# ⚛  L1 Principle — PIC (Particle-in-Cell) — plasma kinetic simulation

**ID:** `L1-346` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Plasma Physics — *PIC kinetic plasma simulation*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** particle trajectories plus fields
> **📡 Carrier:** plasma · **🌫 Noise:** poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554095

---

## 🧠 1. Introduction

**PIC (Particle-in-Cell) — plasma kinetic simulation** is a **linear inverse problem** whose unknown lives in **particle trajectories plus fields** space, within the **PIC kinetic plasma simulation** sub-domain of **Plasma Physics**.

Measurements consist of plasma particle and field diagnostics via a **probes cameras** sensing mechanism.

The forward operator applies, in order: L · particle push operator; L · field interpolate operator; L · charge deposit operator; detector accumulates flux over the exposure window.

Observations are corrupted by Poisson counting noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · particle push → L · field interpolate → L · charge deposit → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.charge_deposit` `L.field_interpolate` `L.particle_push` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.particle_push` | L · particle push operator |
| `L.field_interpolate` | L · field interpolate operator |
| `L.charge_deposit` | L · charge deposit operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Plasma Physics |
| Sub domain | PIC kinetic plasma simulation |
| Carrier | plasma |
| Problem class | linear_inverse |
| Solution space | particle_trajectories_plus_fields |
| Noise model | poisson |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

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

## 📏 5. Operating Range (Ω)

**Center problem class:** `pic` · **Forward operator:** `pic_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 25 |
| N cells | — | 1e+06 |
| N times | — | 5000 |
| N particles | — | 1e+08 |
| Statistical noise | — | 0 |
| Initial dist error | — | 0 |
| Grid dispersion error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N cells | — | 1000.0 – 10000000000.0 |
| N times | — | 100 – 10000000 |
| N particles | — | 10000.0 – 10000000000000.0 |
| Statistical noise | — | 0.0 – 0.3 |
| Initial dist error | — | 0.0 – 0.3 |
| Grid dispersion error | — | 0.0 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 22.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `600` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xb75c4b1f2b2a1a0ea7339a43e1548b59c72958d3797685a4b413ede7357ae632`
- **Chain tx hash:** `0xfb75ec00b441e0858325f45c8d086e8735a09a5f630f4e582c9722ec9625ed58`
- **Chain block:** `41554095`

---

## File Mapping

This bundle consists of: `L1-346.md`, `L1-346.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-346.md` | Source of truth — edit this | Human or LLM |
| `L1-346.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 `L1-346`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._