IDWT (Infinite-Dimensional Wave Theory) is a spectral-geometric framework that derives the full Standard Model — fermion spectrum, gauge couplings, CKM/PMNS matrices, neutrino masses — plus emergent 4D gravity from exactly two inputs: the integer 4 and the electron mass. The theory is formulated on spacetime M∞ with a single master Dirac spinor Ψ∞. It rests on five core postulates that define the non-compact sector structure of M∞, the universal projection and Born rule, the rank-1 interaction kernel, the two-stage observability filter, and the spectral geometry that governs mode selection. Spectral theorems then fix all sectors and multiplicities, yielding predictions in excellent agreement with experiment after small corrections. IDWT (Infinite-Dimensional Wave Theory) derives the entire Standard Model spectrum and most of its parameters from a single mass unit (the electron mass m_e = 0.511 MeV) and two integer seeds (n_down=1, n_strange=4). From these two inputs the theory predicts:- All six quark masses and their ratios- The three charged lepton masses- The three neutrino masses and all oscillation parameters- The W, Z, and Higgs boson masses- sin^2 theta_W, the rho parameter, G_F, and the Higgs vev- The SU(2)_L and SU(3)_c gauge couplings- The Cabibbo angle, |V_us|, |V_cb|, |V_ts|, and Wolfenstein parameter A- The rho(770) meson mass, f_pi, Lambda_QCD, and the proton mass All neutrino predictions use no neutrino data whatsoever:- Neutrinos are strictly Dirac fermions (Majorana mass term is geometrically forbidden)- Neutrinoless double beta decay rate is exactly zero- Normal mass ordering only- m1 = 1.49 ± 0.11 meV- m2 = 8.64 ± 0.61 meV- m3 = 48.9 ± 3.4 meV- Sum m_nu = 59.0 ± 4.1 meV- Delta m^2_21 = 7.24 × 10^{-5} eV²- Delta m^2_31 = 2.39 × 10^{-3} eV- m2/m1 = 5.807 ± 0.012- Effective beta-decay mass m_beta = 2.4 ± 0.2 meV- Effective Majorana mass m_beta beta = 0 exactly The entire framework is expressed as a compact set of 12 spectral theorems governing the low-lying spectrum of a Dirac operator on an infinite-dimensional product manifold. The original geometric/combinatorial picture (laser-cavity mode selection, quasicrystal-style projection, combinatorial branching from a single seed) remains intact and is now derived as direct consequences of the spectral triple. All quoted predictions are reproduced by a single open-source Python script from the two minimal inputs alone. No other free parameters are used. The neutrino mass sum Sum m_nu ≈ 59 meV and the exact prediction m_beta beta = 0 are near-term falsifiable tests. The spectral formulation opens clean connections to spectral geometry, noncommutative geometry, and quasicrystal theory.