Physics from Existence I: The Equation

No theory has simultaneously derived all 26 free parameters of the Standard Model. This paper shows that three axioms about existence—existence is bivalent (n ∈ {0, 1}, i.e. n 2=n), existence is uncertain (σ ∈ (0, 1)), and non-existence is forbidden (σ̸=0)—uniquely determine the equation V = −H as an algebraic identity, from which over 20 physical quantities are derived with zero free parameters, all agreeing with experiment to 0.0006%–2.4% accuracy. 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. The Schr¨odinger equation is derived as a transfer matrix from this potential and the unitmass kinetic term fixed by Cencov’s theorem. This equation has exactly three bound ˇ states (discrete solutions), corresponding to the three generations of fermions. The spatial dimension d = 3 follows from three conditions—bound-state preservation, spin-statistics, and propagating gravity. The mathematical structure unfolding from this coincidence reproduces the gauge group SU(3)×SU(2)×U(1). More than 20 physical constants are derived from this structure, including 1/α = 137.0367 (0.0006%), αs = 0.1179 (0.01%), sin2 θW = 3/13 (0.2%), the chargedlepton mass ratio R = 1.5293 (0.006%), and sin θC = 0.2245 (0.05%). The results further predict the absolute neutrino masses (Σmν = 59.3 meV), normal mass ordering, and strictly zero neutrinoless double-beta decay, yielding eight testable predictions. These physical quantities are not independent parameters—they are all derived from the same equation