# 📐  L2 Spec — Linear State-Space System Analysis — Nominal + Mismatch Specs

**ID:** `L2-426-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-426`](/artifact/l1/L1-426)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.25 · **Delta tier:** 5
> **⛓ On-chain block:** 41555243

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| Noise snr db | dB | 0 – 60 |
| System order n | N | 2 – 50 |
| Sampling rate hz | Hz | 10 – 100000.0 |
| Condition number kappa | — | 10 – 1000000.0 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.02 + 0.03 * (100 / condition_number_kappa) ** 0.3
```

## 3. Difficulty

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

## 4. Fingerprint

`5c945ebdf329c087187eb2a87a4d368fcad827960eaf4270b04d174d345c2a14`

## 5. On-chain Registration

- **Chain hash:** `0x5d2c833012107585a16a6ea7adb91a1b7ba24b9f7ea3fc896aaea53ed94f4aad`
- **Chain tx hash:** `0x172904dee02f11fabc67c9b04b51f829106be6305da75fbfe0594074ab49d61d`
- **Chain block:** `41555243`

---

## File Mapping

This bundle consists of: `L2-426-001.md`, `L2-426-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-426-001.md` | Source of truth — edit this | Human or LLM |
| `L2-426-001.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 `L2-426-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._