Physics from Existence I: The Equation

No theory has simultaneously derived all 26 free parameters of the Standard Model. In this paper, extending the quantum indefiniteness of existence to the existence of the universe itself, we show that three axioms about existence — existence is bivalent (n ∈ {0,1}, i.e. n² = n), existence is uncertain (σ ≠ 1), and non-existence is forbidden (σ ≠ 0) — uniquely determine the single equation V = −H as an algebraic identity, and that the mathematical structure derived from its exact algebraic expansion corresponds to the various structures of the Standard Model. As a result, 26 physical constants in total are reproduced with no adjustable parameters; all those with established experimental values agree with experiment to 0.0006%–5.3% accuracy. Derived from the axioms of existence, V = −H is the canonical free energy of a single binary degree of freedom n ∈ {0,1}, determined as the Legendre transform of the Fermi-Dirac distribution. From this potential and the kinetic term of the canonical normalisation (g = 1, §2.4), the Schrödinger equation is derived as a transfer matrix, and we show that it has exactly three bound states (discrete solutions), corresponding to the three generations of fermions. The spatial dimension d = 3 follows from three conditions — preservation of the well, spin-statistics, and propagating gravity — and the Lie-algebra structure unfolding from this double coincidence (N = d = 3) reproduces the gauge group SU(3)×SU(2)×U(1). Twenty-six physical constants are derived from this structure, including 1/α = 137.035999084 (all orders, matching CODATA 2018 to all displayed digits; the leading term is 137.0368 at 0.0006%, and the correction series is proved in Paper II), α_s = 0.1179 (0.07%), sin²θ_W = 0.23122 (<0.01%), the charged-lepton mass ratio R = 1.5293 (0.006%), and sinθ_C = 0.2245 (0.10%). The results further predict the absolute neutrino masses (Σm_ν = 59.50 meV once the absolute scale is set by Δm²₂₁) and strictly zero neutrinoless double-beta decay, among other testable predictions. These quantities are not independent input parameters — they are all computed from the same mathematical structure fixed by V = −H. All of these numerical values are reproducible with the attached verification code.