Vacuum Mechanics: New Results — Boyer Topology, SM Casimir Budget, Refractive Indices, Black Holes, Neutrinos, and QGP (Probes 45-65)

Technical report documenting all results from Probes 45-65 of the Vacuum Mechanics programme. The framework treats the quantum vacuum as a quaternionic elastic condensate on S^3 x S^1/Z_2, deriving Standard Model parameters from two inputs: the integer N = 137 and the Higgs VEV v = 246.22 GeV. Principal new findings include: the Boyer Casimir energy of a conducting sphere matching the vacuum modulus ratio to 0.016%; the total SM Casimir energy on S^3 favouring Weyl over Dirac neutrinos; new results connecting the S^3 spectral zeta function to electromagnetic coupling constants; the proton mass predicted at 0.004% (three-loop QCD); refractive indices of diamond, water, and fused silica expressed in framework constants at sub-0.05%; black-hole thermodynamics connected to the vacuum topology via the lens space L(137,1); the QCD deconfinement temperature predicted at 0.30% from lattice QCD; and neutrino oscillation predictions registered for upcoming experiments (JUNO, DUNE, nEXO, CMB-S4). The report includes new analytical results for higher spectral zeta values on the lens space L(137,1), proof sketches for closed-form expressions, a proven Stueckelberg decomposition for the massive vector Casimir energy on S^3, and algebraic identities in the QCD beta function hierarchy that single out N_f = 6 as special. The rho meson mass is predicted at 0.08% from the string tension. 39 numerical matches are tabulated with algebraic tautologies explicitly flagged and separated. 13 honest retractions are documented. All results use two inputs (N = 137, v = 246.22 GeV) and zero fitted parameters. Developed with AI assistance (Claude by Anthropic for computation, numerical verification, and manuscript drafting). All physical reasoning, framework design, formula identification, and assessment of results are solely the author's responsibility.