# ⚛  L1 Principle — Reactor Thermal-Hydraulics — coupled T/H with neutronics

**ID:** `L1-359` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Nuclear Engineering — *RELAP / CTF core thermal-hydraulic transient*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** temp flow reactor core
> **📡 Carrier:** thermal · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554097

---

## 🧠 1. Introduction

**Reactor Thermal-Hydraulics — coupled T/H with neutronics** is a **nonlinear inverse problem** whose unknown lives in **temp flow reactor core** space, within the **RELAP / CTF core thermal-hydraulic transient** sub-domain of **Nuclear Engineering**.

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

The forward operator applies, in order: L · two phase flow operator; L · fuel rod conduction operator; L · coolant energy 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 · two phase flow → L · fuel rod conduction → L · coolant energy → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.coolant_energy` `L.fuel_rod_conduction` `L.two_phase_flow` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.two_phase_flow` | L · two phase flow operator |
| `L.fuel_rod_conduction` | L · fuel rod conduction operator |
| `L.coolant_energy` | L · coolant energy operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Nuclear Engineering |
| Sub domain | RELAP / CTF core thermal-hydraulic transient |
| Carrier | thermal |
| Problem class | nonlinear_inverse |
| Solution space | temp_flow_reactor_core |
| Noise model | gaussian |
| Integration axis | temporal |
| 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:** `thermal_hydraulics` · **Forward operator:** `thermal_hydraulics_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 30 |
| N axial | — | 24 |
| N samples | — | 1000 |
| N assemblies | — | 193 |
| Fuel k error | — | 0 |
| Friction factor error | — | 0 |
| Boiling correlation error | — | 0 |
| Heat transfer coeff error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N axial | — | 1 – 100 |
| N samples | — | 100 – 100000 |
| N assemblies | — | 1 – 1000 |
| Fuel k error | — | 0.0 – 0.1 |
| Friction factor error | — | 0.0 – 0.2 |
| Boiling correlation error | — | 0.0 – 0.3 |
| Heat transfer coeff error | — | 0.0 – 0.3 |

## 🎯 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 = `600` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x566757c58309bb7484c76db4bb549387fe8154c6777c8ed44e12a808a7f3d70a`
- **Chain tx hash:** `0xbb8a53776d3c15cfbb239abd438b7dfece7cf8ae6ff8adc765e57faa6690ead0`
- **Chain block:** `41554097`

---

## File Mapping

This bundle consists of: `L1-359.md`, `L1-359.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-359.md` | Source of truth — edit this | Human or LLM |
| `L1-359.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 `L1-359`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._