# ⚛  L1 Principle — Neutron Radiography and Tomography

**ID:** `L1-130` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Scientific Instrumentation — *Neutron transmission imaging complementary to X-ray*
> **🎯 Problem class:** linear tomographic inverse · **🧮 Solution space:** attenuation map
> **📡 Carrier:** neutron · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554213

---

## 🧠 1. Introduction

**Neutron Radiography and Tomography** is a **linear tomographic reconstruction** whose unknown lives in **attenuation map** space, within the **Neutron transmission imaging complementary to X-ray** sub-domain of **Scientific Instrumentation**.

Measurements consist of neutrons transmitted through the sample via a **transmission attenuation** sensing mechanism.

The forward operator applies, in order: L · absorb · lambert operator; L · project · ray operator; pixel-level spatial averaging on the detector.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Beer-Lambert linear; CT reconstruction via FBP/ASTRA. Mismatch: beam hardening (lambda-dependent), scatter, flux inhomogeneity, motion.

## ⚙ 2. Forward Model

Physical chain: **x** → L · absorb · lambert → L · project · ray → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.project.ray` `L.absorb.lambert` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.absorb.lambert` | L · absorb · lambert operator |
| `L.project.ray` | L · project · ray operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Scientific Instrumentation |
| Sub domain | Neutron transmission imaging complementary to X-ray |
| Carrier | neutron |
| Problem class | linear_tomographic_inverse |
| Solution space | attenuation_map |
| Noise model | shot_poisson |
| Integration axis | projection |
| Difficulty delta | 3 |
| L dag | 2.7 |

## 📡 4. Measurement Model

Beer-Lambert linear; CT reconstruction via FBP/ASTRA. Mismatch: beam hardening (lambda-dependent), scatter, flux inhomogeneity, motion.

| Metric | Value |
|---|---|
| Metric | attenuation_NMSE |
| Secondary | spatial_resolution_um |

## 📏 5. Operating Range (Ω)

**Center problem class:** `neutron_tomography` · **Forward operator:** `neutron_radiographic_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 1024 |
| W | px | 1024 |
| N proj | — | 360 |
| L over d | — | 500 |
| Pixel um | µm | 50 |
| Beam hardening | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 4096 |
| W | px | 128 – 4096 |
| N proj | — | 10 – 2000 |
| L over d | — | 50 – 2000 |
| Pixel um | µm | 5 – 500 |
| Motion blur | — | 0.0 – 5.0 |
| Beam hardening | — | 0.0 – 0.3 |
| Limited angles | — | 0 – 120 |
| Scatter fraction | — | 0.0 – 0.3 |
| Flux inhomogeneity | — | 0.0 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** NMSE 5e-3

| Metric | Range |
|---|---|
| Nmse | 0.0001 – 0.1 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **attenuation_NMSE**, with κ = `200` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x1762642813882dedbb853691ccc843957c3315e2239980116db89db7b68b2940`
- **Chain tx hash:** `0x6c5adda00528028c9a90556c47a6c59e5889c066be928670a8f9d161158ca247`
- **Chain block:** `41554213`

---

## File Mapping

This bundle consists of: `L1-130.md`, `L1-130.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-130.md` | Source of truth — edit this | Human or LLM |
| `L1-130.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 `L1-130`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._