# ⚛  L1 Principle — Cryogenic Storage Boiloff — MLI heat-leak estimation

**ID:** `L1-206` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Heat Transfer — *Multi-layer insulation heat-leak inverse*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** heat leak W per m2
> **📡 Carrier:** thermal · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554035

---

## 🧠 1. Introduction

**Cryogenic Storage Boiloff — MLI heat-leak estimation** is a **linear inverse problem** whose unknown lives in **heat leak W per m2** space, within the **Multi-layer insulation heat-leak inverse** sub-domain of **Heat Transfer**.

Measurements consist of thermal radiation / temperature measurements via a **boiloff flowmeter** sensing mechanism.

The forward operator applies, in order: L · radiation between layers operator; L · gas conduction operator; L · solid conduction 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 · radiation between layers → L · gas conduction → L · solid conduction → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.solid_conduction` `L.gas_conduction` `L.radiation_between_layers` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.radiation_between_layers` | L · radiation between layers operator |
| `L.gas_conduction` | L · gas conduction operator |
| `L.solid_conduction` | L · solid conduction operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Heat Transfer |
| Sub domain | Multi-layer insulation heat-leak inverse |
| Carrier | thermal |
| Problem class | linear_inverse |
| Solution space | heat_leak_W_per_m2 |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 3 |
| L dag | 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:** `mli_boiloff` · **Forward operator:** `mli_boiloff_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| T c k | — | 77 |
| T h k | — | 300 |
| Snr db | dB | 30 |
| N layers | — | 20 |
| N samples | — | 200 |
| Layer spacing error | — | 0 |
| Vacuum pressure error | — | 0 |
| Layer emissivity error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| T c k | — | 4 – 250 |
| T h k | — | 77 – 500 |
| Snr db | dB | 0 – 40 |
| N layers | — | 1 – 100 |
| N samples | — | 10 – 10000 |
| Layer spacing error | — | 0.0 – 0.3 |
| Vacuum pressure error | — | 0.0 – 0.001 |
| Layer emissivity error | — | 0.0 – 0.3 |

## 🎯 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 = `200` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x601eeb79b9b6cd4da18dc611371345fe2e8f6150229ee037df88151a2c19f1df`
- **Chain tx hash:** `0x6412fa9dc0b912c7ea35cf766cb4f1287504277a7194bf393aa0a154ac8a9c7d`
- **Chain block:** `41554035`

---

## File Mapping

This bundle consists of: `L1-206.md`, `L1-206.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-206.md` | Source of truth — edit this | Human or LLM |
| `L1-206.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 `L1-206`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._