# ⚛  L1 Principle — Ideal MHD — magnetohydrodynamics infinite-conductivity limit

**ID:** `L1-342` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Plasma Physics — *Ideal MHD plasma simulation*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** plasma B u rho T spacetime
> **📡 Carrier:** plasma · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554081

---

## 🧠 1. Introduction

**Ideal MHD — magnetohydrodynamics infinite-conductivity limit** is a **linear inverse problem** whose unknown lives in **plasma B u rho T spacetime** space, within the **Ideal MHD plasma simulation** sub-domain of **Plasma Physics**.

Measurements consist of plasma particle and field diagnostics via a **langmuir probe bdotfield** sensing mechanism.

The forward operator applies, in order: mass-balance: ∂_t ρ + ∇·(ρv) = 0; L · momentum lorentz operator; L · induction operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → Continuity equation → L · momentum lorentz → L · induction → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.induction` `L.momentum_lorentz` ∂_t ρ + ∇·(ρv) x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.continuity` | Mass-balance: ∂_t ρ + ∇·(ρv) = 0 |
| `L.momentum_lorentz` | L · momentum lorentz operator |
| `L.induction` | L · induction operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Plasma Physics |
| Sub domain | Ideal MHD plasma simulation |
| Carrier | plasma |
| Problem class | linear_inverse |
| Solution space | plasma_B_u_rho_T_spacetime |
| Noise model | gaussian |
| 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:** `ideal_mhd` · **Forward operator:** `ideal_mhd_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 256 |
| W | px | 256 |
| Z | — | 128 |
| Snr db | dB | 25 |
| N times | — | 500 |
| Bc error | — | 0 |
| Rho error | — | 0 |
| B field error | — | 0 |
| Temperature error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 2048 |
| W | px | 32 – 2048 |
| Z | — | 16 – 1024 |
| Snr db | dB | 0 – 40 |
| N times | — | 50 – 100000 |
| Bc error | — | 0.0 – 0.2 |
| Rho error | — | 0.0 – 0.2 |
| B field error | — | 0.0 – 0.1 |
| Temperature 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 = `700` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x094b240ce49152ed372797943e5a6ff1c785b8bd9e7acc12253e7c2cd57c0749`
- **Chain tx hash:** `0x22ee0542582470af5b01ab08c9fa548c2204ad518e0bca8010ed0efabd9a8616`
- **Chain block:** `41554081`

---

## File Mapping

This bundle consists of: `L1-342.md`, `L1-342.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-342.md` | Source of truth — edit this | Human or LLM |
| `L1-342.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 `L1-342`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._