# 📐 L2 Spec — Underwater Normal Modes — modal propagation (KRAKEN) Mismatch-Only Spec
**ID:** `L2-263-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-263`](/artifact/l1/L1-263)
> **🎯 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 | — | 32 – 1024 |
| N modes | — | 3 – 100 |
| Freq hz | Hz | 20 – 5000 |
| Ssp error | — | 0.0 – 0.02 |
| Waveguide depth error | — | 0.0 – 5.0 |
| Bottom sound speed error | — | 0.0 – 0.2 |
## 2. Tolerance (ε)
**Type:** `fn`
```
17.0 + 1.5*log2(N_modes/3) + 0.25*SNR_dB - 30.0*ssp_error - 15.0*bottom_sound_speed_error
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |
## 4. Fingerprint
`ee20d10b62e4a8b2e1bc22547ffbfc35bc9a8927f64057b85f6b2a4e2bd270bd`
## 5. On-chain Registration
- **Chain hash:** `0x7fd686156356c7c52e916d1def0b28eece8ea8490c362cff5f68aec5e9c71e4c`
- **Chain tx hash:** `0xcf91e19a870d42f18a92779a823cee6cb67d46af853e291f42273e32b695808c`
- **Chain block:** `41554052`
---
## File Mapping
This bundle consists of: `L2-263-001.md`, `L2-263-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-263-001.md` | Source of truth — edit this | Human or LLM |
| `L2-263-001.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 `L2-263-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._