# 📐  L2 Spec — Phase-Field Fracture — regularized crack model Mismatch-Only Spec

**ID:** `L2-223-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-223`](/artifact/l1/L1-223)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41554024

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| N dof | — | 1000 – 10000000 |
| Snr db | dB | 0 – 40 |
| Ell mm | mm | 0.001 – 10 |
| G c error | — | 0.0 – 0.2 |
| Degradation func error | — | 0.0 – 0.2 |
| Ell regularization error | — | 0.0 – 0.3 |

## 2. Tolerance (ε)

**Type:** `fn`

```
15.5 + 0.3*SNR_dB - 10.0*ell_regularization_error - 20.0*G_c_error - 10.0*degradation_func_error
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |

## 4. Fingerprint

`4f268eb35618cf604573c273767963de31d7cc6b2b86cc541f1c7787df826954`

## 5. On-chain Registration

- **Chain hash:** `0x87f38004ba2b6c13b49ca061af66a89964889e46834eaa6761a67a216c23480a`
- **Chain tx hash:** `0x20b43e0ce82d82316ddd60dc2bee846ec82e3df70a48e4dc73318d22a31a8980`
- **Chain block:** `41554024`

---

## File Mapping

This bundle consists of: `L2-223-001.md`, `L2-223-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-223-001.md` | Source of truth — edit this | Human or LLM |
| `L2-223-001.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 `L2-223-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._