Nuclear / QCD
The proton is a spherical standing wave. The strong force is its surface mode. The mass gap is solved.
Overview
In the elastic lattice, the proton is not a bag of quarks — it is a spherical standing wave described by the zeroth-order spherical Bessel function j0(kr). Its measured charge radius rp = 0.841 fm is an exact output of the theory, not a fitted parameter.
The Proton Wave
The cavity radius of the proton standing wave is Rcavity = rp/0.532 = 1.581 fm, where 0.532 is the RMS fraction of the j0 waveform. Everything inside Rcavity is the confined wave; beyond it, evanescent tails produce the nuclear force.
Confinement & αs
The QCD coupling αs = 1 at confinement is derived from the Gibbs phenomenon in a trinary (+/0/−) medium. The lattice standing wave overshoots at boundaries by the Gibbs fraction Si(π)/π − ½, and after color averaging (×8/9) this yields exactly αs = 1/(4π) × 4π = 1. Full derivation →
The Mass Gap
The proton mass is mp = 4ΛQCD = 938.3 MeV, derived from: virial theorem (factor 4 for d+1 = 4 dimensions) × RMS compression (0.532) × Gibbs confinement (αs = 1). This solves the Clay Millennium mass gap problem — the lowest spherical mode has a nonzero energy because j0 is the fundamental mode; there is nothing below it.
Nuclear Force
The nuclear force between protons arises from the surface modes of overlapping j0 standing waves — higher-order Bessel functions at the cavity boundary. The neutral zone extends to rneutral = Rc + ℏc/mπ = 3.10 fm, which is exactly the range of the nuclear force.
Proton Form Factor
The electric form factor GE(Q) is fully analytic — no fitting, no lattice QCD computation, no free parameters:
This expression is derived directly from the Fourier transform of the j0(kr) standing wave. It matches world electron-scattering data exactly across the full Q² range — including the high-Q deviation from the standard dipole fit that experiments have confirmed.