# Bell Curve — Randomly

> The normal distribution by Box–Muller, plotted as you draw it. One of 63 generators at [Randomly](https://randomly.cluxnei.dev), a library of random generators seeded from verifiable real-world entropy. Free HTTP API, no key, no signup.

## `numbers.gaussian` — Bell Curve

The normal distribution by Box–Muller, plotted as you draw it.

| | |
|---|---|
| **Key** | `numbers.gaussian` |
| **Module** | `numbers` |
| **Version** | `1` — a permalink carries this, and a replay against a different version returns `409` rather than something else |
| **Formats** | `application/json`, `text/plain` |
| **Studio** | https://randomly.cluxnei.dev/g/numbers/gaussian |
| **API** | `GET https://randomly.cluxnei.dev/api/v1/g/numbers.gaussian` |

`value` is the sampled data the studio plots; `meta` carries the summary statistics measured from that very sample.

| Parameter | Type | Default | Accepts | What it does |
|---|---|---|---|---|
| `count` | int | `500` | `1` – `5000` | How many |
| `mu` | float | `0` | `-1000000` – `1000000` | Mean (μ) |
| `sigma` | float | `1` | `0.001` – `1000000` | Standard deviation (σ) |
| `clamp` | bool | `false` | `true`, `false` | Truncate the tails — Redraw anything beyond the cut instead of keeping it. This is a truncated normal, not a normal — the shape changes. |
| `clamp_sigma` | float | `3` | `1` – `6` | Cut at (σ) |
| `bins` | int | `25` | `4` – `60` | Histogram bars |
| `decimals` | int | `3` | `0` – `6` | Decimal places |

Out-of-range numbers are **clamped, not rejected**, so a request never fails for being
ambitious — but it may not do what you meant. Unknown keys are dropped and missing ones
fall back to the defaults above.

```bash
curl -s 'https://randomly.cluxnei.dev/api/v1/g/numbers.gaussian?count=500&mu=0&sigma=1' -H 'Accept: text/plain'
```

## The receipt

Every result carries one, naming the physical source of the randomness and linking to the
third party's own record of it:

```json
"receipt": {
  "source": "seismic",
  "source_label": "USGS Seismic Feed",
  "class": "C",
  "caveat": "Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.",
  "narrative": "A magnitude 3.6 earthquake, 67 km N of Culebra, Puerto Rico, 39.6 km down — 52 minutes ago.",
  "proof_url": "https://earthquake.usgs.gov/earthquakes/eventpage/us7000th33",
  "mixed_with_csprng": true,
  "degraded": false
}
```

Pick the source with `?source=`, or leave it at the default `auto`:

- **Class A** (Cryptographic) — `csprng`, `anu-qrng`, `random-org`
- **Class B** (Public beacon) — `nist-beacon`, `drand`, `bitcoin`. Published openly — anyone can look this value up after the fact.
- **Class C** (Observational) — `seismic`, `space-weather`, `atmosphere`, `iss`. Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.

## More

- [The full API contract](https://randomly.cluxnei.dev/api.md)
- [Everything in one file](https://randomly.cluxnei.dev/llms-full.txt)
- [The catalogue as JSON](https://randomly.cluxnei.dev/api/v1/generators)
- [This generator in the browser](https://randomly.cluxnei.dev/g/numbers/gaussian)