# ⚛  L1 Principle — Point Reactor Kinetics — power transient modeling

**ID:** `L1-357` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Nuclear Engineering — *Coupled precursor/power ODEs for reactivity insertion*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** reactivity time and power
> **📡 Carrier:** neutron · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554097

---

## 🧠 1. Introduction

**Point Reactor Kinetics — power transient modeling** is a **linear inverse problem** whose unknown lives in **reactivity time and power** space, within the **Coupled precursor/power ODEs for reactivity insertion** sub-domain of **Nuclear Engineering**.

Measurements consist of neutrons transmitted through the sample via a **ex core detectors** sensing mechanism.

The forward operator applies, in order: L · precursor balance operator; L · power balance operator; L · delayed neutrons 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 · precursor balance → L · power balance → L · delayed neutrons → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.delayed_neutrons` `L.power_balance` `L.precursor_balance` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.precursor_balance` | L · precursor balance operator |
| `L.power_balance` | L · power balance operator |
| `L.delayed_neutrons` | L · delayed neutrons operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Nuclear Engineering |
| Sub domain | Coupled precursor/power ODEs for reactivity insertion |
| Carrier | neutron |
| Problem class | linear_inverse |
| Solution space | reactivity_time_and_power |
| 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:** `pointkinetics` · **Forward operator:** `pointkinetics_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 30 |
| N groups | — | 6 |
| N samples | — | 1000 |
| Rho error | — | 0 |
| Lambda error | — | 0 |
| Beta eff error | — | 0 |
| Generation time error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N groups | — | 1 – 10 |
| N samples | — | 100 – 100000 |
| Rho error | — | 0.0 – 0.1 |
| Lambda error | — | 0.0 – 0.1 |
| Beta eff error | — | 0.0 – 0.1 |
| Generation time error | — | 0.0 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 25.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xde713502edc70c8b4e58593b58072e264d5d8bcd263d3449a8321ec13c68adc2`
- **Chain tx hash:** `0xf17a2c44dc3a9a54d63ba209c86163bc3105d6f5d5734074b2c67ad6e13ea7aa`
- **Chain block:** `41554097`

---

## File Mapping

This bundle consists of: `L1-357.md`, `L1-357.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-357.md` | Source of truth — edit this | Human or LLM |
| `L1-357.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 `L1-357`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._