# ⚛  L1 Principle — Neutron Diffraction (powder / single crystal)

**ID:** `L1-135` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Scientific Instrumentation — *Neutron elastic diffraction for magnetic + H-site structures*
> **🎯 Problem class:** parametric structure refinement · **🧮 Solution space:** atomic magnetic structure
> **📡 Carrier:** neutron · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554214

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## 🧠 1. Introduction

**Neutron Diffraction (powder / single crystal)** is a **parametric structure refinement** whose unknown lives in **atomic magnetic structure** space, within the **Neutron elastic diffraction for magnetic + H-site structures** sub-domain of **Scientific Instrumentation**.

Measurements consist of neutrons transmitted through the sample via a **nuclear magnetic diffraction** sensing mechanism.

The forward operator applies, in order: L · diffract · bragg operator; L · project · rescipocal operator; integration over the solid angle of incidence/emission.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Crystalline-structure refinement linear in peak intensities; limited-resolution phase problem resolved by known symmetry.

## ⚙ 2. Forward Model

Physical chain: **x** → L · diffract · bragg → L · project · rescipocal → Angular integration → **y** (detector).

```
y = ∫dΩ `L.project.rescipocal` `L.diffract.bragg` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.diffract.bragg` | L · diffract · bragg operator |
| `L.project.rescipocal` | L · project · rescipocal operator |
| `int.angular` | Integration over the solid angle of incidence/emission |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Scientific Instrumentation |
| Sub domain | Neutron elastic diffraction for magnetic + H-site structures |
| Carrier | neutron |
| Problem class | parametric_structure_refinement |
| Solution space | atomic_magnetic_structure |
| Noise model | shot_poisson |
| Integration axis | angular |
| Difficulty delta | 3 |
| L dag | 2.7 |

## 📡 4. Measurement Model

Crystalline-structure refinement linear in peak intensities; limited-resolution phase problem resolved by known symmetry.

| Metric | Value |
|---|---|
| Metric | Rwp |
| Secondary | atomic_position_RMSE_angstrom |

## 📏 5. Operating Range (Ω)

**Center problem class:** `powder_rietveld` · **Forward operator:** `neutron_powder_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N atoms | — | 20 |
| N points | — | 10000 |
| Lambda a | — | 1.5 |
| Absorption correction | — | 0 |
| Preferred orientation | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N atoms | — | 1 – 1000 |
| N points | — | 1000 – 100000 |
| Lambda a | — | 0.5 – 6.0 |
| Absorption correction | — | 0.0 – 0.3 |
| Magnetic interference | — | 0.0 – 0.5 |
| Preferred orientation | — | 0.0 – 0.5 |
| Background model error | — | 0.0 – 0.2 |
| Thermal diffuse scatter | — | 0.0 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** Rwp 0.05

| Metric | Range |
|---|---|
| Rwp | 0.01 – 0.3 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **Rwp**, with κ = `300` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xfe56338a5def18317f82f6ab6bfebc6a7a9bcc173c3c379767c92b9b6ecc24dc`
- **Chain tx hash:** `0x2bfa0458c4f840f39ec95ebaee6097b399673e727b65d33dff0bdf3210c13cbe`
- **Chain block:** `41554214`

---

## File Mapping

This bundle consists of: `L1-135.md`, `L1-135.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-135.md` | Source of truth — edit this | Human or LLM |
| `L1-135.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 `L1-135`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._