Boolean Support Does Not Determine Commutator Accessibility

This paper studies whether generator-labelled Boolean support determines commutator accessibility in a fixed sectorized skew-Hermitian system. It separates five typed layers: direct generator support, routed projected composition, full-word support, projected commutator support, and cutoff-relative Lie depth. The exact theorem layer gives a three-dimensional same-support counterexample. Two systems have identical generator-indexed Boolean support but different commutator support and different exact Lie depth. The paper also gives a four-class partition by direct and commutator support, a centered one-dimensional sufficient criterion for local bracket emergence, and the image-kernel and rectangular rank-protection boundaries for matrix-valued projected products. A declared computational S4 case study records ten direct channels, two bracket-emergent channels, two channels with routed-product and full-word support but machine-zero simple commutators, and seventy-six channels unreached through the declared depth-three cutoff. Machine-zero cancellations are numerical evidence rather than exact equalities. The separate 48-product audit is restricted to already-direct channels and does not certify matrix-level emergence or low-order-to-depth completion. Version 2.0 replaces the historical repair-calculus framing of version 1. It does not retain the Type I-IV taxonomy or claim a global repair theorem, represented genericity, moving accessibility walls, or determination of full Lie depth from low-order support. These remain separate research questions. 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.