# 📐  L2 Spec — Landau-de Gennes Liquid Crystal Theory Mismatch-Only Spec

**ID:** `L2-479-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-479`](/artifact/l1/L1-479)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.45 · **Delta tier:** 5
> **⛓ On-chain block:** 41555304

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| L1 pn | — | 1.0 – 30.0 |
| Mesh n | N | 32 – 512 |
| T over tc | — | 0.85 – 1.05 |
| Cell gap um | µm | 1 – 100 |
| Anchoring w j m2 | — | 1e-06 – 0.001 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.012 + 0.01*abs(T_over_Tc - 0.98) + 0.005*abs(log10(anchoring_W_J_m2 / 1e-4))
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.45 |
| Delta tier | 5 |

## 4. Fingerprint

`d9305bfa2d876066bb1dc7a09e824144d6ca9ea77a1213d39ffbd55c9ad46a7e`

## 5. On-chain Registration

- **Chain hash:** `0xedfabf26b0775a021d36b33839ba77dff1e2776fd19352f3dddc9e13ad011344`
- **Chain tx hash:** `0xf3ececf6d197beb4731b973a5c81d4fcff5f7a0b5ca6d8c08a04205874678e99`
- **Chain block:** `41555304`

---

## File Mapping

This bundle consists of: `L2-479-001.md`, `L2-479-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-479-001.md` | Source of truth — edit this | Human or LLM |
| `L2-479-001.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 `L2-479-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._