# 📐  L2 Spec — Expansion Microscopy (ExM) — physical hydrogel expansion Mismatch-Only Spec

**ID:** `L2-014-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-014`](/artifact/l1/L1-014)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.45 · **Delta tier:** 5
> **⛓ On-chain block:** 41554158

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| H | px | 256 – 4096 |
| W | px | 256 – 4096 |
| Na | — | 1.0 – 1.49 |
| F expand | — | 2.0 – 20.0 |
| Pixel nm | nm | 30 – 200 |
| Peak photons | photons | 50 – 5000 |
| Labeling loss | — | 0.0 – 0.3 |
| Expansion anisotropy | — | 0.0 – 0.1 |
| Expansion factor drift | — | 0.0 – 0.1 |

## 2. Tolerance (ε)

**Type:** `fn`

```
22.0 + 2.0 * log10(peak_photons / 50) + 0.5 * log2(F_expand / 2) - 20.0 * expansion_anisotropy
```

## 3. Difficulty

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

## 4. Fingerprint

`6a8df18900a4172113b07845b8eb37c5ff0d2f99a878f007a5fd2392a50efb6d`

## 5. On-chain Registration

- **Chain hash:** `0x11380f051a24dd296e73b53d5b624fd14980b8798af39459d41d10a383f9c0b2`
- **Chain tx hash:** `0xd5f864a07354993c4024376d516683af1471e50179cc453c8ea4a695b0d28795`
- **Chain block:** `41554158`

---

## File Mapping

This bundle consists of: `L2-014-001.md`, `L2-014-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-014-001.md` | Source of truth — edit this | Human or LLM |
| `L2-014-001.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 `L2-014-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._