Unitary Rank Two Fixed Field Equiv
Abstract
Actual unitary rank two fixed field equiv 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.
Definition 1.1 (coordinateEquiv).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryRankTwoFixedFieldEquiv.coordinateEquiv
Formalization. D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryRankTwoFixedFieldEquiv.coordinateEquiv (✓ std3).
Source. Repository-derived.
Commentary.
An explicit actual group equivalence for any nonzero anti-fixed scaling element.
Theorem 1.2 (coordinateEquiv backward).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryRankTwoFixedFieldEquiv.coordinateEquiv_backward
Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryRankTwoFixedFieldEquiv.coordinateEquiv_backward (✓ std3). ∎
Source. Repository-derived.
Commentary.
The parameterized coordinateEquiv backward statement describes the actual unitary geometry or prescribed ordered-product construction. Its Lean telescope retains every field, rank, involution, input and equality hypothesis shown.
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.