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

**ID:** `L2-450-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-450`](/artifact/l1/L1-450)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.38 · **Delta tier:** 5
> **⛓ On-chain block:** 41555281

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| N dof | — | 2 – 10 |
| N obstacles | — | 0 – 50 |
| T horizon s | s | 0.1 – 10.0 |
| Joint vel limit rad s | s | 0.5 – 10.0 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.85 + 0.05 * exp(-N_obstacles / 10)
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.38 |
| Delta tier | 5 |

## 4. Fingerprint

`6df8b978c879ca4fbdc87c4c59c400cba8f8a92f65a08990a1d1f3d76488c561`

## 5. On-chain Registration

- **Chain hash:** `0xa3e84dd8a5fac69dc43f46b1059249c3d9de5e753732e1893d01310f3f56d983`
- **Chain tx hash:** `0x211b9617052582025a238d1642f5706e3f8d74e3c3b06e67e4fbadb25e936a0b`
- **Chain block:** `41555281`

---

## File Mapping

This bundle consists of: `L2-450-001.md`, `L2-450-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-450-001.md` | Source of truth — edit this | Human or LLM |
| `L2-450-001.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 `L2-450-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._