# E108: Orthogonality heatmap for characters

```{figure} ../_static/experiments/e108_hero.png
:alt: E108 hero
:class: experiment-hero

E108: Orthogonality heatmap for characters
```

**Tags:** `number-theory`, `dirichlet-characters`, `model-checking`, `visualization`, `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

- Visualize orthogonality relations via inner-product matrices.

## 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/e108.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

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

```{literalinclude} ../params/e108.json
:language: json
```

:::

## References

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

## Related experiments

- {doc}`e065` (Orthogonality matrix for Dirichlet characters.)
- {doc}`e102` (E102: Dirichlet convolution identity zoo)
- {doc}`e121` (E121: Möbius inversion as convolution undo)
- {doc}`e106` (E106: Character gallery: real vs. complex)
- {doc}`e077` (Indicator via character orthogonality (sanity check).)