# 📐 L2 Spec — SPH — smoothed particle hydrodynamics Mismatch-Only Spec
**ID:** `L2-186-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-186`](/artifact/l1/L1-186)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41553971
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N times | — | 100 – 1000000 |
| N particles | — | 1000.0 – 10000000000.0 |
| Boundary error | — | 0.0 – 0.3 |
| Pressure instability | — | 0.0 – 0.3 |
| Kernel bandwidth error | — | 0.0 – 0.3 |
## 2. Tolerance (ε)
**Type:** `fn`
```
14.0 + 0.3*SNR_dB - 15.0*kernel_bandwidth_error - 8.0*pressure_instability - 10.0*boundary_error
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |
## 4. Fingerprint
`bc6844383923aa2efedf0ad3c96fa4fa8f011ff69b3b53bb1ab6d947ee3a85d4`
## 5. On-chain Registration
- **Chain hash:** `0x4f983ea79a80b5280ad79b192d08f770771552d136fd92e6338eb7d1ec317528`
- **Chain tx hash:** `0xa15a1cf910e418017f11a6ccaa2a6c5d5f850dc206add8c41c9cecbf09ab733d`
- **Chain block:** `41553971`
---
## File Mapping
This bundle consists of: `L2-186-001.md`, `L2-186-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-186-001.md` | Source of truth — edit this | Human or LLM |
| `L2-186-001.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 `L2-186-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._