# ⚛  L1 Principle — Participating Media — RTE with gas/soot emission-absorption

**ID:** `L1-200` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Heat Transfer — *Line-by-line gas spectroscopy + soot radiation*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D soot concentration and temp
> **📡 Carrier:** thermal · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554034

---

## 🧠 1. Introduction

**Participating Media — RTE with gas/soot emission-absorption** is a **nonlinear inverse problem** whose unknown lives in **3D soot concentration and temp** space, within the **Line-by-line gas spectroscopy + soot radiation** sub-domain of **Heat Transfer**.

Measurements consist of thermal radiation / temperature measurements via a **multispectral pyrometer** sensing mechanism.

The forward operator applies, in order: L · gas absorb operator; L · soot emit operator; L · line by line operator; detector sums all spectral bands.

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

## ⚙ 2. Forward Model

Physical chain: **x** → L · gas absorb → L · soot emit → L · line by line → Spectral integration → **y** (detector).

```
y = Σ_λ `L.line_by_line` `L.soot_emit` `L.gas_absorb` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.gas_absorb` | L · gas absorb operator |
| `L.soot_emit` | L · soot emit operator |
| `L.line_by_line` | L · line by line operator |
| `int.spectral` | Detector sums all spectral bands |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Heat Transfer |
| Sub domain | Line-by-line gas spectroscopy + soot radiation |
| Carrier | thermal |
| Problem class | nonlinear_inverse |
| Solution space | 3D_soot_concentration_and_temp |
| Noise model | gaussian |
| Integration axis | spectral |
| Difficulty delta | 5 |
| L dag | 3.7 |

## 📡 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:** `participating_media` · **Forward operator:** `participating_media_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 128 |
| W | px | 128 |
| Z | — | 32 |
| Snr db | dB | 30 |
| N freqs | — | 32 |
| N species | — | 4 |
| Gas conc error | — | 0 |
| T nonuniformity | — | 0 |
| Band model error | — | 0 |
| Soot index error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 1024 |
| W | px | 32 – 1024 |
| Z | — | 8 – 256 |
| Snr db | dB | 0 – 40 |
| N freqs | — | 4 – 1024 |
| N species | — | 1 – 20 |
| Gas conc error | — | 0.0 – 0.2 |
| T nonuniformity | — | 0.0 – 0.3 |
| Band model error | — | 0.0 – 0.2 |
| Soot index error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 20.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `700` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x05baf99467fc03a6446d5b0f15ddcb519c4f23c94754a4d2d78ced4c41f7a9ce`
- **Chain tx hash:** `0xd41fabba8faaa5072f72587e28bc8c12d851c9770b915b04eed21833f66d16e2`
- **Chain block:** `41554034`

---

## File Mapping

This bundle consists of: `L1-200.md`, `L1-200.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-200.md` | Source of truth — edit this | Human or LLM |
| `L1-200.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 `L1-200`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._