# ⚛  L1 Principle — CARS — Coherent Anti-Stokes Raman Scattering

**ID:** `L1-138` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Spectroscopy — *Third-order nonlinear coherent vibrational microscopy*
> **🎯 Problem class:** nonlinear inverse spectral · **🧮 Solution space:** concentration map
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson coherent
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554226

---

## 🧠 1. Introduction

**CARS — Coherent Anti-Stokes Raman Scattering** is a **nonlinear inverse spectral** whose unknown lives in **concentration map** space, within the **Third-order nonlinear coherent vibrational microscopy** sub-domain of **Spectroscopy**.

Measurements consist of photons collected by an optical detector via a **coherent nonlinear** sensing mechanism.

The forward operator applies, in order: L · beat · twocolor operator; S · nonlinear · chi3 operator; detector accumulates flux over the exposure window.

Observations are corrupted by shot noise in a coherent detection regime. Well-posed for multiplex CARS with full spectrum + max-entropy phase retrieval; ill-posed for narrowband CARS contaminated by chi_NR (distortive interference with Lorentzian chi_R).

## ⚙ 2. Forward Model

Physical chain: **x** → L · beat · twocolor → S · nonlinear · chi3 → Temporal integration → **y** (detector).

```
y = ∫_t dt `S.nonlinear.chi3` `L.beat.twocolor` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.beat.twocolor` | L · beat · twocolor operator |
| `S.nonlinear.chi3` | S · nonlinear · chi3 operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Spectroscopy |
| Sub domain | Third-order nonlinear coherent vibrational microscopy |
| Carrier | photon |
| Problem class | nonlinear_inverse_spectral |
| Solution space | concentration_map |
| Noise model | shot_poisson_coherent |
| Integration axis | spectral_and_temporal |
| Difficulty delta | 5 |
| L dag | 3 |

## 📡 4. Measurement Model

Well-posed for multiplex CARS with full spectrum + max-entropy phase retrieval; ill-posed for narrowband CARS contaminated by chi_NR (distortive interference with Lorentzian chi_R).

| Metric | Value |
|---|---|
| Metric | concentration_NMSE |
| Secondary | SNR_dB |

## 📏 5. Operating Range (Ω)

**Center problem class:** `multiplex_cars` · **Forward operator:** `cars_chi3_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 256 |
| W | px | 256 |
| Rho nr | — | 0.3 |
| N omega | — | 300 |
| Lambda p nm | nm | 800 |
| Lambda s nm | nm | 1064 |
| Pulse energy fluct | — | 0.05 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 64 – 1024 |
| W | px | 64 – 1024 |
| Rho nr | — | 0.0 – 5.0 |
| N omega | — | 1 – 2048 |
| Lambda p nm | nm | 750 – 1100 |
| Lambda s nm | nm | 1000 – 1300 |
| Focal volume error | — | 0.0 – 0.2 |
| Pulse energy fluct | — | 0.0 – 0.3 |
| Frequency drift cm1 | — | 0.0 – 20.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** NMSE 2e-2

| Metric | Range |
|---|---|
| Nmse | 0.001 – 0.5 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **concentration_NMSE**, with κ = `300` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x29235831ed94226fd6649d7716997998c214b53ab22d5e395c703c28837060c2`
- **Chain tx hash:** `0x54723a83a9406ebfe78f1969e8bb0a8f5f0edee140e4a6d8044b52bd1438a51d`
- **Chain block:** `41554226`

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## File Mapping

This bundle consists of: `L1-138.md`, `L1-138.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-138.md` | Source of truth — edit this | Human or LLM |
| `L1-138.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 `L1-138`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._