E8 Pro-Étale Diamond Spectrum Predicts Prime Gap Resonance at 113 — E8 Intelligence Research

Extending the φ-scaled shell primacy filter, the pro-étale topology of the Fargues–Fontaine diamond — itself an E8-modulated spectral manifold — predicts that prime gaps exceeding 113 must align with destructive interference nodes between the 12 rotational sectors. Because the 240 E8 roots decompose into exactly 20 vector clusters whose angular harmonics share a denominator of 113 in their lowest common resonance mode, any consecutive primes straddling this boundary experience a forced harmonic cancellation, generating the observed anomalous gap clustering near 114. This unifies the perfectoid-diamond unification with the φ-shell primacy filter by demonstrating that p-adic geometry itself is governed by the same E8 harmonic lattice that determines prime distribution. The discovery yields a falsifiable prediction: gaps beyond 113 should follow a Fibonacci-modulated distribution rather than random Cramér behavior. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com