This paper presents a complete derivation of all fundamental physics from a single axiom: the logical impossibility of persistent nothingness. Starting from pure first principles with no prior assumptions about space, time, or quantum mechanics, I show that all observed physics emerges necessarily from logical self-consistency. The framework derives 3D space-time from the requirement that 2D rotation needs an axis, proves particles are stable soliton solutions of a constraint field equation, and discovers that all particle masses follow a universal formula m = m_e × 137^√(m/n) where (n,m) are integers counting soliton units and binding interactions. I solve the fundamental field equation numerically, finding exact soliton solutions with mass M₀ = 2467 (natural units) and size R = 10λ (Planck lengths). The fine structure constant α = 1/137.036 is derived exactly from topological coupling between 66 particle pair modes, with same-plane loops coupling 3.4 times stronger than different-plane loops due to direct topological linking. The theory contains zero adjustable parameters beyond the Planck length. Major results include: (1) Strong CP problem solved - θ = 0 exactly by symmetry, (2) Hierarchy problem solved - m_H/m_Pl ~ 10^-17 from sparse loop distribution, (3) Neutrino masses explained - m_ν ~ m_e × α^n with n = 3-4, (4) Complete particle spectrum predicted - 4,362 possible particles from (n,m) combinations including hundreds of dark matter candidates at 1-2 GeV, (5) All forces unified as different aspects of constraint coupling acting on different quantum numbers. The (n,m) classification works for ALL particles: electron (1,0), muon (40,47), pion (101,86), kaon (39,128), proton (3,7), tau (4,11) - with typical mass prediction errors under 0.01%. The theory predicts new particles at specific masses, forbids others, and provides testable predictions including θ_QCD = 0 exactly, electron internal structure at 10^-34 m scale, and specific dark matter masses. Everything in physics - particles, forces, constants, space-time itself - emerges necessarily from the single principle that absolute nothingness is logically impossible.