# 📐  L2 Spec — Kalman Filter State Estimation — Nominal + Mismatch Specs

**ID:** `L2-427-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-427`](/artifact/l1/L1-427)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.28 · **Delta tier:** 5
> **⛓ On-chain block:** 41555243

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| Q r ratio | — | 0.01 – 100 |
| P obs dim | — | 1 – 10 |
| N state dim | — | 1 – 20 |
| N time steps | — | 10 – 10000 |

## 2. Tolerance (ε)

**Type:** `fn`

```
1.0 + 0.05 * (Q_R_ratio / 1.0) ** 0.1
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.28 |
| Delta tier | 5 |

## 4. Fingerprint

`e924bfa80f06cf6eb0082be7e3a901bfd1c73eb1064fab9134b6d96f5bc7e1eb`

## 5. On-chain Registration

- **Chain hash:** `0x57e87f65616f8bb8c4ba786ddb849d924b82ac61c9886fd785c690409b22aefe`
- **Chain tx hash:** `0x158310e6c4b315ac213af092d705398e91b66dbc1ede35d957e7de128d5f9b99`
- **Chain block:** `41555243`

---

## File Mapping

This bundle consists of: `L2-427-001.md`, `L2-427-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-427-001.md` | Source of truth — edit this | Human or LLM |
| `L2-427-001.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 `L2-427-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._