Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

Part IIUnitary Intrinsic Block Product

Abstract

Actual part iiunitary intrinsic block 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.

Definition 1.1 (positiveSet).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryIntrinsicBlockProduct.positiveSet

Formalization. D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryIntrinsicBlockProduct.positiveSet (✓ std3).

Source. Repository-derived.

Commentary.

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

Definition 1.2 (negativeSet).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryIntrinsicBlockProduct.negativeSet

Formalization. D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryIntrinsicBlockProduct.negativeSet (✓ std3).

Source. Repository-derived.

Commentary.

The parameterized negativeSet 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 uniform intrinsic five block product).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryIntrinsicBlockProduct.actual_uniform_intrinsic_five_block_product

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

Source. Repository-derived.

Commentary.

One uniform length and cutoff cover every ordered U L U L U target, with original divisor powers and one correction chosen before all targets. Whole-SU width is consumed separately, through its proved factorization.

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