Part IIUnitary Relative Field Product
Abstract
Actual part iiunitary relative field 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.
Theorem 1.1 (actual relative field two batch).
Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryRelativeFieldProduct.actual_relative_field_two_batch
Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryRelativeFieldProduct.actual_relative_field_two_batch (✓ std3). ∎
Source. Repository-derived.
Commentary.
Genuine relative-field PRODUCT arithmetic. Lambda belongs to F0; BOTH batches and all coefficients are fixed before EVERY full-F target. A trace-zero target also has witnesses ALL in the actual trace-zero line. This is consumed by the skew-Hermitian P reconstruction.
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.