1719 — Matrix-Valued Mixture Faces Produce the Coefficient Commutator
Scope
This is a hypothetical algebraic falsifier of Entry 1718, not a claim that the frozen cosmological source contains matrix-valued mixture weights.
Let the two incomparable face transports act on a coefficient fiber by endomorphisms , and retain a mixed labelled coefficient .
Interchange defect
The two blowup orders transport the mixed occurrence to
Therefore
The defect vanishes exactly on the commuting specialization relevant to ordinary scalar probability weights. Generic integral unipotent test matrices give a nonzero defect.
Classification
The two labelled faces and their intersection already exist. A nonzero commutator therefore calls for a coefficient-level braiding/interchange cell, not a new carrier incidence. This is a clean example of sector-specific coefficient complexity over a fixed carrier.
Durable artifacts
research/benincasa/checkers/matrix_mixture_interchange.rsresearch/benincasa/results/matrix-mixture-interchange.jsonresearch/benincasa/matrix-mixture-interchange.md
Next source gate
Before extending this branch, identify an independently derived cosmological coefficient system with noncommuting face transports. In its absence, the physical mixture lane stops at the commutative result of Entries 1715–1718.