E102: Dirichlet convolution identity zoo

E102 hero

E102: Dirichlet convolution identity zoo

Tags: number-theory, model-checking, visualization, dirichlet-convolution, multiplicative, arithmetic-functions

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

  • Verify classic convolution identities numerically on 1..N (μ1=ε, φ1=id, 1*1=τ).

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_convolution_identity_errors.png

  • params.json

  • report.md

Notes

  • Max errors: {‘mu1-eps’: 0, ‘phi1-id’: 0, ‘11-tau’: 0, ‘id1-sigma’: 0}

  • All should be exactly 0 for these sieve-based implementations.

params.json (snapshot)
{
  "n_max": 20000
}

References

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