# ⚛  L1 Principle — Inverse Synthetic Aperture Radar (ISAR) — rotating-target imaging

**ID:** `L1-252` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Electromagnetics — *ISAR range-Doppler imaging of maneuvering targets*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D target reflectivity
> **📡 Carrier:** em · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554000

---

## 🧠 1. Introduction

**Inverse Synthetic Aperture Radar (ISAR) — rotating-target imaging** is a **linear inverse problem** whose unknown lives in **2D target reflectivity** space, within the **ISAR range-Doppler imaging of maneuvering targets** sub-domain of **Electromagnetics**.

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

The forward operator applies, in order: L · pulse doppler operator; L · motion compensate operator; L · range doppler map 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 · pulse doppler → L · motion compensate → L · range doppler map → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.range_doppler_map` `L.motion_compensate` `L.pulse_doppler` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.pulse_doppler` | L · pulse doppler operator |
| `L.motion_compensate` | L · motion compensate operator |
| `L.range_doppler_map` | L · range doppler map operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Electromagnetics |
| Sub domain | ISAR range-Doppler imaging of maneuvering targets |
| Carrier | em |
| Problem class | linear_inverse |
| Solution space | 2D_target_reflectivity |
| 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:** `isar` · **Forward operator:** `isar_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Prf hz | Hz | 1000 |
| Snr db | dB | 20 |
| N pulses | — | 256 |
| Phase error | — | 0 |
| N range bins | — | 256 |
| Motion error | — | 0 |
| Cross range aberration | — | 0 |
| Doppler ambiguity error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Prf hz | Hz | 10 – 100000 |
| Snr db | dB | -10 – 40 |
| N pulses | — | 32 – 4096 |
| Phase error | — | 0.0 – 0.2 |
| N range bins | — | 64 – 4096 |
| Motion error | — | 0.0 – 0.3 |
| Cross range aberration | — | 0.0 – 0.3 |
| Doppler ambiguity 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:** `0x096365c677c8ba5352962ca84cb8838e263f41fd3333297fa7916b30ef79b545`
- **Chain tx hash:** `0x7a1c7ce4120ec5b42fc8b5708ab2631b8fee401941ef43d193b9aca857d6f769`
- **Chain block:** `41554000`

---

## File Mapping

This bundle consists of: `L1-252.md`, `L1-252.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-252.md` | Source of truth — edit this | Human or LLM |
| `L1-252.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 `L1-252`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._