# 📐  L2 Spec — Optimal Experimental Design — Nominal + Mismatch Specs

**ID:** `L2-500-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-500`](/artifact/l1/L1-500)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.4 · **Delta tier:** 5
> **⛓ On-chain block:** 41555320

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| P parameters | — | 2 – 20 |
| Sigma2 noise | — | 0.01 – 1.0 |
| N experiments | — | 5 – 100 |
| Nonlinearity level | — | 0.1 – 2.0 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.70 + 0.10 * (N_experiments / 20) ** 0.3
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.4 |
| Delta tier | 5 |

## 4. Fingerprint

`a0c3d6cf239c0bed1721988002f89bf1d7adca6a0ff5d369a899195a2930f001`

## 5. On-chain Registration

- **Chain hash:** `0x758b4f2f43266807fd0093019aed8f72740f30f073349b525cbd638ba817805e`
- **Chain tx hash:** `0x5cd6edfadc8c22eb0f8563f3411adc7cc02a93beb3c918bcd5413a27fbae6163`
- **Chain block:** `41555320`

---

## File Mapping

This bundle consists of: `L2-500-001.md`, `L2-500-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-500-001.md` | Source of truth — edit this | Human or LLM |
| `L2-500-001.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L2-500-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._