# ⚛  L1 Principle — Muon Tomography (cosmic-ray scattering imaging)

**ID:** `L1-132` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Scientific Instrumentation — *High-Z imaging via cosmic-ray muon MCS*
> **🎯 Problem class:** statistical scattering inverse · **🧮 Solution space:** z eff map
> **📡 Carrier:** muon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554214

---

## 🧠 1. Introduction

**Muon Tomography (cosmic-ray scattering imaging)** is a **statistical scattering inverse** whose unknown lives in **z eff map** space, within the **High-Z imaging via cosmic-ray muon MCS** sub-domain of **Scientific Instrumentation**.

Measurements consist of muons traversing or stopping in the target via a **multiple coulomb scatter** sensing mechanism.

The forward operator applies, in order: L · scatter · MCS operator; L · project · pathlength operator; pixel-level spatial averaging on the detector.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Reconstruction is Poisson-limited at low flux; angular resolution O(10 mrad) at GeV. Hybrid stopping-power techniques (muon decay counting) add info.

## ⚙ 2. Forward Model

Physical chain: **x** → L · scatter · MCS → L · project · pathlength → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.project.pathlength` `L.scatter.MCS` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.scatter.MCS` | L · scatter · mcs operator |
| `L.project.pathlength` | L · project · pathlength operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Scientific Instrumentation |
| Sub domain | High-Z imaging via cosmic-ray muon MCS |
| Carrier | muon |
| Problem class | statistical_scattering_inverse |
| Solution space | z_eff_map |
| Noise model | shot_poisson |
| Integration axis | angular |
| Difficulty delta | 5 |
| L dag | 2.7 |

## 📡 4. Measurement Model

Reconstruction is Poisson-limited at low flux; angular resolution O(10 mrad) at GeV. Hybrid stopping-power techniques (muon decay counting) add info.

| Metric | Value |
|---|---|
| Metric | Z_eff_NMSE |
| Secondary | spatial_resolution_mm |

## 📏 5. Operating Range (Ω)

**Center problem class:** `muon_tomography` · **Forward operator:** `muon_tomo_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N muon | — | 1e+07 |
| Acq time hours | — | 24 |
| Tracker res mm | mm | 1 |
| Momentum unknown | — | 1 |
| Flux inhomogeneity | — | 0.1 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N muon | — | 10000.0 – 1000000000.0 |
| Acq time hours | — | 1 – 720 |
| Tracker res mm | mm | 0.1 – 10 |
| Momentum unknown | — | 0 – 1 |
| Angular resolution | — | 1 – 50 |
| Flux inhomogeneity | — | 0.0 – 0.3 |
| Background contamination | — | 0.0 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** Z_eff NMSE 0.05

| Metric | Range |
|---|---|
| Z eff nmse | 0.001 – 0.5 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **Z_eff_NMSE**, with κ = `500` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x0436233d55ed7be6c8e7fb25b3f12095bf1dddc715c8d211b09b8fe891f7186f`
- **Chain tx hash:** `0xd2cb17040d07b2d73365c1164590e156449b2ef2f50fc6c212316256be757b3c`
- **Chain block:** `41554214`

---

## File Mapping

This bundle consists of: `L1-132.md`, `L1-132.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-132.md` | Source of truth — edit this | Human or LLM |
| `L1-132.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 `L1-132`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._