Observable Dynamics of Sectorized Observable Frameworks

Part IX of the RIME program. Paper VIII identifies the Sectorized Observable Framework (SOF) as the common observable architecture in which the RIME observables R1, R2, D, and J_acc arise naturally. Paper IX studies observable dynamics: how SOFs deform, how observable trajectories evolve, how different time scales appear, and why different deformation spaces produce different observable dynamics over the same observable architecture. We define a deformation of an SOF as a parameterized family of sectorized observable data: a varying space, a varying sector decomposition, and a varying observable family, indexed by a parameter t. This family is viewed as a path in a provisional deformation category for SOF trajectories. Accessibility deformations induce trajectories of the support shadow, commutator-survival shadow, first-depth shadow, and accessibility jet. Other SOF species induce registered analogue shadows, such as plateau functions, spectral gaps, communicating-class profiles, or proxy norms. The main structural object is observable dynamics: the collection of trajectories, time scales, plateaus, and wall loci attached to an SOF deformation. The Observable Wall Pullback Principle states that, for an admissible SOF deformation and a discrete observable shadow O, the wall of O is contained in, and under exact discriminant hypotheses is realized as, the pullback of a rank, support, spectral, or filtration discriminant of the corresponding continuous field. Paper IX provides the dynamic counterpart to Paper VIII's static unity. The same observable ladder may produce different time scales, plateaus, repairs, and walls because different systems move in different deformation spaces. Source repository: https://github.com/dooven-prime/rime-lite This work is part of the Representation-Induced Mechanics and Evolution (RIME) research program.