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The solution satisfies the natural bounds Q∈L^∞_t H^1_x ∩ L^2_t H^2_x and u∈L^∞_t L^2_x ∩ L^2_t H^1_x, the distributional form of the equations, and the expanded Leray--Hopf type energy inequality.","weakest_assumption":"The stable bulk assumption c>0 on the Landau-de Gennes potential; the argument relies on this for the energy estimates and is explicitly restricted to it via the uniaxial reduction shown in the last section."}},"verdict_id":"5b4f077b-c7aa-4c93-9185-7070f6c2abf1"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:604e6b845420ec767c1ffa87c175952b64e0ae565f39fac4d0be809503cbbc30","target":"record","created_at":"2026-05-20T00:03:35Z","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":"db508d4d2674c4c425328d0cf9a72481332cf60ae511184bb2e047fb8394de06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-16T13:44:33Z","title_canon_sha256":"35ce6f70b1f32d83d5991b43e4bc22c7098aeee77c75932d21dd9f9549b57f4b"},"schema_version":"1.0","source":{"id":"2605.16997","kind":"arxiv","version":1}},"canonical_sha256":"daeb4a348653cafba63a5b0cbaa462714d73a3d2029685c65ee4c66078e379aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"daeb4a348653cafba63a5b0cbaa462714d73a3d2029685c65ee4c66078e379aa","first_computed_at":"2026-05-20T00:03:35.133412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:35.133412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cyhaaiw0BcYU8TE0/OT7V37svrUEgxjniR6CqEOtp9hLRKSjKHljFx6Vmu6U9GC+WAWUzPe5t9WbvbbhsWNuAA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:35.134162Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16997","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:604e6b845420ec767c1ffa87c175952b64e0ae565f39fac4d0be809503cbbc30","sha256:3fd51d3cde14f4cd4c7de0e162a3bf39c1590db15f490e66b897ed9ae953972e"],"state_sha256":"d84d28f9eeb5dc87067a08ea4bc8bd0fab61555669934361b79161b48d9eeb36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"grWfv/DP8b9NkFlPObVl620UrfZPT9Lx8TlFeuevYNJqhGm4CX8GtOrogRhhN0PjDz+QF31Ldt1aRqM3IT1+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:39:36.592879Z","bundle_sha256":"8ee636cf14c579538ab78b60da2348f471fb4186566b3c93f6d179eb86095ae3"}}