GW Echo Time Ratio

τ-Formula

t₊/t₋ = ι_τ⁻² ≈ 8.57

Derivation

The proton charge radius is set by the Compton wavelength of the proton, scaled by the $T^2$ fiber geometry:

The factor $4 = 2^(τ^3)-1 = 2^2$ counts the two independent charge-weighted $T^2$ winding directions ($2$ polarities $×$ $2$ lobes); the proton charge radius is the Compton wavelength times the number of charged pathways on $L$.

Comparison with the CREMA muonic hydrogen measurement:

This resolves the proton radius puzzle (pre-2019 CODATA value $0.8768\,fm$) by selecting the muonic hydrogen value as correct.

Source

This prediction is derived in the Physics Ledger (Chapter 47 — hyperfine-structure), Books IV–V of Panta Rhei.