The Standard Model Mass Spectrum from the Planck Mass: Single-Input Derivation on the Golden-Ratio Ladder, Validated Against PDG 2024

We derive the absolute mass spectrum of the Standard Model from a single physical input: the Planck mass m_P = √(ℏc/G). With m_P fixed at its CODATA value 1.2209 × 10²² MeV, every charged elementary fermion mass (six quarks, three charged leptons), every massive gauge boson mass (W, Z, Higgs), and the masses of forty named hadrons sit inside structurally predicted brackets on the golden-ratio ladder, with no further fitted parameters. The structural identity that closes the dimensional bridge is the Planck-electron rung gap r_P − r_e = 107, derived from two independent identities: the Planck-Higgs hierarchy gap r_P − r_H = D⁴ = 81 at the spatial dimension D = 3, and the Higgs-electron bracket m_H/m_e ∈ (φ²⁵, φ²⁶). The empirical Planck-electron ratio log_φ(m_P/m_e) = 107.08 sits inside the predicted bracket [107, 108]. The bracket prediction for the electron mass is m_e ∈ (0.328, 0.531) MeV, containing the empirical value 0.5110 MeV near the upper edge. Each subsequent particle mass is computed as m_X = m_P · φ^(k_X − k_P) with k_X a structural integer fixed by the particle's quark content and angular-momentum structure. The Standard Model's twelve mass parameters (the charged-fermion Yukawa couplings) are eliminated; the framework retains one universal scale (the Planck mass, equivalently Newton's constant G). All fifty-two predictions are verified against the 2024 Particle Data Group review. Six cross-module unifiers organise the catalogue: the SM mass-spectrum unifier covers eight elementary particles, the charged-lepton ladder bundles (e, μ, τ) at gap-9, the meson ladder bundles (K, D, J/ψ, B) with gap pattern (2, 1, 1), the EW boson ladder bundles (W, Z, H) with adjacency at the half-octave boundary, the heavy-quarkonium grand unifier bundles charmonium-B_c-bottomonium with strict bracket adjacency, and the hadron-spectrum grand unifier bundles all preceding into seven adjacent rung brackets. We list four classes of falsifier and identify the within-bracket position as the principal residual.