Part IIUnitary Ambient Even UProduct
Abstract
Actual part iiunitary ambient 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 product).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryAmbientEvenUProduct.actual_uniform_ambient_even_U_product
Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryAmbientEvenUProduct.actual_uniform_ambient_even_U_product (✓ std3). ∎
Source. Repository-derived.
Commentary.
ALL actual positive unitary targets in every even ambient rank 2(d+2)+2. Chosen length/cutoff precede every field/rank/tuple, ONE actual unitary inner correction precedes ALL targets, and actual positive unitary witnesses give the ordered exact-length VALUES. No central/radical/decomposition/coverage premise is retained.
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.