# ⚛  L1 Principle — Monte Carlo Neutron Transport — stochastic particle tracking

**ID:** `L1-360` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Nuclear Engineering — *MCNP / OpenMC continuous-energy MC transport*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** tally expected values with variance
> **📡 Carrier:** neutron · **🌫 Noise:** poisson
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554098

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## 🧠 1. Introduction

**Monte Carlo Neutron Transport — stochastic particle tracking** is a **linear inverse problem** whose unknown lives in **tally expected values with variance** space, within the **MCNP / OpenMC continuous-energy MC transport** sub-domain of **Nuclear Engineering**.

Measurements consist of neutrons transmitted through the sample via a **tally scores** sensing mechanism.

The forward operator applies, in order: L · sample source operator; L · track particle operator; L · score tally operator; int · stochastic operator.

Observations are corrupted by Poisson counting noise. Statistical convergence O(1/sqrt(N_histories)); bias via biased sampling; ill-posed for very deep penetration.

## ⚙ 2. Forward Model

Physical chain: **x** → L · sample source → L · track particle → L · score tally → int · stochastic → **y** (detector).

```
y = `int.stochastic` `L.score_tally` `L.track_particle` `L.sample_source` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.sample_source` | L · sample source operator |
| `L.track_particle` | L · track particle operator |
| `L.score_tally` | L · score tally operator |
| `int.stochastic` | Int · stochastic operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Nuclear Engineering |
| Sub domain | MCNP / OpenMC continuous-energy MC transport |
| Carrier | neutron |
| Problem class | linear_inverse |
| Solution space | tally_expected_values_with_variance |
| Noise model | poisson |
| Integration axis | stochastic |
| Difficulty delta | 10 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Statistical convergence O(1/sqrt(N_histories)); bias via biased sampling; ill-posed for very deep penetration.

| Metric | Value |
|---|---|
| Metric | tally_rel_uncertainty_percent |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `mc_neutron_transport` · **Forward operator:** `mc_neutron_transport_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 30 |
| N cells | — | 10000 |
| N tallies | — | 50 |
| N histories | — | 1e+07 |
| Ace data error | — | 0 |
| Source biasing error | — | 0 |
| Variance reduction error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N cells | — | 10 – 1000000 |
| N tallies | — | 1 – 10000 |
| N histories | — | 10000.0 – 100000000000.0 |
| Ace data error | — | 0.0 – 0.05 |
| Source biasing error | — | 0.0 – 0.2 |
| Variance reduction error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 2.0

| Metric | Range |
|---|---|
| Tally rel | 0.1 – 30.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **tally_rel_uncertainty_percent**, with κ = `800` and δ = `10`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xff707605f77f25c0a80b1d2fb42a81948c2d5c44cf6d1236b89f84329fc59e5a`
- **Chain tx hash:** `0x64b83291c7ed683e5cfc62f63eda49da55effdd07636ff0bac0131e3f3bb93fd`
- **Chain block:** `41554098`

---

## File Mapping

This bundle consists of: `L1-360.md`, `L1-360.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-360.md` | Source of truth — edit this | Human or LLM |
| `L1-360.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 `L1-360`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._