Part IIUnitary Central Inner Torus
Abstract
Actual part iiunitary central inner torus 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 unitary central diagonal inner).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryCentralInnerTorus.actual_unitary_central_diagonal_inner
Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryCentralInnerTorus.actual_unitary_central_diagonal_inner (✓ std3). ∎
Source. Repository-derived.
Commentary.
Full actual central unitary diagonal-similitude action, realized by ONE determinant-one ambient UNITARY inner correction before ALL g. The multiplier is a genuine fixed-field unit; the normalization and determinant absorber are constructed, not supplied as a normal form.
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.