Structural Correspondence and Conditional No-go Results for the Alpha-Ladder Program

We isolate the mathematically rigorous content of the Alpha-Ladder correspondence from its physical program. The paper is organised into three strict tiers. The structural core consists of one theorem and two propositions: (A) a conformal-subalgebra and coset proposition placing the Fibonacci RCFT inside the K3 worldsheet CFT at the (1) ⁶ Gepner point via the chain G₂, ₁ ⊂ SO (7) ₁ ⊂ SO (12) ₁, while explicitly not claiming a full tensor-factor equivalence of the K3 CFT; (B) a lattice-theoretic rank theorem for algebraic K3 surfaces of Picard number 1, giving rank TX = 21; and (C) a dictionary proposition exhibiting the Alpha-Ladder formula as the substitution instance of an algebraic identity in K3/Fibonacci invariants. The no-go tier consists of one finite-range obstruction and four no-go theorems, ruling out the scanned STUracetrack range, the single-modulus racetrack class under the Planck/string hierarchy constraint (upgraded in this revision from a scan-based argument to an analytic bound that holds independently of the flux/condensate quantisation), BCOV F₁-exponentiation on K3, the AGN one-loop Einstein-term threshold on K3, and the PF₁₁ F-theory hypercharge identification; a sixth negative result (four standard UV classes tested jointly: LVS, heterotic M-theory, KKLT, warped throat) is given as a proposition at qualitative rigour rather than as a no-go theorem. The conjectural tier states three open program-level conjectures; these use the species-scale interpretation Nₛp ∼ αEM⁻²¹ as a hypothesis, not as an input to any theorem-tier claim. Every statement is labelled as Theorem, Proposition, Lemma, Corollary, Computation, No-go, Conjecture, Definition, or Remark; no theorem-tier claim depends on unstabilised moduli or on a species bound. The paper does not claim a first-principles derivation of Newton's constant.