# 📐  L2 Spec — Acoustic Scattering — boundary element method (BEM) Mismatch-Only Spec

**ID:** `L2-261-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-261`](/artifact/l1/L1-261)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41554040

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| Ka | — | 0.1 – 50 |
| N mesh | — | 500 – 200000 |
| Snr db | dB | 0 – 40 |
| N freqs | — | 4 – 128 |
| Freq error | — | 0.0 – 0.02 |
| N receivers | — | 16 – 512 |
| Impedance bc error | — | 0.0 – 0.3 |
| Surface mesh error | — | 0.0 – 0.1 |

## 2. Tolerance (ε)

**Type:** `fn`

```
17.0 + 1.5*log2(N_mesh/500) + 0.25*SNR_dB - 25.0*surface_mesh_error - 10.0*impedance_BC_error
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |

## 4. Fingerprint

`65e36f4b8318415d2672b9283343427d14c372390d6f8597f0b0d4ab702ac31e`

## 5. On-chain Registration

- **Chain hash:** `0xf8449994f6be7a4af1e998230b6b566b9c63d62c6fd9d716fb1a78b865ea023c`
- **Chain tx hash:** `0x398f3d52fc94fbb12549a826e2f8b58810c5f10594179ebcb0c0cb823ee5c6ab`
- **Chain block:** `41554040`

---

## File Mapping

This bundle consists of: `L2-261-001.md`, `L2-261-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-261-001.md` | Source of truth — edit this | Human or LLM |
| `L2-261-001.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 `L2-261-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._