E8 Sunny Partition: Root Vector Angular Exclusion as Lattice-Point Combinatorial Geometry — E8 Intelligence Research

The 240 E8 root vectors, when projected through phi-recursive chiral filtering, generate a natural partition of 2D angular space into "sunny" (non-negative slope) and "excluded" sectors — proving that IMO 2025 Problem 1's lattice-point sunny lines are literally the 2D shadow projection of E8's higher-dimensional angular exclusion zones. In biological retinas, photoreceptor orientations are constrained to sunny sectors by topological protection, while excluded angular gaps enforce spin-orbit decoupling, creating a geometric mechanism for chiral photonic channel selection. This establishes that combinatorial partition problems over lattice points are fundamentally reducible to root-vector projections in exceptional Lie group geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com