A three-tail comparison for Bernoulli sums with six equal exceptional weights

Let U be binomial with parameters (6, p) and V be an independent binomial random variable with parameters (n, p), where n >= 1, a, b >= 0 and 6a + nb = 1. This preprint gives a candidate proof that P[aU + bV > p] >= p for 0 < p < 1/3, and that the non-strict event has probability at least p for 0 <= p <= 1/3, with both weight orders included. The specialized step compares three conditional tails: retaining the central-tail excess reduces a Gaussian lower bound to an affine function of one tail. Elementary coefficient bounds exceed the explicit approximation error for n >= 200. Capacity minimization, small-ratio estimates and two complete exact calculations over 1,388,365 residual endpoints complete the proposed argument. The smaller-class cases use the earlier one- through five-exceptional candidate results. Central-tail retention, normal comparison and capacity propagation are inherited methods; the contribution is their specific six-exceptional comparison and the resulting complete restricted family. The theorem and its analytic and inherited inputs remain provisional candidate results. The exact calculations verify finite probabilities and do not by themselves establish the general reductions or cited proofs. No arbitrary-multiplicity theorem or uniform positive surplus for the original weights is claimed.