Vacuum Mechanics: How the Quaternion Finally Made the Standard Model Make Sense

The vacuum is treated as a quaternionic elastic condensate with Poisson ratio nu = 0.4555. Two inputs -- the quaternion algebra H and the electroweak vacuum expectation value v = 246.22 GeV -- determine 25 of the 26 Standard Model parameters, of which 19 achieve sub-0.5% accuracy against PDG values with zero fitted parameters. The shear-to-bulk modulus ratio M_K = mu/kappa = 4pi/137 = 0.09172 organises all couplings, masses, and mixing angles into a single algebraic structure. Key results: alpha = 1/137 (MacCullagh-Larmor identification), alpha_s = 9M_K/7 = 0.1179 (0.06%), m_H = 125.4 GeV (0.13%), M_Pl = 1.22 x 10^19 GeV (0.01%), all nine fermion masses at 0.14% RMS, the baryon asymmetry eta = (4/3)M_K^9 = 6.13 x 10^-10 (0.4%), and the cosmological constant across 120 orders of magnitude (0.4%). A pi/N expansion pattern organises all PMNS corrections to tribimaximal mixing. The Born rule is conditionally derived (reducing quantum postulates from 2 to 1). Full GR follows from Lovelock's theorem. 36 falsifiable predictions, 8 quantitative failures, and 9 honest retractions are documented. This paper consolidates and supersedes Papers I-IX. v2: Revised after dual peer review (adversarial AI reviewer + independent AI review). Changes include: - Added derivation sketches for all 7 previously marginal derivation chains (alpha_s, sin^2 theta_W, y_tau, y_b, w, DM/baryon ratio, NLO coefficients) - Added 14 previously absent discoveries, including the lepton asymmetry cross-domain connection (eta_L = -(17/7)*MK^9) - Added "Open Threads" section documenting 11 suggestive connections not yet established - Added alpha variation episode (3.1-sigma signal systematically killed by 4 tests) - Added confinement section (Type-I, kappa_GL = sqrt(MK)) - Added Z2 energy wall explanation, seven-mode decomposition, neutrino warp power derivation - Explicit F_n table for all 9 fermion masses (resolves NLO opacity) - Jarlskog invariant added to failures table (now 8 failures) - Discovery order disclosure for NLO coefficients (fitted first, interpreted second) - Distinguished retrodictions from genuine predictions - Historical table entries nuanced per reviewer feedback - Born rule claim properly attributed to Gleason (1957) - All 77 framework discoveries now accounted for (49 full, 7 upgraded, 14 added, 7 correctly absent) v3: Revised after hostile external review + new computational results. Changes include: - NLO spectral reformulation: The two-loop QCD beta coefficient beta_1 = 26 (Caswell-Wilczek 1974) connects to the NLO mass coefficients: d_g0 = (beta_1 - N_c^2)/beta_0 = (26-9)/7 = 17/7. The identity beta_1 = b_0 + N_f + N_c^2 holds uniquely at N_c = 3 (with N_f = 6 fixed from dim(Isom(S^3)) = dim(SO(4)) = 6), providing a third independent "why N_c = 3" argument. - S^3 spectral reformulation of d_g0: d_g0 = (lambda_1 + lambda_2 + dim(Isom(S^3))) / Delta_3 = (3 + 8 + 6)/7 = 17/7, where lambda_k = k(k+2) = dim(SU(k+1)) are the S^3 Laplacian eigenvalues. New identities: b_0 = dim(SU(2)) + dim(SU(3)) = 11, N_f = dim(SO(4)) = 6. - RS one-loop integral (Level 2 computation): The bare RS overlap integral computed numerically for all 9 fermions with physical bulk masses gives d_g0_eff ranging from 1.86 (top) to 2.71 (electron), with the muon matching 17/7 to 1.2%. Sector-averaged regression gives 23% deviation with wrong-sign d_g1. Documented as failure #9. The gap between "identified" and "derived" is quantified but not closed. - DESI Y3 (DR2) data comparison: Actual posterior chains from data.desi.lbl.gov analysed. Under constant-w assumption (shared by the framework and Lambda-CDM): w_0|w_a=0 = -0.954 +/- 0.024. Framework matches to 0.0 sigma; Lambda-CDM is 1.9 sigma off. Full parameter comparison table added (6 parameters, all sub-2 sigma). Honesty note added addressing the w_a conditioning methodology. - Forward reference to Paper 11 (in preparation): The S^3 spectral structure extends to atomic physics, where lambda_k = dim(SU(k+1)) determines the hydrogen atom shell structure and the periodic table. - Hostile reviewer corrections: Eq. 20 computational procedure clarified (F_n are outputs, not free inputs). Abstract parameter claim corrected to "two NLO coefficients identified from species counting." M_W tree-level corrected to 77.8 GeV (3.2%). Top mass updated to PDG 2024 (172.57 GeV). Analogue gravity citation added (Barcelo, Liberati, Visser 2005). Historical table condensed. Now 9 documented failures. Developed with AI assistance (Claude Opus 4.5/4.6 by Anthropic for computation and drafting; DeepSeek for independent peer review). All physical reasoning, model construction, and interpretation are the author's.