mertens-meter

• Weights the Farey stack by mu(n), the node a/b carrying sum_{k <= N/b} mu(kb), and counts how often that equals M(floor(N/b)).
• Checks the global readout sum_{n <= x} M(floor(x/n)) = 1 at every x through 20000.
• Builds M(x)/sqrt(x) for x = 1..50000 from a linear Mobius sieve, resamples it uniformly in log x on 8192 points, Hann-windows it and takes the real FFT power spectrum.
• Reads the axis as gamma = 2 pi f, keeps local maxima above three times the band median over 8 < gamma < 55, and matches each of the first eight nontrivial zeta zeros to its nearest peak.

RUN

uv run python research/lab/py/mertens-meter/mertens_meter.py

Under a second. Domain is the source domain: N_mertens = 50000, N_stack = 200, N_readout = 20000, 8192 log samples.

WITNESSES

• farey.md:128 to farey.md:135, the eight rows in order: 14.1347 | 13.94 | 0.20, 21.0220 | 20.90 | 0.12, 25.0109 | 24.97 | 0.04, 30.4249 | 30.19 | 0.23, 32.9351 | 32.52 | 0.42, 37.5862 | 37.74 | 0.16, 40.9187 | 40.64 | 0.27, 43.3271 | 42.97 | 0.36
• research/claims/:53 the readout sum_{n <= N} M(floor(N/n)) = 1 holds at every N through 20000, zero breaches
• research/claims/:346 detected 13.94, 20.90, 24.97, 30.19, 32.52, 37.74, 40.64, 42.97, errors 0.04 to 0.42

NOTE

• The bin width is 0.5806, so every error above sits inside one bin: this is a rendering, not a measurement.
• farey.md:117 calls the node brightness M(floor(N/b)) and farey.md:118 marks that Proved; the generator sums mu(kb), and the two agree at only 64 of 200 denominators. Repeated at farey.md:233, research/claims/:53 and research/claims/:346.