Linearized Commutativity Geometry on the Generator-Set Moduli Space

This paper studies weighted generator averages on the generator-set moduli space. It distinguishes the commutativity locus, the normality locus, and local normal spectral charts. It also separates direct support derived from represented operators from direct support derived from a declared Lie-generator registration. The theorem and computational-certificate layers derive exact normalized commutator derivative formulas and evaluate the full complex-real Jacobian in the canonical 228-dimensional Rubik realization. The commutator derivative has numerical rank 11 and nullity 7. After adjoining the linearized normality equations, the combined derivative has numerical rank 14 and nullity 4. Its kernel contains both exact class-scaling gauges, while three inverse-pair-symmetric quarter-turn axis directions yield sample points that pass the declared complex128 commutativity, Hermiticity, and normality gates. The normality-gated pointwise registrations give nine sectors at the canonical point, with represented-operator and Lie-generator direct-support counts of 438 and 408. Each of the three tested quarter-turn axis samples at weight 1.1 gives fifteen sectors, represented-operator support count 1006, and Lie-generator support count 832. These are pointwise computational observations and do not establish coherent projector continuation between the registered endpoints. Version 2.0 replaces the historical global-stratification and accessibility-wall framing of version 1. It withdraws the earlier 9-to-24--35 fragmentation counts and the untyped 438-to-6334 support count, which resulted from applying a Hermitian eigensolver to commuting but nonnormal averages. The paper does not claim a seven-dimensional smooth commutativity manifold, a nonlinear spectral atlas, a universal accessibility-wall hierarchy, or a moving-wall theorem. Routed compositions, full words, projected commutators, word depth, and Lie depth remain separately typed objects requiring separate certificates. Source repository: https://github.com/dooven-prime/rime-lite Paper V of the Representation-Induced Mechanics and Evolution (RIME) program. Independent researcher; no institutional affiliation.