# 📐  L2 Spec — Grain Growth and Recrystallization Mismatch-Only Spec

**ID:** `L2-331-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-331`](/artifact/l1/L1-331)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.45 · **Delta tier:** 5
> **⛓ On-chain block:** 41554131

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| T k | — | 300 – 2000 |
| Grid n | N | 64 – 2048 |
| F pinning | — | 0 – 0.2 |
| T anneal s | s | 1 – 100000 |
| Initial grains | — | 100 – 1000000 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.04 * (1 + 0.1 * mismatch_severity)
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.45 |
| Delta tier | 5 |

## 4. Fingerprint

`5736c9e36c0e8df32ceb21601262422eee6bfc138bff7d7b99544df17df61240`

## 5. On-chain Registration

- **Chain hash:** `0x5db4b58fd2f6eb2c715d5ecc3775d1572a48ebbd8bc00e79259f038150ee276c`
- **Chain tx hash:** `0x4fac9551eaaf48f0c9ecc1a01ebd37730d9612bbdb6346c1f35738e3c770ec00`
- **Chain block:** `41554131`

---

## File Mapping

This bundle consists of: `L2-331-001.md`, `L2-331-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-331-001.md` | Source of truth — edit this | Human or LLM |
| `L2-331-001.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 `L2-331-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._