Part IIUnitary Ambient General Even UProduct
Abstract
Actual part iiunitary ambient general even 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 ambient even U general prescribed product).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryAmbientGeneralEvenUProduct.actual_uniform_ambient_even_U_general_prescribed_product
Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryAmbientGeneralEvenUProduct.actual_uniform_ambient_even_U_general_prescribed_product (✓ std3). ∎
Source. Repository-derived.
Commentary.
Entire actual positive U in all even ranks 2(d+2)+2, arbitrary genuine prescribed D/Phi tuples. Both decompositions and all three suppliers are proved inputs; no coverage, lift or action/power identity is assumed.
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.