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 the
Riemann zeta function around the Guth-Maynard bound A(sigma) <= 15/(3+5 sigma).

First, the classical zero-detection pipeline is formalized as an explicit
two-player length-selection game and solved exactly. The Ingham, Huxley,
Guth-Maynard and Jutila exponents all arise as closed-form straddle-closure
values, each accompanied by a machine-checkable dual certificate. For the
stated 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 the
diagonal edge of the certificate is matched by an explicit example whenever
M^(2-2 sigma) <= T.

Second, an entropy ledger shows that within the Guth-Maynard Fourier
framework every additional leg of the cyclic Gram moment costs a factor
T_1^(1/3) at both critical configurations, which closes the r >= 4 route.

Third, the extremal rational-concentration scenario is verified to be a
simultaneous fixed point of four independent constraint families, including
a Rudin-Chang bound over the Q-dissociated log-prime system; a universal
height law B = T_1^(1/3) emerges across the whole range.

Finally a single Alignment Hypothesis on linear-form correlations of
mollified Möbius coefficients is isolated and its exact price computed: it
yields A(3/4) <= 420/191 but leaves the uniform exponent 30/13 invariant.

All exponent arithmetic is verified in exact rational arithmetic. No new
unconditional zero-density exponent is claimed; the contribution is the
certification of optimality for the stated inputs, the barrier map, and the
conditional results. Verification code is available at the repository linked
below.