mertens-stack.md

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Mertens stack

  • 2026-08-28 [Verified] Weighting the Farey stack by mu(n) renders a Mertens-type sum at every node, Sum_{k <= N/b} mu(kb) at a/b and M(N) at b = 1, and the log-space power spectrum of M(x)/sqrt(x) shows the first eight nontrivial zeta zeros, detected at 13.94, 20.90, 24.97, 30.19, 32.52, 37.74, 40.64, 42.97 against 14.1347, 21.0220, 25.0109, 30.4249, 32.9351, 37.5862, 40.9187, 43.3271, errors 0.04 to 0.42 inside one bin of width 0.5806; the zeros are known to far beyond any precision a moire can reach, so this is a rendering and not a measurement. Witness: lab/py/mertens-meter.