Accessibility Repair Calculus

Paper V of the RIME program. This paper studies fixed sectorized operator systems and asks what repairs binary support after path-commutator cancellation. It introduces the local R1/R2 repair calculus for length-2 accessibility witnesses, separates Type I--IV obstruction mechanisms, identifies cancellation and incidence as exceptional loci, and formulates the program-level completion question of when the observable pair (R1,R2) determines the first-depth invariant D. The paper is part of the RIME program on spectral, transport, and accessibility structures in finite represented operator systems. Papers I--III form the initial RIME trilogy; Paper IV develops fixed collision geometry; Paper VI studies generator-set deformation and accessibility walls; Paper VII develops generic accessibility completion. Source repository: https://github.com/dooven-prime/rime-lite This work forms Part V of the Representation-Induced Mechanics and Evolution (RIME) research program. Foundational archive DOI: 10.5281/zenodo.21108197