf52a14dd5dbd126447"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aXmZfwZvbB1pYh6cVuVXDN0krdfWbjdl0QfntSpyQd0E0+Wl+s5q2GN05OO16EOThCCK+taMGZHzgE1adk5qCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:45:14.170470Z","bundle_sha256":"9b3fb8fcfde3e7a9e1f48d87d07045432e0e10c2037ad9aa7f6922cd9d9273dc"}}