The asymptotic binary Delsarte LP value is strictly below the second MRRW bound

Let R_LP(δ) be the asymptotic value of Delsarte's linear program for binary codes of relative distance δ, and let M₂(δ) be the fully optimised second McEliece–Rodemich–Rumsey–Welch exponent. The equality of these two quantities has been proposed as the endpoint of a programme for determining the Delsarte optimum and was later recorded as a conjectural limitation of the method. We prove that the equality is false at every nontrivial distance. More precisely, for every 0 < δ < 1/2, R_LP(δ) ≤ κ_bin(δ) := min{κ_H(δ), κ_CW(δ)} < M₂(δ). The two variational exponents on the right are those of the binary projection kernels introduced in Chapter 2 of "Ten Advances in Mathematics and Theoretical Computer Science" (OpenAI, 2026). There they are evaluated by summing the kernels over a code. We read the same kernels in the dual direction: a trace Cauchy–Schwarz estimate gives the positive constant coefficient needed to bound the value of the Delsarte program itself. For the constant-weight branch we also give a complete finite Rodemich–Delsarte lifting. It averages a Johnson kernel over all affine layers, handles arbitrary Hamming thresholds, including odd ones, and yields the factor 2^n / C(n,w) before passage to the exponent. The projection kernels, the constant-coefficient estimate, the lifting mechanism and the strict comparison κ_bin < M₂ are attributed inputs; the contribution is their combination at the level of the LP optimum and its consequences. To our knowledge, this is the first global strict separation of the asymptotic binary Delsarte LP value from the fully optimised second MRRW bound. It refutes Conjecture 6 of Kalai (2024) and the equality targeted by step 1 of Navon–Samorodnitsky (2005, §1.2). Two complete standard-library drivers reproduce finite Hamming- and Johnson-scheme consistency checks; neither is used in place of an analytic proof. The broader methodological message is that present AI systems can generate highly plausible mathematical proof narratives, but they cannot yet be trusted to settle deep open problems without independent human verification. In this case, the human audit remains undefeated.