Abstract For a century, quantum mechanics and general relativity have resisted unification. This paper shows that both theories are two limits of a single geometric constant: κ = 3, the perimeter‑to‑diameter ratio of a regular hexagon. At the Planck scale, spacetime is a discrete, regular hexagonal A₂ lattice. Coarse‑graining this lattice by powers of 3 defines a scale ladder Lₙ = ℓP × 3ⁿ, and the geometric constant runs with the ladder rung: κ (n) = π − (π−3) ·3⁻²ⁿ. The measured constants of nature – ħ, G, α, particle masses, coupling constants – are not fundamental; they are averages over the transition from the discrete hexagon (κ=3) to the continuum circle (π). The true bottom constants are offset from the measured values by the holonomy deficit Δ = (π−3) /π ≈ 0. 04507. This deficit appears in every major anomaly of modern physics: the proton radius puzzle, the Hubble tension, the dark matter fraction, the dark energy residual, the baryon asymmetry of the universe, the muon g‑2 anomaly, and the 95 GeV scalar excess. The framework derives all 19 free parameters of the Standard Model from first principles, leaving no dimensionless free parameters. No equation of Planck, Einstein, Schrödinger, Dirac, or Hawking is changed. Their constants are understood as averages over a geometric transition they had no way of knowing existed. The framework reproduces the measured constants of the Standard Model and accounts for the principal anomalies of modern physics from a single geometric input.
Cameron Howlett (Mon,) studied this question.