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Unitary Powered Conjugation

Abstract

Actual unitary powered conjugation 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 (diagonalSL pow val).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryPoweredConjugation.diagonalSL_pow_val

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

Source. Repository-derived.

Commentary.

The parameterized diagonalSL pow val statement describes the actual unitary geometry or prescribed ordered-product construction. Its Lean telescope retains every field, rank, involution, input and equality hypothesis shown.

Theorem 1.2 (diagonalSL pow inv val).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryPoweredConjugation.diagonalSL_pow_inv_val

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

Source. Repository-derived.

Commentary.

The parameterized diagonalSL pow inv val statement describes the actual unitary geometry or prescribed ordered-product construction. Its Lean telescope retains every field, rank, involution, input and equality hypothesis shown.

Theorem 1.3 (actual powered conjugation).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryPoweredConjugation.actual_powered_conjugation

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

Source. Repository-derived.

Commentary.

The parameterized actual powered conjugation statement describes the actual unitary geometry or prescribed ordered-product construction. Its Lean telescope retains every field, rank, involution, input and equality hypothesis shown.

Theorem 1.4 (actual powered transvection).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/UnitaryPoweredConjugation.actual_powered_transvection

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

Source. Repository-derived.

Commentary.

The parameterized actual powered transvection 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.

References