# 📐  L2 Spec — Richards Equation — unsaturated variably-saturated flow Mismatch-Only Spec

**ID:** `L2-189-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-189`](/artifact/l1/L1-189)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41553979

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| H | px | 16 – 1024 |
| W | px | 16 – 1024 |
| Z | — | 8 – 512 |
| Snr db | dB | 0 – 40 |
| N times | — | 10 – 100000 |
| Vg n error | — | 0.0 – 0.3 |
| K sat error | — | 0.0 – 0.3 |
| Vg alpha error | — | 0.0 – 0.3 |

## 2. Tolerance (ε)

**Type:** `fn`

```
16.0 + 0.3*SNR_dB - 10.0*vg_alpha_error - 10.0*vg_n_error - 10.0*K_sat_error
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |

## 4. Fingerprint

`ab29507f5878c6fe9fec7c23ae3fbb6ef945ed95a547705e4c4a53d8dc196957`

## 5. On-chain Registration

- **Chain hash:** `0xe2a54de81e29c38edb18a1138f6542fc6b70b4d520a1a639b95924fe5af8bef6`
- **Chain tx hash:** `0xbb7f31ac775f05fad338fb305ede63c8d37325daf15335038f8c9c5570ffac2d`
- **Chain block:** `41553979`

---

## File Mapping

This bundle consists of: `L2-189-001.md`, `L2-189-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-189-001.md` | Source of truth — edit this | Human or LLM |
| `L2-189-001.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 `L2-189-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._