Vacuum Mechanics: Probes 45-107 — Master Equation, DESI Dark Energy, Lens Space Topology, and Framework Purification

Technical report documenting all results from Probes 45-107 of the Vacuum Mechanics programme, including the complete lens space topology programme, DESI dark energy confirmation, and a rigorous framework purification audit. 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. 107 probes conducted, yielding 373+ discoveries and 13 honestly documented retractions. Principal findings include: the master equation n^2-2n-3=0 with unique root N_c=3 generating all SM integers (proven theorem); the counting spectral zeta proven information-theoretically optimal (proven theorem); the exact evaluation zeta_c(2) = pi^2/12 - 11/16 by partial fractions; the Chern quantization conditional derivation of alpha=1/137 from lens space topology; the DESI DR2 confirmation of w_0=-0.954 at 0.03 sigma (framework is the best dark energy model by BIC, beating both LCDM and CPL); the w_a "tension" resolved from 3.3-4.6 sigma to ~1.4 sigma via 10,000-trial Monte Carlo proving CPL overfitting; the Boyer Casimir energy at 0.016%; the SM Casimir budget favouring Weyl neutrinos (88/240 = 11/30); the proton mass at 0.004%; the d-invariant spectrum uniquely selecting p=137; and the K3 structural connection n(n^2-1)=24. FRAMEWORK PURIFICATION (Probe 107): A rigorous self-audit reclassified all predictions by purity of derivation. Results: 15 bulletproof sub-0.1% predictions using only N=137 and v (no external data, no scanning, no fitting); the 9-mass NLO/NNLO system found to be effectively fitted (0/12 coefficients derivable from first principles); refractive index identifications (n(water)=4/3 etc.) confirmed as numerical coincidences (3 hits from ~125 framework rationals = expected noise); M_W corrected from 0.09% to -3.1% at tree level (previous result was 70% external data). The purification reduced the headline count from 20 to 15 but every surviving claim is defensible under adversarial scrutiny. A systematic scan of 5 million trials showed the framework produces fewer coincidences than random chance (anti-numerology: 6 hits vs 64.8 expected). The topology programme (Probes 83-101) exhaustively explored lens space invariants. Standard tools are exhausted; no path to closing the remaining postulate was found. The CS-spectral incompatibility was triple-confirmed and permanently closed. Independent professor assessment: 6/10 ("strong conditional proof with one unproven premise"). Revised five-year forecast (post w_a resolution): 42% mixed, 27% survives, 21% validates, 10% fails. Survival probability through 2030: ~57%. 72 computational verifications with 0 failures. 10 proven exact algebraic results. 22 proven theorems. 14 negative domains confirmed. 11 falsifiable predictions with experimental timelines (JUNO ~2027, Cs-Rb ~2027, DESI Y5 ~2027, CMB-S4 ~2028, DUNE ~2030). 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.