We present The Archetype, a non-perturbative theoretical framework that achievesarithmetic unification of fundamental constants through the even unimodular Lorentzianlattice II25,1 and the coefficients of the modular j-invariant. Unlike traditionalunification models that rely on free parameters or anthropic selection from a vastlandscape of vacua, The Archetype derives physical observables directly from latticeinvariants and moonshine coefficients without external inputs.The model is built upon a 26-node resonant Hamiltonian proven to be Hermi-tian and spectrally bounded, ensuring unitary time evolution and a stable vacuumground state. By projecting the path integral measure onto the genus-zero subspaceof the Monster module, the framework resolves the 10120 discrepancy in the cos-mological constant via modular suppression. Parameter-free derivations yield theinverse fine-structure constant α−1 ≈ 137.036, the proton-to-electron mass ratio≈ 1836.15, and the Higgs boson mass mH ≈ 125.11 GeV, in excellent agreementwith current measurements.Furthermore, we address the emergence of continuous spacetime from the dis-crete lattice substrate via celestial holography and Mellin transforms, demonstrat-ing that smooth manifold structure and Poincar´e invariance arise as observer-dependent holographic projections. Ultraviolet completeness is established througha non-trivial renormalization group fixed point at g∗ ≈ 0.85. Testable predictionsare provided for the 2026–2028 experimental window, including specific CMB poweranomalies at l ≈ 1800–2200 and a graviton mass bound below 10−32 eV/c².The Archetype offers a novel paradigm in which physical reality emerges as adirect consequence of deep mathematical symmetries, providing a pathway towardresolving longstanding unification challenges. Keywords: lattice unification, Monstrous Moonshine, asymptotic safety, arithmeticconstants, celestial holography, emergent spacetime