Part IIUnitary Prescribed UProduct
Abstract
Actual part iiunitary prescribed uproduct supplies the parameterized matrix, finite-field or ordered-product identities consumed by the whole-SU K5 width and intrinsic prescribed-product proof paths. All original hypotheses and actual carriers are retained; this source provides no oracle for bare automorphism recognition.
Theorem 1.1 (actual uniform all rank unitary U prescribed product).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryPrescribedUProduct.actual_uniform_all_rank_unitary_U_prescribed_product
Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryPrescribedUProduct.actual_uniform_all_rank_unitary_U_prescribed_product (✓ std3). ∎
Source. Repository-derived.
Commentary.
Arbitrary-rank, arbitrary genuine prescribed diagonal-similitude/field positive-U PRODUCT. The same fixed length and field cutoff cover BOTH parities; ONE global SU correction is chosen BEFORE all targets.
The results concern special-unitary matrix groups over finite fields. Their geometric setting is Nikolov and Segal, On finitely generated profinite groups, II: Products in quasisimple groups, Annals of Mathematics 165 (2007), 239-273, DOI 10.4007/annals.2007.165.239. Prescribed-product statements retain their field-size, rank and automorphism hypotheses.