# 📐  L2 Spec — k.p Perturbation Theory Mismatch-Only Spec

**ID:** `L2-326-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-326`](/artifact/l1/L1-326)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.45 · **Delta tier:** 5
> **⛓ On-chain block:** 41554085

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| N bands kp | — | 4 – 30 |
| Include soc | — | True – False |
| K range a inv | — | 0.01 – 1.0 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.03 * (1 + 0.1 * mismatch_severity)
```

## 3. Difficulty

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

## 4. Fingerprint

`9782248cf6106368f288a68f76b28057eb7f964cb309b1fc0c0ac378d8647842`

## 5. On-chain Registration

- **Chain hash:** `0x5c4e0957ea011e51199793cdb923441be7e48cee055fe0576a5f1c8559a5630b`
- **Chain tx hash:** `0xb933e113e2ceaeebafc12feb149a0da764cfc52243792dba545930850e35fe64`
- **Chain block:** `41554085`

---

## File Mapping

This bundle consists of: `L2-326-001.md`, `L2-326-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-326-001.md` | Source of truth — edit this | Human or LLM |
| `L2-326-001.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 `L2-326-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._