The N.E.A. Grand Compendium: The Computational Ontology of the Crystalline Universe

The N.E.A. Grand Compendium consolidates the Network EmergentArchitecture: a derivation of fundamental physics from a singlelogical primitive. Central result. The gauge groups of the Standard Model are notassumed. They are derived from the geometry of the causal lattice: K4 -> SU(3), octahedron -> SU(2), C8 edge -> U(1). The K4 cycle space is explicitly isomorphic to the root system ofsu(3). Three fermion generations follow from the S4 symmetry of thecube; the color triplet follows from the A4 symmetry of thetetrahedron; the weak doublet follows from the binary tetrahedralgroup 2T. Dirac fermions emerge from defect quantum walks on thediamond lattice with the Clifford algebra verified to machineprecision. Full details are given in P: Particle Genesis (DOI:10.5281/zenodo.22658923). Four forces, one equation. Gravity, electromagnetism, the strongforce, and the weak force are modes of one causal equation: dphi/dt = sqrt(1 - 2phi) * (nabla^2 phi - mu_i^2 phi + Delta sigma_i). Forces differ only by carrier, inverse range parameter mu_i, andsource density sigma_i. The static limit is the bandwidth-closureequation nabla^2 f_ext^2 + mu_i^2 (1 - f_ext^2) = 2 Delta sigma_i, f_ext^2 = 1 - 2phi. Logical primitive. The framework begins with the existence of atleast one decidable statement. From this follow Being, difference,change, the discrete Tick, the Being Tax B = 1, and the Pythagoreanbandwidth law f_int^2 + f_ext^2 = B^2 = 1. Three topological genes. The numerical sector is generated by d = 3, U_EM = 0.4*pi, U_weak = 10*sqrt(3). The inverse fine-structure constant is computed as alpha^{-1} = 25*sqrt(3)*pi + 1 = 137.035, with deviation 7.6 ppm from CODATA. The weak mixing angle is sin^2 theta_W = 1/(1+pi) - Delta/(4*pi) = 0.23079, with deviation 0.18%. The fermion mass spectrum follows a compacttopological chain. Heavy-quark deviations are below 2%, with the topquark at 0.02%. The CP-violating phase appears as the topologicalcandidate arctan(5/2) = 68.20 degrees, deviating 0.87% fromexperiment. Topological scale skeleton. The fundamental scales are locked by alpha_G^{-1} = N_max^5 / R, m_p / Z = f_geo * (sqrt(R)/(1+R)) * N_max^{1/2}, l_P / lambda_Z = (1+R) / (f_geo * N_max^3), with exponent closure -6 + 1 + 5 = 0. Deviations are 0.12%, 0.017%,and 0.043%. The native scales are t_Tick = hbar / Z = 1.619e-21 s, a_0 = hbar c / Z = 485.26 fm. The geometric correction factor is f_geo = 1 + Delta/(4*pi) =1.010660. Candidate higher-order corrections are graded as heuristiceffective settlements, not first-principles derivations. Falsifiability. Dark matter and dark energy are not particle-like.All dark matter annihilation, decay, direct-detection, and dark-energyparticle signals must be strictly zero. A single confirmed signalwould falsify the framework. The positive prediction is that thecritical surface density scales with cosmic expansion,Sigma_crit(z) proportional to H(z). At z = 2 this threshold isamplified by a factor of 3.03; JWST and ALMA high-redshift rotationcurves provide the decisive test.