Exact Certificates, Moment Ledgers, and a Three-Wall Barrier Map for Zero-Density Estimates at the Guth-Maynard Frontier

We study the exponent-level structure of zero-density estimates for theRiemann zeta function around the Guth-Maynard bound A(sigma) <= 15/(3+5 sigma). First, the classical zero-detection pipeline is formalized as an explicittwo-player length-selection game and solved exactly. The Ingham, Huxley,Guth-Maynard and Jutila exponents all arise as closed-form straddle-closurevalues, each accompanied by a machine-checkable dual certificate. For thestated input library the value 15(1-sigma)/(3+5 sigma) is exactly optimal on[7/10, 39/50], Proposition 12.1 of Guth-Maynard is provably neutral, and thediagonal edge of the certificate is matched by an explicit example wheneverM^(2-2 sigma) <= T. Second, an entropy ledger shows that within the Guth-Maynard Fourierframework every additional leg of the cyclic Gram moment costs a factorT_1^(1/3) at both critical configurations, which closes the r >= 4 route. Third, the extremal rational-concentration scenario is verified to be asimultaneous fixed point of four independent constraint families, includinga Rudin-Chang bound over the Q-dissociated log-prime system; a universalheight law B = T_1^(1/3) emerges across the whole range. Finally a single Alignment Hypothesis on linear-form correlations ofmollified Möbius coefficients is isolated and its exact price computed: ityields A(3/4) <= 420/191 but leaves the uniform exponent 30/13 invariant. All exponent arithmetic is verified in exact rational arithmetic. No newunconditional zero-density exponent is claimed; the contribution is thecertification of optimality for the stated inputs, the barrier map, and theconditional results. Verification code is available at the repository linkedbelow.