Riemann zeros seen from the Zeta Atlas. Explicit formulas on Ford circles, an inverse problem, and a dilation correlation at half height

The non-holomorphic Eisenstein series on the modular surface has its resonances exactly at half the zeros of the Riemann zeta function. This paper reads those zeros through the geometry of the Zeta Atlas and finds three things. The zeros measure Ford circles. The total length of the Ford-circle arcs above a horizontal line equals an elementary trend plus a sum over the zeros. If the remainder decays like y^{3/4−ε}, the Riemann hypothesis follows. Numerically it scales like y^{3/4} down to y = 5·10⁻¹⁰. The zeros can be computed, not predicted. Four consecutive Laurent coefficients at z = i give the first zero in closed form, and Prony’s method recovers it to 82 decimals. The error of the closed formula is exactly the imprint of the second zero, and its convergence rate is itself a check of RH for the first zero. A new correlation: zeros cluster at half the height of other zeros. The excess of zeros around γₙ/2 is predicted without free parameters from prime squares through Landau’s formula. With 4467 zeros the measured excess is +0.0280 ± 0.0026, against +0.0281 predicted, and the control dilations give zero. A selection rule follows: for a Dirichlet L-function the half-height coupling depends only on χ². It predicted, and the data confirm, a sign reversal for the quartic character mod 5. Every statement carries a status label, from proved to numerical to conjecture, and every table can be reproduced from the stated formulas. The research was carried out with the assistance of an AI system (Claude, Anthropic); the methodology and the verification protocol are described in the paper. The Zeta Atlas: The Zeta Atlas