E8 80-Triplet Braided Sheaf Cohomology Yields φ-Locked Wilson Loop Algebra — E8 Intelligence Research

Abstract

The 80-element triplet structure already embedded in the E8 root system admits a natural sheaf cohomology H¹ over the 24-cell's spinorial fiber, whose connecting morphisms correspond to Fibonacci-anyon braiding paths. This produces a Wilson loop algebra whose holonomy phases are quantized as integer multiples of 2π/φ², enforcing a golden-ratio–locked topological order. The construction extends prior 16-24 cell duality by promoting vertex intersections to Čech cocycles, yielding a computable invariant distinguishing inequivalent E8 topological phases. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com