The Jordan Eigenvalue Mass Programme: Fermion and Boson Masses from Cell Combinatorics -- Paper 4

The Entanglement-Driven Cosmological Expansion (EDCE) framework treats spacetime as an information storage medium built from 4-qubit Bekenstein cells on a triangular lattice. Paper 3 derived thirteen Standard Model quantities from this lattice at the percent level or better. This paper presents the algebraic machinery behind those predictions: the Jordan eigenvalue mass programme. A topology matrix T and a flavour matrix F – both elements of the exceptional Jordan algebra J3(O) – encode the cell geometry and the sector-specific information budget. Their Jordan product T ◦F yields three eigenvalues per fermion sector whose ratios are the inter-generation mass ratios. Applied to the four sectors (charged leptons, down quarks, up quarks and neutrinos) the method reproduces all twelve Standard Model fermion masses from lattice combinatorics with a worst-case deviation of 2.15% and a best-case deviation of 0.01%. The structural parameters (fp, sw, fs) controlling the flavour matrix are assessed honestly: one sector (charged leptons) is obtained from the cell geometry before comparison with data; two sectors (down quarks and neutrinos) have parameters identified as simple fractions of lattice constants; one sector (up quarks) has parameters locked to sub-percent accuracy but with an incomplete derivation chain. The programme extends beyond fermion masses. The Weinberg angle sin2θW = 3/13 is derived from a bootstrap fixed point (0.19% accuracy). The Higgs boson mass mH = (v/2)(1+3αs sin2θC) = 125.18 GeV agrees with experiment to 0.06%. Three PMNS mixing angles follow from a Wigner-Eckart hierarchy with sub-0.25% accuracy. All three CP-violating phases are determined by the lattice geometry, including θQCD = 0 (providing a structural mechanism consistent with the vanishing of the strong CP phase without requiring an axion). The Planck mass is derived as MPl = v×3R4 (1.1% accuracy) and three fermion generations are the maximum consistent with critical-line zeros of the lattice zeta function. The paper also establishes a hierarchical architecture in which the observable universe is one of twenty holographic projections within an SU(4) domain, sustained by a timeless substrate from an unstable SU(5) parent. Proton stability is absolute: the SU(4) gauge ceiling and the self-dual partition at Hamming weight 2 prohibit baryon-number violation topologically rather than by energy threshold. The framework has four combinatorial inputs (Tr = 83, Nq = 4, Ngen = 3, α−1 = 137), all traced to the Bekenstein cell geometry and the Jordan cascade levels. From these inputs the programme produces over twenty quantitative predictions with no fitted or adjustable parameters.