Part IIUnitary Radical Boundary Diagonal Normalization
Abstract
Actual part iiunitary radical boundary diagonal normalization 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 radical boundary diagonal inner).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryRadicalBoundaryDiagonalNormalization.actual_unitary_radical_boundary_diagonal_inner
Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryRadicalBoundaryDiagonalNormalization.actual_unitary_radical_boundary_diagonal_inner (✓ std3). ∎
Source. Repository-derived.
Commentary.
Actual boundary diagonal normalization. Rank k+6 provides a third reflected pair to absorb the determinant independently of the selected boundary coefficient. The exact adjusted action holds on ALL matrices.
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.