E121: Möbius inversion as convolution undo

E121 hero

E121: Möbius inversion as convolution undo

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

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

  • Recover a function from its Dirichlet convolution with 1 via Möbius inversion.

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_multiplicativity_failures.png

  • params.json

  • report.md

Notes

  • Tested coprime pairs (attempted): 3000

  • Failure counts: {‘mu’: 0, ‘phi’: 0, ‘tau’: 0, ‘sigma’: 0, ‘omega_add’: 0, ‘bigomega_add’: 0}

  • These should be 0 (within the sampled range and for coprime pairs).

params.json (snapshot)
{
  "n_max": 100000,
  "pairs": 3000
}

References

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