G–α Bridge Identity

τ-Formula

α_G = α¹⁸ · √3 · (1 − 3α/π)

Derivation

a_0^barea_0^dress \;=\; 1 - ι_τι_τ \;=\; κ_Dκ_B \;≈\; 2.378,

where $κ_D = 1 - ι_τ$ is the gravitational coupling and $κ_B = ι_τ^2$ is the baryonic coupling. The ratio is the square root of the holonomy-to-baryon coupling ratio—the same ratio that governs the Silk damping scale (Chapter (ch:book5-ch56-falsification-pack)).

This unification is significant: the same algebraic structure ($κ_D/κ_B$) that determines galactic dynamics also determines the CMB damping scale. In $Λ$CDM, these are unrelated phenomena. In Category $τ$, they share a common origin in the coherence kernel.

Source

This prediction is derived in the Numerical Physics Ledger (Chapter 63 — dark-sector), Books IV–V of Panta Rhei.