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Part IIUnitary Even PProduct

Abstract

Actual part iiunitary even pproduct 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 skew two batch).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryEvenPProduct.actual_skew_two_batch

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

Source. Repository-derived.

Commentary.

Simultaneous reconstruction of ALL genuine P coordinates. Upper parameters are freely solved, their paired entries are forced by the true involution, and diagonal witnesses lie in the trace-zero line.

Theorem 1.2 (actual even P two batch inner product).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryEvenPProduct.actual_even_P_two_batch_inner_product

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

Source. Repository-derived.

Commentary.

Actual even P VALUE PRODUCT inside the ambient SU(2d+2). Both genuine INNER UNITARY correction batches precede ALL targets; all original positive divisor powers and ordered VALUES are retained.

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