Conditional Derivation of the Alpha-Ladder Formula

We give an explicit conditional derivation of the Alpha-Ladder formula G = (φ²/2)(1 + 3 α_EM² + (φ/2) α_EM³) α_EM²¹ ℏc / m_e² from four physical hypotheses:(A1) a Fayet–Iliopoulos / species tower whose leading count is N_sp = α_EM⁻²¹;(A2) saturation of the species bound M_Pl² = N_sp M_sp²;(A3) a species-electron bridge M_sp = m_e √(nE₈) / d_τ = m_e √2 / φ; and(A4) moduli stabilisation at the (1)⁶ Gepner point of the K3 moduli space with specific quadratic and cubic OPE corrections. None of these assumptions is proved here. The refined A3 absorbs the Fibonacci/E₈ prefactor φ²/2 directly into the species-scale identification, so the prefactor is no longer an independent assumption. The vanishing of the α_EM¹ coefficient is demoted to a Proposition derived from SL(2, ℂ)-invariance of the vacuum. The quadratic and cubic coefficients 3 and φ/2 retain the status of assumptions rather than propositions, because the supporting computation admits normalisation choices that re-input the answer — a status we declare openly. The paper's deliverable is the implication (A1) ∧ (A2) ∧ (A3) ∧ (A4) ⇒ Alpha-Ladder, not a first-principles derivation of the formula. The status of each assumption is tracked against the conjectures and no-go results of the companion theorem paper.