# E102: Dirichlet convolution identity zoo

```{figure} ../_static/experiments/e102_hero.png
:alt: E102 hero
:class: experiment-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 (μ*1=ε, φ*1=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).

```{include} ../reports/e102.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

::: {dropdown} params.json (snapshot)
:open:

```{literalinclude} ../params/e102.json
:language: json
```

:::

## References

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

## Related experiments

- {doc}`e063` (Dirichlet convolution playground)
- {doc}`e121` (E121: Möbius inversion as convolution undo)
- {doc}`e108` (E108: Orthogonality heatmap for characters)
- {doc}`e111` (E111: Euler product vs. Dirichlet series for L(s,χ))
- {doc}`e052` (Totient ratio landscape)