# 📐  L2 Spec — Phonon Dispersion Relations Mismatch-Only Spec

**ID:** `L2-317-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-317`](/artifact/l1/L1-317)

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

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| Q grid | — | 8 – 256 |
| N atoms | — | 1 – 100 |
| N neighbor shells | — | 1 – 20 |

## 2. Tolerance (ε)

**Type:** `fn`

```
1.5 * (1 + 0.1 * mismatch_severity)
```

## 3. Difficulty

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

## 4. Fingerprint

`a6f8d5ba233f7d47ac08b2ff37fbe49246c2e838a3ea9b0e7e3d477564cf369d`

## 5. On-chain Registration

- **Chain hash:** `0x61277490709abb904ffc704283ae16f6fa98e665bc1b161e08f82d48e9e32329`
- **Chain tx hash:** `0x3ed43d416d3422242501d95a8ab5b9a166671eb84464cb33ea65870ccc84c8ea`
- **Chain block:** `41554083`

---

## File Mapping

This bundle consists of: `L2-317-001.md`, `L2-317-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-317-001.md` | Source of truth — edit this | Human or LLM |
| `L2-317-001.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 `L2-317-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._