E116: Gram points and zero-counting heuristics

E116 hero

E116: Gram points and zero-counting heuristics

Tags: analysis, model-checking, visualization, riemann-zeta, gram-points, zeta-zeros

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

  • Compare Gram-point heuristics and simple zero-counting diagnostics over a finite range.

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_zero_count_vs_rvm.png

  • params.json

  • report.md

Notes

  • Observed sign changes up to T: 38

  • RVM main term at last observed T: 37.454

  • Coarse scan undercounts (missed multiple zeros within a single dt bin) but tracks the growth trend.

params.json (snapshot)
{
  "dps": 40,
  "dt": 0.2,
  "t_max": 120.0
}

References

  • See the zeta / zeros background pages in docs/background/.