Nuclear Physics · April 2026
The Four Forces and the Nucleons
The proton is a single standing-wave configuration of 94 ℚ-rational eigenmodes on a 4D 600-cell, sharing the E₈ root system with its Galois twin, the neutron. The four forces emerge from the geometry of this object.
Key Results
Four forces from one polytope
The proton and neutron are not separate objects but Galois conjugates on the 600-cell — the same standing-wave architecture viewed through two algebraic embeddings. The four fundamental forces are four distinct geometric operations on this single polytope, and gravity emerges as a residual spectral mismatch rather than a fundamental interaction.
1
The proton and neutron are Galois conjugates on the 600-cell — one object viewed through two algebraic embeddings of ℚ(√5).
2
The four fundamental forces are four distinct geometric operations on the same polytope: D₄ triality, icosian ring multiplication, Galois involution, and bridge-line projection.
3
Gravity emerges as the residual spectral mismatch when the 600-cell is embedded in E₈ — not a fundamental force but a geometric shadow.
4
The gravitational coupling constant is derived from the icosian ring structure without free parameters.
Kill Conditions
K1: Gravitational coupling derivation deviating from measured value by more than 1% — E₈ embedding falsified
K2: Discovery of a fifth force not accommodated by the 600-cell geometry — polytope model falsified