Observable Dynamics of Sectorized Observable Frameworks

This paper defines the typed deformation layer of the Sectorized Observable Framework (SOF). It begins from a declared static SOF realization and introduces local deformation charts with fixed labels, carrier conventions, comparison maps, and policies. A general parameter domain becomes an observable trajectory only after a one-parameter path is selected. The framework keeps operator/word, Lie/Hall, state, spectral, proxy, and closure fields distinct. Exact first-hit depth and cutoff-truncated depth are separate objects. An exact finite depth requires a first-hit certificate containing a witness at the reported level and verified non-hits at every lower level; a finite unreached value is not mathematical infinity. Response times are defined relative to a declared trajectory, parameterization, normalization, norm, orientation, threshold, and censoring policy. The principal theorem is the Observable Wall Pullback Inclusion. Under explicit admissibility and local-constancy hypotheses, the wall of a selected discrete shadow is contained in the pullback of its typed discriminant. Equality requires pullback-exactness, while transverse crossing of a locally separating hypersurface supplies a geometric sufficient condition along a selected trajectory. Two exact constructions separate policy-relative response mechanisms. A three-sector model distinguishes first-order direct norm scaling from second-order simple-commutator norm scaling under a common threshold. A calibrated exponential model proves an ordered half-response inequality, with a finite three-sector Computational Certificate yielding 30 < 1380. A neural-network audit records endpoint-normalized sampled proxy response times 60 < 80 < 120 only as a Computational Observation; no proxy-to-binary-shadow or proxy-to-depth theorem is claimed. The results concern typed deformation records, observable trajectories, wall pullbacks, and policy-relative response diagnostics. They do not establish a complete weak deformation category, a universal wall hierarchy, an intrinsic rate invariant, a universal accessibility ladder, or an unconditional bridge among operator/word, Lie/Hall, state, and proxy carriers. Version 2.0 replaces the broad deformation-category and untyped accessibility-ladder language of version 1 with carrier-qualified deformation records. It distinguishes exact, truncated, observed-upper-bound, and censored outcomes; separates domain-level deformation families from ordered trajectories; introduces pullback-exact and trajectory-exact discriminants; and narrows the numerical evidence to source-addressed certificates and observations at their declared levels. Source repository: https://github.com/dooven-prime/rime-lite Paper IX of the Representation-Induced Mechanics and Evolution (RIME) program. Independent researcher; no institutional affiliation.