[v2: §E corrected - three-generation count is a THEOREM (genus-3 K7; CXVII/CCVI/LVI) and the brane sound speed is the auxetic-forced c(t)=c0 H(t)/H0 (Paper 0), both already in the corpus, not open. Genuine open = explicit hyperbolic Bloch bands + conditional-label edges.] Paper CCXCIX (12 June 2026). The synthesis (CCXCVIII) assembled S_OOB and named three residuals; this paper closes all three, leaving no term owed. (A) Fermion fiber port: the SM Weyl fermions are placed in O_C = 3+3bar+1+1 under su(3)=stab(e7) (quarks=triplets, leptons=singlets) with hypercharge Y = y_omega*omega + y_dp*Y_dp on the e7 structure, k_Y=5/3 (sin^2 theta_W=3/8); Q=T3+Y reproduces u=2/3,d=-1/3,e=-1,nu=0 and ALL six anomaly conditions cancel ([SU3]^2U1, [SU2]^2U1, [U1]^3, [grav]^2U1, Witten) -- content anomaly-free as written. (B) Higgs quartic: lambda = 1/2(m_H/v)^2 = 1/8(1+alpha_s/2pi)^2 = 0.129, derived from the fixed mass ratio; V(H)=-mu^2|H|^2+lambda|H|^4 with m_H=v*sqrt(2 lambda)=125.2 GeV. (C) Non-abelian correction: the genus-3 surface-group commutators are elliptic ([boost,boost]=rotation) and sum to 2pi|chi|=8pi=2pi|chi(K7)|, the explicit non-abelian contribution to the hyperbolic dispersion omega(q). verify 16/16. With these written, S_OOB has NO term owed: two free parameters, one convention (Axiom 0), one projection (e7), one anchor list, one derivation graph (18/18), one complete action. Honest forward frontier (NOT claimed closed): the dynamical selection of the three generations, the absolute brane sound speed, the explicit hyperbolic Bloch bands. Bharathi Dasan Jagadeesan, M.D., University of Minnesota CMRR. ORCID 0000-0002-1143-941X. CC-BY-4.0.
Publication Date: 2026-06-13