Vacuum Mechanics: New Series — From Spectral Geometry to Fermion Masses, Nuclear Binding, and the Framework Boundary (Papers I-V)

Five papers deriving consequences of the quaternionic vacuum condensate framework established in Papers I-IX (Zenodo, 2026) and consolidated in Paper 10 (DOI: 10.5281/zenodo.19234951).Paper I (10pp) proves two theorems about the spectral zeta function of the Laplacian on S³: (1) ζ_u(s) ∈ ℚ[π²] for all positive integer s, and (2) the rational-part numerators satisfy b(s) = [4^s + C(2s,s)]/2. The unique Pythagorean decomposition 137 = 4² + 11² = dim(ℍ)² + b₀² is established as a Gaussian integer norm.Paper II (7pp) derives all six NLO mass-formula coefficients from two Casimir vacuum energy ratios on S³: R_M = E(Maxwell)/E(scalar) = 22 and R_D = E(Dirac)/E(scalar) = 8. The identity R_M = 2b₀ is proven from Bernoulli numbers and holds exclusively at N_c = 3. Nine charged-fermion masses are reproduced at 0.14% RMS with zero fitted parameters. The proton charge radius r_p = 4ℏc/m_p = 0.8412 fm matches muonic hydrogen to 0.04%.Paper III (14pp) traces the master identity λ_k(S³) = dim(SU(k+1)) across domains: periodic table orbital blocks, crystal field splitting (Δ_tet/Δ_oct = Q_K² = 4/9), five DFT functional parameters (zero fitted), gold's colour (γ = 1/√Q_K), the glueball mass spectrum (four ratios at 0.05-0.2%), and Fibonacci anyons at Chern-Simons level k = 3. A sharp framework boundary is documented via six negative probes.Paper IV (11pp) proves that the QCD colour Casimir C_F = 4/3 equals (N_c+1)/N_c exclusively at N_c = 3, and traces this ratio through baryogenesis, DFT exchange, MHD turbulence (exponent gap 1/6 = 1/N_f), the She-Leveque intermittency formula, and the Abraham-Lorentz electromagnetic mass problem. A physical argument for the Yang-Mills mass gap is presented.Paper V (9pp) derives all five Weizsäcker SEMF coefficients from framework constants. The headline result a_A/a_V = 3/2 = 1/Q_K (0.24%) connects nuclear isospin to the Koide lepton mass fraction. The axial coupling g_A = 1 + 3M_K = 1.275 (0.033%) and neutron lifetime τ = 878.7 s (favouring bottle over beam) are new predictions.Total: 51 pages, ~180 results, 3 proven theorems, 7 sub-0.1% predictions, zero fitted parameters beyond v = 246.22 GeV.