Structural Admissibility of the E8 History Semigroup

This work proposes a structural framework preceding physical dynamics, in which the admissibility of stable physical description is determined by purely geometric and informational constraints. We introduce the concept of a history semigroup, formalizing discrete update order, irreversibility, and information-preserving evolution without assuming quantum fields, spacetime continuity, or dynamical laws. Imposing structural admissibility conditions—including discrete self-duality, statistical isotropy, and capacity-preserving evolution—strongly constrains the dimensionality of the internal substrate. Remarkably, these constraints select the E8E_8E8 lattice as the unique configuration satisfying maximal packing efficiency and isotropic stability at the eight-dimensional threshold. A projection principle from the admissible eight-dimensional substrate to an effective four-dimensional representation is formulated, incorporating scalarization and temporal multiplexing. Within this structure, dimensionless coupling values arise as geometric invariants rather than dynamical parameters. In particular, the inverse fine-structure constant emerges as a numerical ideal value, α−1≈137.035999,\alpha^{-1} \approx 137.035999,α−1≈137.035999, derived from Casimir-ratio geometry and projection-volume factors. Small deviations from this ideal value are interpreted as phase shifts induced by mass-dependent loading effects. The framework establishes structural conditions under which stable physical constants become admissible, positioning physical laws as emergent constraints of representational stability.