# 📐  L2 Spec — Phase-Field Allen-Cahn Dynamics Mismatch-Only Spec

**ID:** `L2-327-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-327`](/artifact/l1/L1-327)

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

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| T k | — | 77 – 1500 |
| M phi | — | 0.1 – 100 |
| Dx nm | nm | 0.5 – 100 |
| Kappa | — | 0.1 – 10 |
| Grid n | N | 64 – 1024 |

## 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

`3cfdd187b9016311f34b42a8a0e3ea668408abe74957bb3214844b7ead47d204`

## 5. On-chain Registration

- **Chain hash:** `0xb40230cbe01d3428e42eb626e617a694b18c096c9adaed060ec408b3baffbdc4`
- **Chain tx hash:** `0xc7ddca11398a4bd6f76233e21219a3c97e3c60f82b6c709577514734a358021d`
- **Chain block:** `41554131`

---

## File Mapping

This bundle consists of: `L2-327-001.md`, `L2-327-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-327-001.md` | Source of truth — edit this | Human or LLM |
| `L2-327-001.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 `L2-327-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._