Part IIUnitary Radical Supply
Abstract
Actual part iiunitary radical supply 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 unitary radical fixed torus).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryRadicalSupply.actual_uniform_unitary_radical_fixed_torus
Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryRadicalSupply.actual_uniform_unitary_radical_fixed_torus (✓ std3). ∎
Source. Repository-derived.
Commentary.
A true UNIFORM radical fixed-inner-action result, all ranks k+4 and every original positive divisor power s|q. The Q cutoff 2q+2 precedes all groups/ranks, the same genuine determinant-one unitary h precedes ALL s and ALL targets, and the witness lies in V*, including its corner. No scalar PRODUCT or radical coverage premise is retained. This does not yet handle arbitrary prescribed diagonal/field/graph automorphisms.
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.