# 📐  L2 Spec — GARCH Volatility Estimation — Nominal + Mismatch Specs

**ID:** `L2-445-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-445`](/artifact/l1/L1-445)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.25 · **Delta tier:** 5
> **⛓ On-chain block:** 41555263

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| Beta true | — | 0.5 – 0.99 |
| Alpha true | — | 0.01 – 0.3 |
| T observations | — | 100 – 10000 |
| Structural break prob | — | 0.0 – 0.2 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.05 + 0.03 * (structural_break_prob / 0.1 + 1) ** 0.5
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.25 |
| Delta tier | 5 |

## 4. Fingerprint

`5e9e9545ab46988e8949c8b926895f5cfd34ed35517908cf3c2870e07c7ed3ab`

## 5. On-chain Registration

- **Chain hash:** `0xcd362e833060b07bebe22928168c84b2048ad700139bfa1e0c548c09aa9f6728`
- **Chain tx hash:** `0x3ebe7d75e279a54cce7dc53d666a284ca72c659b672ae774251200576cb33caa`
- **Chain block:** `41555263`

---

## File Mapping

This bundle consists of: `L2-445-001.md`, `L2-445-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-445-001.md` | Source of truth — edit this | Human or LLM |
| `L2-445-001.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 `L2-445-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._