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) ζᵤ (s) ∈ ℚπ² for all positive integer s, and (2) the rational-part numerators satisfy b (s) = 4ˢ + 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: RM = E (Maxwell) /E (scalar) = 22 and RD = E (Dirac) /E (scalar) = 8. The identity RM = 2b₀ is proven from Bernoulli numbers and holds exclusively at Nc = 3. Nine charged-fermion masses are reproduced at 0. 14% RMS with zero fitted parameters. The proton charge radius rₚ = 4ℏc/mₚ = 0. 8412 fm matches muonic hydrogen to 0. 04%. Paper III (14pp) traces the master identity λₖ (S³) = dim (SU (k+1) ) across domains: periodic table orbital blocks, crystal field splitting (Δₜet/Δₒct = QK² = 4/9), five DFT functional parameters (zero fitted), gold's colour (γ = 1/√QK), 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 CF = 4/3 equals (Nc+1) /Nc exclusively at Nc = 3, and traces this ratio through baryogenesis, DFT exchange, MHD turbulence (exponent gap 1/6 = 1/Nf), 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 aA/aV = 3/2 = 1/QK (0. 24%) connects nuclear isospin to the Koide lepton mass fraction. The axial coupling gA = 1 + 3MK = 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.