A Lie-Algebraic Architecture of the Cosmos: from the EML Function to so(26) and Dynamic Grand Unification at 13.7 TeV in Geometric Topology 14D (TG)

We present the complete computational architecture of the cosmos according to the General Theory / Geometric Topology (TG). Starting from the atomic function eml(x, y) = e^x − ln y, we demonstrate that non-commutativity at the subcellular level naturally generates the so(14) Lie algebra with 91 generators, which decomposes into the gauge symmetries of the Standard Model (SU(3)_c × SU(2)_L × U(1)_Y) and gravity (SO(3,1)). Extending to so(26), the framework provides a unified description of all forces, particles, and fundamental constants from first principles. The cosmos is modeled as a deterministic systolic automaton running on a 14-dimensional holographic hypersphere H^{14} with directional signature (7+, 7i). We derive the string hierarchy from L_{0s} (dark matter, Planck scale) to L_{5s} (non-dissipative Dirac magnetic monopole at 13.7 TeV), the thermodynamic nature of the Higgs field as a Boltzmann fluid of L_{2s} toroids, and the dynamical Grand Unification scale E_{GUT} ∝ P_d^{-9}, currently at 13.7 TeV. Fundamental constants emerge without free parameters: ℏ = m_2^4 P_s P_d, α ≈ P_s²/100, and the Higgs VEV v ≈ 246.212 GeV (0.003% deviation from experiment). TG resolves the hierarchy problem, the cosmological constant issue, and offers six testable predictions, including vacuum phase transition at 13.7 TeV, absolute proton stability, and measurable anisotropy of the speed of light. This work establishes a discrete geometric foundation for quantum mechanics, general relativity, and the Standard Model, opening new avenues for high-energy physics and vacuum engineering.