# 📐  L2 Spec — Helmholtz Equation — frequency-domain acoustic scattering / interior field Mismatch-Only Spec

**ID:** `L2-258-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-258`](/artifact/l1/L1-258)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41554039

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| H | px | 64 – 1024 |
| W | px | 64 – 1024 |
| Snr db | dB | 0 – 40 |
| K mean | — | 1 – 200 |
| N freqs | — | 4 – 128 |
| K error | — | 0.0 – 0.05 |
| N receivers | — | 8 – 256 |
| Geometry error | — | 0.0 – 0.05 |
| Impedance bc error | — | 0.0 – 0.3 |
| Receiver pos error | — | 0.0 – 0.02 |

## 2. Tolerance (ε)

**Type:** `fn`

```
18.0 + 1.5*log2(N_freqs/4) + 0.25*SNR_dB - 40.0*k_error - 15.0*geometry_error
```

## 3. Difficulty

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

## 4. Fingerprint

`8ae73d55747a06871b3caba4dd5867f05d09dd72f5a70e46843783c26edfd590`

## 5. On-chain Registration

- **Chain hash:** `0xf84dd72d524a85f96c353da121f10b1673025c59e4f249a2eccaab2259df93d5`
- **Chain tx hash:** `0x877d112d0a30bc00847c4ac820c62bc61a52cf1959cb0b51ca01e1a37b72030f`
- **Chain block:** `41554039`

---

## File Mapping

This bundle consists of: `L2-258-001.md`, `L2-258-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-258-001.md` | Source of truth — edit this | Human or LLM |
| `L2-258-001.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 `L2-258-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._