FOX Theory (Branch B): The Nucleon as Torus Knot T(2,3)

We study the nucleon as a topological soliton of the FOX scalar field. The central result is the algebraic identity m_φ · r_n = 4, exact and independent of the field amplitude Φ_MAX, which simultaneously encodes Newton's constant (G_eff = G, Branch A), the stasis value (φ_m = 1/5, postulate H0), and the residual boson mass.Under working hypothesis H4a — that the nucleon is a torus knot T(p,q), motivated by π₃(SO(3)) = ℤ but not derived from the equations of motion — T(2,3) is established as the unique admissible torus knot satisfying proper closure (gcd = 1), three-colorability (ℤ₃), and minimal toroidal complexity (p+q minimal). Under H4a, four exact invariants are derived: (i)the self-linking number sl(T(2,3)) = 2 in the Seifert framing, φ_in = exp(−4π) (under stated conditions), φ_m(p+q) = 1 (Conjecture T9), and the quarter-wave identity λ_res/r_n = π/2. (ii)The Chern-Weil instanton action of the T(p,q) bundle gives S_inst = π(p+q−1), motivating φ_in = exp(−S_inst) by analogy with Yang-Mills instanton physics. (iii)The resonance conjecture T9 (φ_m = 1/(p+q)) is supported at 9% accuracy. (iv)The BPS parameter β = (m_φ/m_W)² = 200/π ≈ 63.7 is exactly constrained by three independent results. All results conditional on H4a are explicitly labelled.