# 📐  L2 Spec — Phonon Boltzmann Transport Equation Mismatch-Only Spec

**ID:** `L2-497-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-497`](/artifact/l1/L1-497)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.45 · **Delta tier:** 5
> **⛓ On-chain block:** 41554144

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| T k | — | 10 – 1500 |
| N q grid | — | 8 – 64 |
| Grain size um | µm | 0.001 – 1000 |
| Isotope naturality | — | 0.0 – 1.0 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.025 + 0.005*log10(T_K/300+0.1) + 0.003*log10(1000/grain_size_um+0.001)
```

## 3. Difficulty

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

## 4. Fingerprint

`40c115d658f92fd8b0d6ef1c1c2482d518c02cd2830f78e397cf2410a0228f05`

## 5. On-chain Registration

- **Chain hash:** `0x581ab8743339442910b4eae4b84b9ca6ceb5913d42681956b1ab3a15bf7875ee`
- **Chain tx hash:** `0x7894cfaa2410d8e226220ec3daa8b35eefa8a69855ac407ab276d5c4a226bfaa`
- **Chain block:** `41554144`

---

## File Mapping

This bundle consists of: `L2-497-001.md`, `L2-497-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-497-001.md` | Source of truth — edit this | Human or LLM |
| `L2-497-001.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 `L2-497-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._