# 📐  L2 Spec — GW Approximation for Quasiparticle Energies Mismatch-Only Spec

**ID:** `L2-319-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-319`](/artifact/l1/L1-319)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.45 · **Delta tier:** 5
> **⛓ On-chain block:** 41554083

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| N omega | — | 10 – 200 |
| N kpoints | — | 1 – 1000 |
| Cutoff ev | — | 200 – 2000 |
| N bands gw | — | 20 – 1000 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.07 * (1 + 0.1 * mismatch_severity)
```

## 3. Difficulty

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

## 4. Fingerprint

`b9e394c5daa950bdcae2603130636b3b0b72d95ea5da394257ef4b4df542992d`

## 5. On-chain Registration

- **Chain hash:** `0x778883b1f9bb427605b830d6a66619d9a7a6cf95af4b1376e1eb38f8d9a2601c`
- **Chain tx hash:** `0x627840fdc6db1d16c0db614d6b43a1cdea75ce6bcf0f58afd65353fc21753586`
- **Chain block:** `41554083`

---

## File Mapping

This bundle consists of: `L2-319-001.md`, `L2-319-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-319-001.md` | Source of truth — edit this | Human or LLM |
| `L2-319-001.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 `L2-319-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._