Unitary Width Levi Extraction
Abstract
Actual unitary width levi extraction 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 (endpoint middle det).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryWidthLeviExtraction.endpoint_middle_det
Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryWidthLeviExtraction.endpoint_middle_det (✓ std3). ∎
Source. Repository-derived.
Commentary.
Actual determinant of the constructed principal block, including empty blocks.
Theorem 1.2 (endpoint levi radical).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryWidthLeviExtraction.endpoint_levi_radical
Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryWidthLeviExtraction.endpoint_levi_radical (✓ std3). ∎
Source. Repository-derived.
Commentary.
Complete actual endpoint-stabilizer decomposition. No Levi, determinant, unitarity, or decomposition input is supplied for the constructed factors.
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.