We study the nucleon as a topological soliton of the FOX scalar field. The central result is the algebraic identity m_φ · rₙ = 4, exact and independent of the field amplitude ΦMAX, which simultaneously encodes Newton's constant (Gₑff = G, Branch A), the stasis value (φₘ = 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, φᵢn = exp (−4π) (under stated conditions), φₘ (p+q) = 1 (Conjecture T9), and the quarter-wave identity λᵣes/rₙ = π/2. (ii) The Chern-Weil instanton action of the T (p, q) bundle gives Sᵢnst = π (p+q−1), motivating φᵢn = exp (−Sᵢnst) by analogy with Yang-Mills instanton physics. (iii) The resonance conjecture T9 (φₘ = 1/ (p+q) ) is supported at 9% accuracy. (iv) The BPS parameter β = (m_φ/mW) ² = 200/π ≈ 63. 7 is exactly constrained by three independent results. All results conditional on H4a are explicitly labelled.
Adrien le Hardy de Beaulieu (Sat,) studied this question.