Yehi

This monograph introduces YEHI as an axiomatic framework founded on a single generative principle asserting that 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. Layer behavior is governed through size, duplication, cover, rank, and extent, while patterns describe systematic variations across ordered sequences. Mapping provides a method for constructing and comparing models through successive layer formation, enabling structured counting, extended numerical representation, and the comparison of infinite constructions through their internal arrangement rather than by quantity alone. Dimensional organization emerges from patterns of partial cover. One-dimensional arrays arise from ordered chains, while higher-dimensional configurations develop through repeated embedding at intersections. Certain structures contain a Projective Core—a region excluded from dimensional construction that nevertheless influences surrounding configurations through directed propagation from a concentrated structural origin. Ordered transitions between models are governed by steps, while Stride Plans regulate the adaptation of spatial frequency (SF) and time frequency (TF). These processes give rise to measures analogous to spatial and temporal entropy and to conservation-like relations that preserve structural continuity under transition. Internal magnitude matching enables comparison between models of differing magnitude, while dependency and generators ensure continuity through enforced retraction and sustained self-reference. Taken together, these developments establish 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.