Three Integers and a Mass: Deriving the Standard Model Input Set

Paper 1 derived 23 Standard Model parameters from four inputs (α, m_e, m_µ, Λ_tube) and three topological integers (p = 2, q = 1, k = 3). We show that three of those four inputs —α, m_µ, and Λ_tube — are themselves derivable from the three topological integers (p = 2, q =1, k =R/r =3) and a single measured mass m_e. The fine-structure constant follows from Skilton’s integer right triangle (88,105,137), whose generators (11,4) we identify as null worldtube (NWT) quantum numbers: ps = 2k +p^2 +q^2 = 11, qs = p^2 = 4. The muon mass follows from the Koide formula with topology-determined angle θK = (6π+2)/9. The proton mass — and hence Λ_tube — follows from the Lenz formula m_p/m_e = 6π^5, now structurally explained as 2k × π^(p^2+q^2). The complete derivation chain from (2,1,3) + m_e to all 23 SM parameters requires no free parameters beyond one mass scale.