# 📐  L2 Spec — Shape Optimization — Nominal + Mismatch Specs

**ID:** `L2-499-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-499`](/artifact/l1/L1-499)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.3 · **Delta tier:** 5
> **⛓ On-chain block:** 41555320

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| Step size dt | — | 0.01 – 1.0 |
| N control pts | — | 10 – 200 |
| Regularization alpha | — | 0.001 – 0.1 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.25 + 0.05 * log10(N_control_pts / 50)
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.3 |
| Delta tier | 5 |

## 4. Fingerprint

`4dc800ca580fad3405f87549eb0c06cc6ad240bee3ee00e487eadc42b791e3ad`

## 5. On-chain Registration

- **Chain hash:** `0xcef0bcf668a2b1da03122bfd26efed58b35fea1a3e2bd79f41ccf95c33cdb52f`
- **Chain tx hash:** `0x061ea417169b0df71020de63a6bf54a059c05a385d1a2292f3eac2d91329b502`
- **Chain block:** `41555320`

---

## File Mapping

This bundle consists of: `L2-499-001.md`, `L2-499-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-499-001.md` | Source of truth — edit this | Human or LLM |
| `L2-499-001.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 `L2-499-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._