# 📐  L2 Spec — Topology Optimization (SIMP) — Nominal + Mismatch Specs

**ID:** `L2-498-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-498`](/artifact/l1/L1-498)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.35 · **Delta tier:** 5
> **⛓ On-chain block:** 41555320

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| N e | — | 100 – 10000 |
| V f | — | 0.3 – 0.7 |
| Filter r | — | 1.5 – 5.0 |
| Penalty p | — | 1 – 5 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.40 + 0.05 * (V_f - 0.5) / 0.2
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.35 |
| Delta tier | 5 |

## 4. Fingerprint

`86e230d19743e7d5a90937e7c36a7d37406fc4cb769590a1714336d908b24f15`

## 5. On-chain Registration

- **Chain hash:** `0x0bc9d048d1072052fe42d638560b391b0ddbbc5d3d4246837e0a2193ce020580`
- **Chain tx hash:** `0xb4e53a3fc07f7e64e830ff53a5caa4f3d8076f70709ad83def2d776365c36455`
- **Chain block:** `41555320`

---

## File Mapping

This bundle consists of: `L2-498-001.md`, `L2-498-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-498-001.md` | Source of truth — edit this | Human or LLM |
| `L2-498-001.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 `L2-498-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._