# 📐  L2 Spec — 4D-Var Data Assimilation — Nominal + Mismatch Specs

**ID:** `L2-435-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-435`](/artifact/l1/L1-435)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.42 · **Delta tier:** 5
> **⛓ On-chain block:** 41555261

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| Window hours | — | 1 – 24 |
| N observations | — | 100 – 10000000 |
| State dimension n | N | 100 – 1000000 |
| Observation density | — | 0.1 – 10.0 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.3 + 0.2 * (6 / window_hours) ** 0.2
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.42 |
| Delta tier | 5 |

## 4. Fingerprint

`f5f2869c48d5c08512154f769066f37113e5c26e9d33a91f5e5d3fd4a8fff2a1`

## 5. On-chain Registration

- **Chain hash:** `0xfb6a75216ee680f057c988cd3286abe5577cb86319dc215174c4afe8672073c3`
- **Chain tx hash:** `0x478c1b8dd7f22ec26dfd18ec25dc3041f56e73b4f39185b95f62f7f2bc1623b5`
- **Chain block:** `41555261`

---

## File Mapping

This bundle consists of: `L2-435-001.md`, `L2-435-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-435-001.md` | Source of truth — edit this | Human or LLM |
| `L2-435-001.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 `L2-435-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._