# 📐 L2 Spec — DNS — direct numerical simulation Mismatch-Only Spec
**ID:** `L2-180-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-180`](/artifact/l1/L1-180)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41553970
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| H | px | 256 – 16384 |
| W | px | 256 – 16384 |
| Z | — | 128 – 8192 |
| Snr db | dB | 10 – 60 |
| N times | — | 1000 – 10000000 |
| Bc error | — | 0.0 – 0.2 |
| Re lambda | — | 10 – 2000 |
| Time step error | — | 0.0 – 0.1 |
| Grid sufficiency error | — | 0.0 – 0.2 |
## 2. Tolerance (ε)
**Type:** `fn`
```
15.0 + 0.25*SNR_dB - 15.0*grid_sufficiency_error - 20.0*time_step_error - 10.0*bc_error
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |
## 4. Fingerprint
`115a5eda012444dbe9647deb1dfa60719f56eeb7aed76e3b45df58802cf89778`
## 5. On-chain Registration
- **Chain hash:** `0x9d4a804d0601c9a0a6f090ac26f6868ad848919fb5de7d80ad64c65e53a7f0f0`
- **Chain tx hash:** `0xf00e95c661d6c3792158182b30463d11212164d26a70e5c26f92136454f32f7b`
- **Chain block:** `41553970`
---
## File Mapping
This bundle consists of: `L2-180-001.md`, `L2-180-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-180-001.md` | Source of truth — edit this | Human or LLM |
| `L2-180-001.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 `L2-180-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._