# ⚛  L1 Principle — Laser Heating — short-pulse temperature rise inversion

**ID:** `L1-205` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Heat Transfer — *Ultrafast laser-induced thermal transient*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D temperature transient
> **📡 Carrier:** thermal · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554035

---

## 🧠 1. Introduction

**Laser Heating — short-pulse temperature rise inversion** is a **linear inverse problem** whose unknown lives in **3D temperature transient** space, within the **Ultrafast laser-induced thermal transient** sub-domain of **Heat Transfer**.

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

The forward operator applies, in order: L · laser absorb operator; L · hyperbolic heat operator; L · nonfourier operator; detector accumulates flux over the exposure window.

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

## ⚙ 2. Forward Model

Physical chain: **x** → L · laser absorb → L · hyperbolic heat → L · nonfourier → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.nonfourier` `L.hyperbolic_heat` `L.laser_absorb` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.laser_absorb` | L · laser absorb operator |
| `L.hyperbolic_heat` | L · hyperbolic heat operator |
| `L.nonfourier` | L · nonfourier operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Heat Transfer |
| Sub domain | Ultrafast laser-induced thermal transient |
| Carrier | thermal |
| Problem class | linear_inverse |
| Solution space | 3D_temperature_transient |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 3.3 |

## 📡 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:** `laser_heating` · **Forward operator:** `laser_heating_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 128 |
| W | px | 128 |
| Z | — | 32 |
| Snr db | dB | 30 |
| Fs ghz | GHz | 1 |
| K error | — | 0 |
| Cv error | — | 0 |
| N samples | — | 200 |
| Pulse width error | — | 0 |
| Absorption coeff error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 1024 |
| W | px | 32 – 1024 |
| Z | — | 8 – 256 |
| Snr db | dB | 0 – 40 |
| Fs ghz | GHz | 0.001 – 1000 |
| K error | — | 0.0 – 0.1 |
| Cv error | — | 0.0 – 0.1 |
| N samples | — | 20 – 10000 |
| Pulse width error | — | 0.0 – 0.3 |
| Absorption coeff error | — | 0.0 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 22.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `440` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x9a1d1db81a7eb632422dc7fbc81ab2a4b8b6c25c038239aebd5c9e0f93015265`
- **Chain tx hash:** `0xe889dae0b672e1cedf630e626559328ff90f8493ca381178aa504b833551e0ed`
- **Chain block:** `41554035`

---

## File Mapping

This bundle consists of: `L1-205.md`, `L1-205.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-205.md` | Source of truth — edit this | Human or LLM |
| `L1-205.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 `L1-205`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._