# ⚛  L1 Principle — Resistive MHD — finite-resistivity plasma

**ID:** `L1-343` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Plasma Physics — *Reconnection and resistive tearing modes*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** plasma with reconnection
> **📡 Carrier:** plasma · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554082

---

## 🧠 1. Introduction

**Resistive MHD — finite-resistivity plasma** is a **nonlinear inverse problem** whose unknown lives in **plasma with reconnection** space, within the **Reconnection and resistive tearing modes** sub-domain of **Plasma Physics**.

Measurements consist of plasma particle and field diagnostics via a **soft xray interferometer** sensing mechanism.

The forward operator applies, in order: L · ohm finite operator; L · induction resistive operator; L · reconnect operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Reconnection has multiple scales (resistive, Hall, electron inertia).

## ⚙ 2. Forward Model

Physical chain: **x** → L · ohm finite → L · induction resistive → L · reconnect → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.reconnect` `L.induction_resistive` `L.ohm_finite` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.ohm_finite` | L · ohm finite operator |
| `L.induction_resistive` | L · induction resistive operator |
| `L.reconnect` | L · reconnect operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Plasma Physics |
| Sub domain | Reconnection and resistive tearing modes |
| Carrier | plasma |
| Problem class | nonlinear_inverse |
| Solution space | plasma_with_reconnection |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 10 |
| L dag | 3.7 |

## 📡 4. Measurement Model

Reconnection has multiple scales (resistive, Hall, electron inertia).

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

## 📏 5. Operating Range (Ω)

**Center problem class:** `resistive_mhd` · **Forward operator:** `resistive_mhd_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 512 |
| W | px | 512 |
| Eta | — | 0.0001 |
| Snr db | dB | 25 |
| N times | — | 2000 |
| Bc error | — | 0 |
| Eta error | — | 0 |
| Grid error | — | 0 |
| Hyper resistivity error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 64 – 4096 |
| W | px | 64 – 4096 |
| Eta | — | 1e-08 – 0.1 |
| Snr db | dB | 0 – 40 |
| N times | — | 100 – 100000 |
| Bc error | — | 0.0 – 0.3 |
| Eta error | — | 0.0 – 0.3 |
| Grid error | — | 0.0 – 0.2 |
| Hyper resistivity error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 18.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1000` and δ = `10`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xb348d10247e3937c03804c3d34b771e9ec4832aacde658ed9469bf63c3a3eaee`
- **Chain tx hash:** `0xe5306dc3e3e821a0bac43148341812b0f2ce42b7e6d0e561f9558d77c5e4743e`
- **Chain block:** `41554082`

---

## File Mapping

This bundle consists of: `L1-343.md`, `L1-343.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-343.md` | Source of truth — edit this | Human or LLM |
| `L1-343.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 `L1-343`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._