Volume II (T): The Geometry of Force — Platonic Archetypes, the Tiling Audit, Force-Body Duality, and the Stride-10 Protocol

The second pillar of the N.E.A. framework: Force-Body Duality. Through a systematic audit of the five Platonic solids under the finite-bandwidth constraint B=1, we identify exactly three geometric carriers capable of serving as physical force carriers in three-dimensional Euclidean space: the cube C8 (spatial skeleton), the regular tetrahedron K4 (minimal closed volume anchor), and the regular octahedron (directional addressing framework). The regular dodecahedron and icosahedron are eliminated by bandwidth constraints; they survive only as virtual carriers in the logical layer.

We then conduct the Tiling Audit, proving that the tiling capability of a carrier determines both the range and effective strength of its force. C8 successfully tiles space, diluting its stitching rent across the infinite translational symmetry group, producing the vanishingly weak, long-range gravitational background. K4 cannot tile, trapping its entire cycle-space rent within the simplex, producing the enormously strong, short-range, confined Strong Force. Mass is identified as failed space: the trapped rent of a non-tiling carrier.

The gauge groups are identified as topological invariants of the carrier cycle spaces: K4 (cycle number 3) yields SU(3), the octahedron (6 vertices, 3 mandatory constraints, 3 residual generators) yields SU(2), and C8 intra-cell edges carry U(1). Gravity has no independent carrier and no independent gauge group; spin-2 is the tensorial fingerprint of the inter-cell stitching operation.

The Weak Force is clarified as the 0-to-1 Addressing Protocol: the establishment of directed causal identity along the undirected skeletal edges mandated by the Being Tax. The Stride-10 protocol is established as the minimal logical addressing width (10 causal edges) for non-aliased causal direction resolution in 3D discrete lattices. Two fundamental topological constants are extracted: U_EM = 0.4pi and U_weak = 10sqrt(3), providing the foundational basis for the settlement of all 19 Standard Model parameters in Volume III.