# 📐  L2 Spec — Vlasov Equation — collisionless kinetic plasma Mismatch-Only Spec

**ID:** `L2-344-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-344`](/artifact/l1/L1-344)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41554098

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| N v | — | 16 – 2048 |
| N x | — | 16 – 2048 |
| Snr db | dB | 0 – 40 |
| N times | — | 50 – 100000 |
| Initial f error | — | 0.0 – 0.3 |
| Electric field error | — | 0.0 – 0.2 |
| Grid phase space error | — | 0.0 – 0.2 |

## 2. Tolerance (ε)

**Type:** `fn`

```
11.0 + 0.3*SNR_dB - 10.0*grid_phase_space_error - 15.0*electric_field_error - 8.0*initial_f_error
```

## 3. Difficulty

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

## 4. Fingerprint

`9792b5b06e7064647dabff1ba16a29dc7e28c6212af5c252489b51772115a08b`

## 5. On-chain Registration

- **Chain hash:** `0xe542a1b76a1e0cd2234e181de65ea68d1fbd8401613fcba584c0f0937a96f246`
- **Chain tx hash:** `0x1b144eac2a5df6cbe98f5fe4d51a595b478f52c11cf6d53849d6dd45ca7894d7`
- **Chain block:** `41554098`

---

## File Mapping

This bundle consists of: `L2-344-001.md`, `L2-344-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-344-001.md` | Source of truth — edit this | Human or LLM |
| `L2-344-001.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 `L2-344-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._