comprehensivetheory.org · R-Cube Geometric Model

Gluon Exchanges
in the Restricted Cube

U1 × [U2×SU(2)] × [U3×SU(3)] | Я ⟩

RḠ · GB̄ · BR̄ gluon exchanges in proton · Cornell V(r) = −(4α_s/3r) + σr · σ ≈ 0.18 GeV²

⬡ THREE-STEP ALGEBRAIC PROTON MODEL

|Ψ₀⟩

Ground · Solved

──Alg₁──▶

|H_udu⟩

State A

──Alg₂──▶

|H_uud⟩

State B

──Alg₃──▶

|H_duu⟩

State C

────────▶

↺ ∞

Phase 1: R U R' F' R U R' U' R' F R2 U' R' · RḠ gluon exchange · udu

Phase 2: R' U L' U2 R U' R' U2 R L · GB̄ gluon exchange · uud

Phase 3: L' R' U2 R U R' U2 L U' R R U R2 F' R U R U' R' F R U' R' · BR̄ → return to |Ψ₀⟩ · duu

Alg₁ · Alg₂ · Alg₃ = Identity · uud = TTV⊗TTV⊗VTV → net charge +1 · RGB corner: e⁺ = TTT · MCY corner: ν = VVV

Planck

GUT

EW Scale

Nuclear/QCD

Hamiltonian

Astrophysical

Cosmological

        Hamiltonian classical scale:

        GR effects ≈ 10⁻²¹ s/s

        QM governs electronics

        Macroscopic mechanics: classical