The Standard Model from Planck-Scale Information Structure: Particle Spectrum, Fermion Masses and Cosmological Observables from Cell Combinatorics -- Paper 3

We reproduce the Standard Model particle spectrum, gauge structure, coupling constants, fermion masses, mixing matrices and cosmological parameters from the Planck-scale triangular cell of the Entanglement-Driven Cosmological Expansion (EDCE) framework, using four combinatorial inputs (Tr = 83, Nq = 4, Ngen = 3, α−1 = 137) with no fitted or adjustable parameters. A single geometric constraint, nP + nB1 + nB2 = 4 qubits per cell, generates the four canonical qubit partitions (1-3, 2-2, 3-1, 0-4) whose lattice combinatorics reproduce the gauge group SU(3)c×SU(2)L×U(1)Y plus gravity, the first-generation fermion table with correct charges and colour multiplicities, an exact confinement theorem, three fermion generations from the three edges of the triangle and the Weinberg angle sin2θW = 1/3 at the unification scale from pure qubit counting. The same cell geometry assigns quantitative values to every dynamical observable. The three gauge couplings are fixed by qubit-partition efficiencies: α−1 = 137 (bare) from cell counting on the 1–3 lattice, αs(MZ) = 3/26 ≈0.115 from the Weinberg bootstrap and sin2θW = 3/13 at the Planck scale, running to 0.231 at MZ on a standard one-loop trajectory. The CKM and PMNS mixing matrices and all three CP phases (δCKM = 3π/8, δPMNS =−π/2, θQCD = 0) follow from cross-pattern geometry and C3 trimer symmetry. The Higgs quartic coupling λ= 1/8 and the tree-level mass mH = v/2 = 123.1 GeV (124.3 GeV at one loop; experiment 125.25 ±0.17 GeV) are derived from bandwidth saturation. The complete fermion mass spectrum follows from Koide-type circulant matrices whose phases obey δ−120◦ = θC/Nc, reproducing nine quark and lepton masses with sub-percent to few-percent accuracy. A single ratio R= Tr×α−1 = 83×137 = 11,371 controls three independent hierarchies: the gauge hierarchy MPl/v= 3R4 (+1.15%), the Hubble constant H0 = 3/4 MPl/R15 = 72.15 km s−1 Mpc−1, and the cosmological constant ρΛ/M4 Pl ∼R−30 ∼10−123. The aeon saturation constraint fixes the last energy scale v, closing the framework with no additional adjustable inputs. Over thirty Standard Model and cosmological observables are reproduced from a single geometric object – a triangular Planck-scale cell encoding four qubits – with thirteen at percent-level accuracy and nine below 2%. Falsification criteria include the absence of step-like features in H(z), detection of proton decay or a fourth fermion generation.