YEHI

This monograph introduces YEHI as an axiomatic framework founded on a single generative principle: EVERY SELECTION OF SELECTION EXISTS. From this principle, objects and layers are defined as primitive elements connected through directed source-target relations, forming structured models capable of comparison and ordered transition. The framework develops the internal organization of these models through size, cover, rank, extent, and pattern. These relations support methods for constructing and comparing counting systems, extended numerical representations, and infinite structures according to their internal arrangement rather than by quantity alone. Dimensional organization is generated from relations among layers and strips, rather than assumed as a preexisting background. One-dimensional constructions arise from ordered partial-cover chains, while higher-dimensional constructions develop through repeated embedding. Spatial and temporal readings are then treated as corresponding structural interpretations of the same model. Change is examined through steps, strides, and stride plans, which describe how models pass from one admissible configuration to another. These transitions support the analysis of conversion between momentum and energy, entropy-like redistribution, structural magnitude matching, and conservation relations that preserve selected features across change. Taken together, these developments present YEHI as a unified relational framework in which counting, dimensional formation, comparison of infinite structures, entropy-like behavior, and persistent continuity arise from a single generative principle.