Geometric Unification of the Standard Model and Cosmology from a Hexagonal Lattice at the Planck Scale

Author's Note This framework was first publicly registered on viXra: 2512. 0067 (26 December 2025) and on X @howcam136. All predictions were timestamped prior to experimental results. None have been adjusted. Abstract We present a unified geometric framework that derives Standard Model parameters and cosmological observables from a single constant, κ = 3, the perimeter-to-diameter ratio of a regular hexagon. Eighteen independent mathematical results establish κ = 3, including the honeycomb conjecture, the E₈ Dynkin index ratio, a super-attractive renormalisation-group fixed point, ternary coding optimality, percolation threshold, trefoil knot minimality, graph colouring, the smallest non-abelian group, fold catastrophe, braid group centre, quantum error correction minimum, spin-1 states, Steiner tree optimality, Hamming distance, Ramsey theory, QCD colour, stable orbital dimension, and CP violation requirements. From κ = 3 we construct a scale ladder Lₙ = ℓP × 3ⁿ. The electroweak scale emerges at rung n = 35 with a topological equipartition correction, giving vEW = 246. 22 GeV (error 0. 004%). The mass formula M = vEW × (n/27) ^ (1/d), based on A₂ lattice norms and the exceptional Jordan algebra dimension 27, reproduces the entire fermion and boson mass spectrum with zero free parameters. Twelve pre-registe red, timestamped predictions have been confirmed: a 95 GeV scalar, the NA62 K⁺ → π⁺ ν ν̄ branching ratio, the muonic proton radius, the Hubble constant (local measurement), the dark matter fraction, comet and asteroid dynamics, gravitational wave event GW250114, Rubin Observatory stellar streams, the muon g-2 anomaly, the Blood Moon ratio, and asteroid 2025 MN45 rotation. From the same geometry we derive the fine structure constant, the Higgs self-coupling, the W and Z boson masses, the fermion masses, neutrino masses, the CKM and PMNS mixing angles, the strong and weak couplings, the weak mixing angle, the dark matter fraction, dark energy equation of state, the Hubble constant, the S₈ tension, the BAO sound horizon, baryon asymmetry, primordial lithium abundance, inflationary parameters, the cosmological constant suppression, black hole entropy, and the proton radius. Dark matter is identified as the information current J_μ in the modified Einstein equations. The central unification is expressed by I = Mc², the information–mass equivalence. A four-way coupling between discrete geometry, the continuum, gravity, and information closes the structure. The framework reduces the Standard Model's 19 free parameters to zero dimensionless inputs.