# 📐  L2 Spec — Optimal Control (LQR) — Nominal + Mismatch Specs

**ID:** `L2-432-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-432`](/artifact/l1/L1-432)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.25 · **Delta tier:** 5
> **⛓ On-chain block:** 41555260

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| Q r ratio | — | 0.01 – 100 |
| N inputs m | m | 1 – 10 |
| System order n | N | 1 – 50 |
| Spectral radius a | — | 0.0 – 0.999 |

## 2. Tolerance (ε)

**Type:** `fn`

```
1.0 + 0.05 * abs(spectral_radius_A - 0.9)
```

## 3. Difficulty

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

## 4. Fingerprint

`28e07d9b807d5c805b765165d161eda3b509e2980a6ab6b2d655a8a4379d7fdc`

## 5. On-chain Registration

- **Chain hash:** `0x833a72f3245c7c6e3f91f800140c61deec1d7d33f871afaf6fd3a59774a3d857`
- **Chain tx hash:** `0x5104e154da7d3f1fd30ac7d3b61bfc645a1209c23b0883675b07bc23531afc16`
- **Chain block:** `41555260`

---

## File Mapping

This bundle consists of: `L2-432-001.md`, `L2-432-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-432-001.md` | Source of truth — edit this | Human or LLM |
| `L2-432-001.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 `L2-432-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._