# ⚛  L1 Principle — Gyrokinetic — 5D reduced plasma kinetic

**ID:** `L1-345` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Plasma Physics — *Magnetic-fusion gyrokinetic simulation*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** gk distribution function 5D
> **📡 Carrier:** plasma · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554095

---

## 🧠 1. Introduction

**Gyrokinetic — 5D reduced plasma kinetic** is a **nonlinear inverse problem** whose unknown lives in **gk distribution function 5D** space, within the **Magnetic-fusion gyrokinetic simulation** sub-domain of **Plasma Physics**.

Measurements consist of plasma particle and field diagnostics via a **beam emission spectroscopy** sensing mechanism.

The forward operator applies, in order: L · gyroaverage operator; L · drift kinetic operator; L · nonlinear coupling operator; int · phase space operator.

Observations are corrupted by additive Gaussian noise. Drift-wave turbulence; nonlinear coupling between Alfven / drift waves.

## ⚙ 2. Forward Model

Physical chain: **x** → L · gyroaverage → L · drift kinetic → L · nonlinear coupling → int · phase space → **y** (detector).

```
y = `int.phase_space` `L.nonlinear_coupling` `L.drift_kinetic` `L.gyroaverage` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.gyroaverage` | L · gyroaverage operator |
| `L.drift_kinetic` | L · drift kinetic operator |
| `L.nonlinear_coupling` | L · nonlinear coupling operator |
| `int.phase_space` | Int · phase space operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Plasma Physics |
| Sub domain | Magnetic-fusion gyrokinetic simulation |
| Carrier | plasma |
| Problem class | nonlinear_inverse |
| Solution space | gk_distribution_function_5D |
| Noise model | gaussian |
| Integration axis | phase_space |
| Difficulty delta | 10 |
| L dag | 3.8 |

## 📡 4. Measurement Model

Drift-wave turbulence; nonlinear coupling between Alfven / drift waves.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `gyrokinetic` · **Forward operator:** `gyrokinetic_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N v | — | 24 |
| N mu | — | 8 |
| Snr db | dB | 25 |
| N radial | — | 256 |
| N binormal | — | 128 |
| N parallel | — | 64 |
| Closure error | — | 0 |
| Gyroaverage error | — | 0 |
| Fluctuation prior error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N v | — | 8 – 128 |
| N mu | — | 4 – 64 |
| Snr db | dB | 0 – 40 |
| N radial | — | 32 – 2048 |
| N binormal | — | 16 – 2048 |
| N parallel | — | 8 – 256 |
| Closure error | — | 0.0 – 0.3 |
| Gyroaverage error | — | 0.0 – 0.2 |
| Fluctuation prior error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 16.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1100` and δ = `10`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xd800089827665a1370b6df83ef1ef09318b00d672a57a4d340efa19752499c6a`
- **Chain tx hash:** `0xeb95499ee7f652b6ad189314d606a996afe69e4f8332d4dea4ed44e8a37da998`
- **Chain block:** `41554095`

---

## File Mapping

This bundle consists of: `L1-345.md`, `L1-345.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-345.md` | Source of truth — edit this | Human or LLM |
| `L1-345.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 `L1-345`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._