# 📐 L2 Spec — Underwater Acoustics — Parabolic Equation (RAM) Mismatch-Only Spec
**ID:** `L2-264-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-264`](/artifact/l1/L1-264)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41554052
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | -5 – 40 |
| N depth | — | 64 – 2048 |
| N range | — | 128 – 8192 |
| Freq hz | Hz | 10 – 2000 |
| Ssp error | — | 0.0 – 0.02 |
| Pade order | — | 1 – 10 |
| Range step dr | — | 0.0 – 1.0 |
| Bottom atten error | — | 0.0 – 0.2 |
| Pade order truncation | — | 0.0 – 0.3 |
## 2. Tolerance (ε)
**Type:** `fn`
```
17.0 + 0.5*pade_order + 0.3*SNR_dB - 30.0*ssp_error - 15.0*bottom_atten_error
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |
## 4. Fingerprint
`027dbee641bf98cc1f66b25938e4f739467a5b3d81ee946a1bcd8a375401e2e6`
## 5. On-chain Registration
- **Chain hash:** `0xc9ee094626ef5592e1644a706380b8ba2ea84da063738c6d1e0b5142ce0846bb`
- **Chain tx hash:** `0x56587bff8f01bfbd82e6bb82b0d8a7f4bc1f4ec724798b12416e22c468763636`
- **Chain block:** `41554052`
---
## File Mapping
This bundle consists of: `L2-264-001.md`, `L2-264-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-264-001.md` | Source of truth — edit this | Human or LLM |
| `L2-264-001.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 `L2-264-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._