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Part IIUnitary Prescribed Lower Product

Abstract

Actual part iiunitary prescribed lower product 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 all rank unitary lower prescribed product).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryPrescribedLowerProduct.actual_uniform_all_rank_unitary_lower_prescribed_product

Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryPrescribedLowerProduct.actual_uniform_all_rank_unitary_lower_prescribed_product (✓ std3). ∎

Source. Repository-derived.

Commentary.

ONE uniform length/cutoff precedes every field/rank/genuine prescribed D/Phi tuple. Actual lower unitary targets have genuine lower unitary witnesses; ONE global SU correction precedes ALL targets, with exact ordered original divisor powers. No opposite transport 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.

References