# ⚛  L1 Principle — Phase Change Material — Stefan moving-boundary problem

**ID:** `L1-202` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Heat Transfer — *Latent-heat tracking (melt/solid boundary)*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** moving interface and T fields
> **📡 Carrier:** thermal · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554034

---

## 🧠 1. Introduction

**Phase Change Material — Stefan moving-boundary problem** is a **nonlinear inverse problem** whose unknown lives in **moving interface and T fields** space, within the **Latent-heat tracking (melt/solid boundary)** sub-domain of **Heat Transfer**.

Measurements consist of thermal radiation / temperature measurements via a **thermocouples xray** sensing mechanism.

The forward operator applies, in order: L · enthalpy operator; L · interface tracking operator; L · heat transport 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 · enthalpy → L · interface tracking → L · heat transport → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.heat_transport` `L.interface_tracking` `L.enthalpy` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.enthalpy` | L · enthalpy operator |
| `L.interface_tracking` | L · interface tracking operator |
| `L.heat_transport` | L · heat transport operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Heat Transfer |
| Sub domain | Latent-heat tracking (melt/solid boundary) |
| Carrier | thermal |
| Problem class | nonlinear_inverse |
| Solution space | moving_interface_and_T_fields |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 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:** `stefan` · **Forward operator:** `stefan_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 128 |
| W | px | 128 |
| Snr db | dB | 30 |
| N sensors | — | 16 |
| K solid error | — | 0 |
| K liquid error | — | 0 |
| Supercool error | — | 0 |
| Latent heat error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 1024 |
| W | px | 32 – 1024 |
| Snr db | dB | 0 – 40 |
| N sensors | — | 4 – 256 |
| K solid error | — | 0.0 – 0.1 |
| K liquid error | — | 0.0 – 0.1 |
| Supercool error | — | 0.0 – 5.0 |
| Latent heat error | — | 0.0 – 0.1 |

## 🎯 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 = `700` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xef9180b73263bebaa1ae1c5c21b02b8607d77a0d415b6edb2e9645e477ec87ed`
- **Chain tx hash:** `0x48784f517e1b75a75d7553fd9bcc549cd76ce6494694fe85e4e082a93e046253`
- **Chain block:** `41554034`

---

## File Mapping

This bundle consists of: `L1-202.md`, `L1-202.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-202.md` | Source of truth — edit this | Human or LLM |
| `L1-202.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 `L1-202`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._