# 📐 L2 Spec — RANS k-epsilon — turbulence closure Mismatch-Only Spec
**ID:** `L2-176-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-176`](/artifact/l1/L1-176)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41553969
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 2048 |
| W | px | 32 – 2048 |
| Z | — | 16 – 1024 |
| Snr db | dB | 0 – 40 |
| C mu error | — | 0.0 – 0.2 |
| C eps error | — | 0.0 – 0.3 |
| Sigma k error | — | 0.0 – 0.3 |
| Wall fn error | — | 0.0 – 0.3 |
## 2. Tolerance (ε)
**Type:** `fn`
```
14.0 + 0.3*SNR_dB - 15.0*C_mu_error - 8.0*sigma_k_error - 10.0*C_eps_error - 10.0*wall_fn_error
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |
## 4. Fingerprint
`97ba8465949cd871da18bb14b7933056cdef8b071bb1cfdc1735a631e7e8bc98`
## 5. On-chain Registration
- **Chain hash:** `0xe65d33b9869b05191648d17cd2236aabe53deadbb7d4441b1f62e47a4cf854a1`
- **Chain tx hash:** `0x4f0062eebf71e64143d68ffab9333ca5516b1ef68a55dc4268b2284338bc2582`
- **Chain block:** `41553969`
---
## File Mapping
This bundle consists of: `L2-176-001.md`, `L2-176-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-176-001.md` | Source of truth — edit this | Human or LLM |
| `L2-176-001.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 `L2-176-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._