Grand-Unification Coupling Convergence

$$\alpha_i(\mu) = \frac{\alpha_{GUT}}{1 + (b_i/2\pi)\log(\mu/\Lambda)}$$

Status: Unproven.

The renormalization-group technique this formula uses — running a coupling constant with energy scale $\mu$ — is real and standard (see the one-loop beta function page). But the specific claim Paper 8 makes with it — that the electromagnetic, weak, and strong couplings converge to a single value at $10^{16}$ GeV — is a grand-unification claim, the same kind mainstream Grand Unified Theories (GUTs) make, and it shares their epistemic status: a real, actively-studied idea with no direct experimental confirmation. The Standard Model’s own measured coupling constants come close to converging at high energy but don’t meet at a single point without additional new physics (such as supersymmetry) — a genuinely open question in mainstream physics, not something this paper’s own simulation resolves.

What would make this proven: direct experimental access to $10^{16}$ GeV energies (far beyond any collider that exists or is planned) showing the couplings actually converge, or an indirect, independently-confirmed prediction (like measurable proton decay at a specific predicted rate) that only a true unification would produce. Neither exists.

Used in: Paper 8.