# ⚛  L1 Principle — Radar Cross-Section — backscatter reconstruction

**ID:** `L1-237` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Electromagnetics — *Monostatic / bistatic RCS*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** rcs vs aspect
> **📡 Carrier:** em · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553987

---

## 🧠 1. Introduction

**Radar Cross-Section — backscatter reconstruction** is a **linear inverse problem** whose unknown lives in **rcs vs aspect** space, within the **Monostatic / bistatic RCS** sub-domain of **Electromagnetics**.

Measurements consist of electromagnetic field measurements via a **radar echo** sensing mechanism.

The forward operator applies, in order: L · incident pw operator; L · scatter target operator; L · coherent sum operator; pixel-level spatial averaging on the detector.

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

## ⚙ 2. Forward Model

Physical chain: **x** → L · incident pw → L · scatter target → L · coherent sum → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.coherent_sum` `L.scatter_target` `L.incident_pw` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.incident_pw` | L · incident pw operator |
| `L.scatter_target` | L · scatter target operator |
| `L.coherent_sum` | L · coherent sum operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Electromagnetics |
| Sub domain | Monostatic / bistatic RCS |
| Carrier | em |
| Problem class | linear_inverse |
| Solution space | rcs_vs_aspect |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 5 |
| L dag | 3.2 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | RCS_error_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `rcs` · **Forward operator:** `rcs_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 25 |
| N freqs | — | 32 |
| N angles | — | 361 |
| Freq ghz | GHz | 10 |
| Freq error | — | 0 |
| Range error | — | 0 |
| Material error | — | 0 |
| Target orientation error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | -5 – 40 |
| N freqs | — | 1 – 512 |
| N angles | — | 36 – 36000 |
| Freq ghz | GHz | 0.1 – 300 |
| Freq error | — | 0.0 – 0.02 |
| Range error | — | 0.0 – 1.0 |
| Material error | — | 0.0 – 0.1 |
| Target orientation error | — | 0.0 – 0.1 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 3.0

| Metric | Range |
|---|---|
| Rcs db | 0.3 – 20.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **RCS_error_dB**, with κ = `500` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xe27c89cd980325966a1b34e66546f563006d702fcf8000f6274d633214802bb5`
- **Chain tx hash:** `0xb6f0e14d2e34e9d8d1c99a022751d39066da9b5ae0ab908c916b2b178ec40fea`
- **Chain block:** `41553987`

---

## File Mapping

This bundle consists of: `L1-237.md`, `L1-237.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-237.md` | Source of truth — edit this | Human or LLM |
| `L1-237.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 `L1-237`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._