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Part IIUnitary Even PUniform

Abstract

Actual part iiunitary even puniform 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 even P prescribed two batch).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryEvenPUniform.actual_even_P_prescribed_two_batch

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

Source. Repository-derived.

Commentary.

Arbitrary genuine paired diagonal/field P tuples. Their ONE ambient unitary INNER correction is constructed BEFORE every P target.

Theorem 1.2 (actual uniform even P prescribed product).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryEvenPUniform.actual_uniform_even_P_prescribed_product

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

Source. Repository-derived.

Commentary.

Chosen-length, all-rank EVEN P Proposition6.10 branch. N(q) and the FIELD cutoff are fixed before every field/rank/prescribed tuple. ONE ambient inner correction is fixed before ALL actual P targets; the witnesses are positive UNITARY ambient matrices, and values are ordered.

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