# 📐 L2 Spec — Helmholtz Scattering — frequency-domain EM scattering Mismatch-Only Spec
**ID:** `L2-233-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-233`](/artifact/l1/L1-233)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41553990
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 2048 |
| W | px | 32 – 2048 |
| Z | — | 32 – 1024 |
| Snr db | dB | 0 – 40 |
| N freqs | — | 1 – 256 |
| K error | — | 0.0 – 0.05 |
| Bc error | — | 0.0 – 0.2 |
| N angles | — | 16 – 4096 |
| Surface error | — | 0.0 – 0.1 |
| Material error | — | 0.0 – 0.1 |
## 2. Tolerance (ε)
**Type:** `fn`
```
17.0 + 0.3*SNR_dB - 40.0*k_error - 20.0*surface_error - 20.0*material_error
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |
## 4. Fingerprint
`10d09d93bb608b0e7d6e56b8338aed725f8f8c04213c2210d84bb30a16b06237`
## 5. On-chain Registration
- **Chain hash:** `0x731ca4153eb570c6306d1edee205741a6430a915a3c4a5499360f8624e568bc1`
- **Chain tx hash:** `0x8ecfe3e09429041ce8bc0c77771f1df2b969fc5937b3b335226b237ba60d50e5`
- **Chain block:** `41553990`
---
## File Mapping
This bundle consists of: `L2-233-001.md`, `L2-233-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-233-001.md` | Source of truth — edit this | Human or LLM |
| `L2-233-001.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 `L2-233-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._