# ⚛  L1 Principle — Nuclear Data — R-matrix resonance evaluation

**ID:** `L1-362` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Nuclear Engineering — *Resonance cross-section parameter inference*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** resonance parameter set
> **📡 Carrier:** neutron · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554106

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## 🧠 1. Introduction

**Nuclear Data — R-matrix resonance evaluation** is a **nonlinear inverse problem** whose unknown lives in **resonance parameter set** space, within the **Resonance cross-section parameter inference** sub-domain of **Nuclear Engineering**.

Measurements consist of neutrons transmitted through the sample via a **xs measurements** sensing mechanism.

The forward operator applies, in order: L · breit wigner operator; L · rmatrix fit operator; L · doppler broaden operator; int · energy operator.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · breit wigner → L · rmatrix fit → L · doppler broaden → int · energy → **y** (detector).

```
y = `int.energy` `L.doppler_broaden` `L.rmatrix_fit` `L.breit_wigner` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.breit_wigner` | L · breit wigner operator |
| `L.rmatrix_fit` | L · rmatrix fit operator |
| `L.doppler_broaden` | L · doppler broaden operator |
| `int.energy` | Int · energy operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Nuclear Engineering |
| Sub domain | Resonance cross-section parameter inference |
| Carrier | neutron |
| Problem class | nonlinear_inverse |
| Solution space | resonance_parameter_set |
| Noise model | gaussian |
| Integration axis | energy |
| Difficulty delta | 5 |
| L dag | 3.3 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | resonance_param_rel_error_percent |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `rmatrix` · **Forward operator:** `rmatrix_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 30 |
| Width error | — | 0 |
| N energy pts | — | 5000 |
| N resonances | — | 100 |
| Peak pos error | — | 0 |
| Temp nuc error | — | 0 |
| Background error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| Width error | — | 0.0 – 0.1 |
| N energy pts | — | 100 – 1000000 |
| N resonances | — | 1 – 5000 |
| Peak pos error | — | 0.0 – 0.02 |
| Temp nuc error | — | 0.0 – 100 |
| Background error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 2.0

| Metric | Range |
|---|---|
| Param rel | 0.2 – 30.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **resonance_param_rel_error_percent**, with κ = `360` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xf18afdccdb466faa8458259f883a7439d2fd424b3568bcc1b7893af2d912852a`
- **Chain tx hash:** `0x2e703c906d9ccbac6238c63e934269c8d3bfd56c1029d20920dc32019b7a8e78`
- **Chain block:** `41554106`

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## File Mapping

This bundle consists of: `L1-362.md`, `L1-362.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-362.md` | Source of truth — edit this | Human or LLM |
| `L1-362.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 `L1-362`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._