# ⚛  L1 Principle — Rayleigh Scattering — molecular / small-particle scattering

**ID:** `L1-244` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Electromagnetics — *Rayleigh regime optical scattering*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** molecular density or aerosol
> **📡 Carrier:** em · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553989

---

## 🧠 1. Introduction

**Rayleigh Scattering — molecular / small-particle scattering** is a **linear inverse problem** whose unknown lives in **molecular density or aerosol** space, within the **Rayleigh regime optical scattering** sub-domain of **Electromagnetics**.

Measurements consist of electromagnetic field measurements via a **photometer** sensing mechanism.

The forward operator applies, in order: L · small particle dipole operator; L · sigma lambda 4 operator; L · polarization operator; integration over the solid angle of incidence/emission.

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

## ⚙ 2. Forward Model

Physical chain: **x** → L · small particle dipole → L · sigma lambda 4 → L · polarization → Angular integration → **y** (detector).

```
y = ∫dΩ `L.polarization` `L.sigma_lambda_4` `L.small_particle_dipole` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.small_particle_dipole` | L · small particle dipole operator |
| `L.sigma_lambda_4` | L · sigma lambda 4 operator |
| `L.polarization` | L · polarization operator |
| `int.angular` | Integration over the solid angle of incidence/emission |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Electromagnetics |
| Sub domain | Rayleigh regime optical scattering |
| Carrier | em |
| Problem class | linear_inverse |
| Solution space | molecular_density_or_aerosol |
| Noise model | gaussian |
| Integration axis | angular |
| Difficulty delta | 3 |
| L dag | 2.8 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `rayleigh` · **Forward operator:** `rayleigh_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 30 |
| N angles | — | 16 |
| N wavelengths | — | 10 |
| Wavelength error | — | 0 |
| Path length error | — | 0 |
| Polarizability error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N angles | — | 1 – 256 |
| N wavelengths | — | 1 – 200 |
| Wavelength error | — | 0.0 – 0.01 |
| Path length error | — | 0.0 – 0.05 |
| Polarizability error | — | 0.0 – 0.1 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 24.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x45ddcc0e2a287a60e5231ec9777ff591b668f03b2bec096b3601ab329ca393dc`
- **Chain tx hash:** `0xc7a705a4da829a1f06329330ed168b9c38d152cf5607f393f6b554c96205b99c`
- **Chain block:** `41553989`

---

## File Mapping

This bundle consists of: `L1-244.md`, `L1-244.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-244.md` | Source of truth — edit this | Human or LLM |
| `L1-244.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 `L1-244`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._