Availability of Temporal and Spatial Structure: A Pre-availability Analysis and Structural Exhaustion

This work presents a structural analysis of availability based on primitive resolvability conditions governing temporal comparability and spatial distinguishability. Time and space are treated as structural objects, each consisting of a conditional domain together with an ordering-type or proximity-type relation. Availability is fixed as a structural validity framework, independent of differentiation and of metric, dynamical, or physical assumptions. When differentiation is specified within this framework, its structure is determined by the joint polarity of order-type and proximity-type resolvability assignments on a path space, fixing a finite availability differentiation space for subsequent structural characterization. A structural exhaustion result is established: under the specified resolvability conditions, the space is complete and admits no further primitive differentiation. This version introduces minor structural clarification in Chapter 8 and a corresponding refinement of the subtitle. Equation formatting and subscript rendering have been unified throughout. No scientific content has been modified.