E101: Reduced residues modulo q: concrete structure

E101 hero

E101: Reduced residues modulo q: concrete structure

Tags: number-theory, dirichlet-characters, model-checking, visualization, totient

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

  • List reduced residues mod q, verify count=φ(q), and summarize simple structure checks.

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_reduced_residues_sizes.png

  • params.json

  • report.md

Notes

  • Checked q values: [10, 12, 15, 21, 30]

  • sizes match phi(q): True

  • Example prefixes of RR(q): {10: [1, 3, 7, 9], 12: [1, 5, 7, 11], 15: [1, 2, 4, 7, 8, 11, 13, 14], 21: [1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20], 30: [1, 7, 11, 13, 17, 19, 23, 29]}

params.json (snapshot)
{
  "q_values": [
    10,
    12,
    15,
    21,
    30
  ]
}

References

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

  • See docs/background/dirichlet-characters.md.