Superstring-Fabric Spacetime (SFS):Geometric Derivation of the Inner String Scale ℓS′,the Instanton Parameter S, and the Proton Charge Radius Rp

The SFS canonical reference (DOI: 10.5281/zenodo.20608900) treated three quantities as external inputs: the inner string scale ℓS′ = Rp = 0.840 fm (proton charge radius), the instanton parameter S = 0.035198, and the PT -sector vortex penetration depth ℓ(q) S = ℓS /2. This companion paper derives all three from SFS geometry alone, without any quark or lepton mass input. The main results are: (1) the factor 5/18 in S is proven to equal Y 2 Q + (T 3)2, a pure hypercharge identity; (2) the gauge kinetic coefficients γkin = ℓ2 S /(4π2) and βkin = ℓ2 S /(8π2) are derived from the U (1) vortex quantization condition and the Weinberg angle ratio; (3) the London depth λv = π√2ℓS is derived from the PA-sector flux quantization; (4) the leading-order instanton parameter is S = 5/(36π), a pure geometric prediction; (5) the proton charge radius satisfies Rp = √Fcore ℓS′ = 0.7773 ℓS′ where Fcore = 0.6041 is derivedfrom the SFS three-string proton geometry; (6) the NLO Ginzburg-Landau correction gives RNLOp = 0.838 fm (−0.25% from experiment); (7) ℓ(q) S = ℓS /2 is derived from the second normal mode of the PT torsion sector. All results carry explicit epistemic verdicts (PROVEN / CONDITIONALLY TRUE / OPEN PROBLEM). No derivation steps are skipped