E105: Mertens M(x): scaling views

E105 hero

E105: Mertens M(x): scaling views

E105 hero

E105: Mertens M(x): scaling views

Tags: number-theory, quantitative-exploration, visualization, mobius, summatory, open-problems

Highlights

  • Focused numeric experiment with a small set of figures.

  • Parameters saved to params.json for reproducibility.

  • Defaults are chosen, so the experiment remains feasible for the CI “slow” suite.

What is computed

  • Plot M(x)=∑_{n≤x} μ(n) and rescalings such as M(x)/√x.

Notes

  • This page summarizes the intent; see the generated report.md in out/ for concrete outputs.

Published run snapshot

If this experiment is included in the docs gallery, include the published snapshot (report + params).

Artifacts

  • figures/fig_01_mertens_M.png

  • figures/fig_02_mertens_rescaled.png

  • params.json

  • report.md

Notes

  • max |M(x)| on 1..N: 134.0

  • Random-walk-like oscillations appear across scales (visual heuristic).

params.json (snapshot)
{
  "n_max": 200000,
  "stride": 5
}

References

  • See the arithmetic-functions background pages in docs/background/.