# E116: Gram points and zero-counting heuristics

```{figure} ../_static/experiments/e116_hero.png
:alt: E116 hero
:class: experiment-hero

E116: Gram points and zero-counting heuristics
```

**Tags:** `analysis`, `model-checking`, `visualization`, `riemann-zeta`, `gram-points`, `zeta-zeros`

## 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

- Compare Gram-point heuristics and simple zero-counting diagnostics over a finite range.

## 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/e116.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

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

```{literalinclude} ../params/e116.json
:language: json
```

:::

## References

- See the zeta / zeros background pages in `docs/background/`.

## Related experiments

- {doc}`e087` (E087: Gram points and spacing)
- {doc}`e088` (E088: Zero counting via Riemann–von Mangoldt)
- {doc}`e115` (E115: Hardy Z: sign changes and zero bracketing)
- {doc}`e086` (E086: Hardy Z(t) near zeros)
- {doc}`e117` (E117: Prime-counting approximations: li(x) and friends)