# ⚛  L1 Principle — Antenna Analysis — radiation pattern inversion

**ID:** `L1-236` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Electromagnetics — *Antenna near/far-field pattern synthesis*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** radiation pattern 2D
> **📡 Carrier:** em · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553987

---

## 🧠 1. Introduction

**Antenna Analysis — radiation pattern inversion** is a **linear inverse problem** whose unknown lives in **radiation pattern 2D** space, within the **Antenna near/far-field pattern synthesis** sub-domain of **Electromagnetics**.

Measurements consist of electromagnetic field measurements via a **anechoic chamber** sensing mechanism.

The forward operator applies, in order: L · source current operator; L · array factor operator; L · radiate farfield 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 · source current → L · array factor → L · radiate farfield → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.radiate_farfield` `L.array_factor` `L.source_current` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.source_current` | L · source current operator |
| `L.array_factor` | L · array factor operator |
| `L.radiate_farfield` | L · radiate farfield operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Electromagnetics |
| Sub domain | Antenna near/far-field pattern synthesis |
| Carrier | em |
| Problem class | linear_inverse |
| Solution space | radiation_pattern_2D |
| Noise model | gaussian |
| Integration axis | spatial |
| 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:** `antenna_radiation` · **Forward operator:** `antenna_radiation_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N phi | — | 361 |
| Snr db | dB | 30 |
| N theta | — | 361 |
| Freq ghz | GHz | 10 |
| Pos error | — | 0 |
| N elements | — | 16 |
| Phase error | — | 0 |
| Amplitude error | — | 0 |
| Mutual coupling error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N phi | — | 36 – 3600 |
| Snr db | dB | 0 – 40 |
| N theta | — | 36 – 3600 |
| Freq ghz | GHz | 0.1 – 300 |
| Pos error | — | 0.0 – 0.05 |
| N elements | — | 1 – 4096 |
| Phase error | — | 0.0 – 0.2 |
| Amplitude error | — | 0.0 – 0.2 |
| Mutual coupling error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 26.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x5f8661333309273fc67e41a7edf222ddbdc9139419daa91591ae219c8aaac3ac`
- **Chain tx hash:** `0x3c0214ed248c0967874325a64faca642db9500843041c074f6e85467c6ba0597`
- **Chain block:** `41553987`

---

## File Mapping

This bundle consists of: `L1-236.md`, `L1-236.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-236.md` | Source of truth — edit this | Human or LLM |
| `L1-236.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 `L1-236`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._