# ⚛  L1 Principle — Ray Tracing (EM) — wireless propagation model

**ID:** `L1-253` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Electromagnetics — *Urban propagation ray tracing (5G/6G)*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** signal strength map
> **📡 Carrier:** em · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554001

---

## 🧠 1. Introduction

**Ray Tracing (EM) — wireless propagation model** is a **linear inverse problem** whose unknown lives in **signal strength map** space, within the **Urban propagation ray tracing (5G/6G)** sub-domain of **Electromagnetics**.

Measurements consist of electromagnetic field measurements via a **rx power map** sensing mechanism.

The forward operator applies, in order: isotropic point-source emission model; L · reflect diffract operator; L · gather paths 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** → Source emission → L · reflect diffract → L · gather paths → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.gather_paths` `L.reflect_diffract` δ_source x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.source_emit` | Isotropic point-source emission model |
| `L.reflect_diffract` | L · reflect diffract operator |
| `L.gather_paths` | L · gather paths operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Electromagnetics |
| Sub domain | Urban propagation ray tracing (5G/6G) |
| Carrier | em |
| Problem class | linear_inverse |
| Solution space | signal_strength_map |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 3.3 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | RSSI_error_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `ray_tracing_em` · **Forward operator:** `ray_tracing_em_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N rx | — | 64 |
| N rays | — | 100000 |
| Snr db | dB | 30 |
| N walls | — | 1000 |
| Freq ghz | GHz | 3.5 |
| Geometry error | — | 0 |
| Material eps error | — | 0 |
| Antenna pattern error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N rx | — | 1 – 10000 |
| N rays | — | 1000 – 100000000 |
| Snr db | dB | 0 – 40 |
| N walls | — | 1 – 100000 |
| Freq ghz | GHz | 0.1 – 300 |
| Geometry error | — | 0.0 – 0.1 |
| Material eps error | — | 0.0 – 0.3 |
| Antenna pattern error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 3.0

| Metric | Range |
|---|---|
| Rssi db | 0.5 – 20.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **RSSI_error_dB**, with κ = `360` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x2b80902bf2d6782d0d99478ed531b8b769ff810669e7d7cf69b8d96afd5cf23b`
- **Chain tx hash:** `0xcc15c77e404ff48d63f9bcf9cfa621aeb3922cbe82ed7190eef7fc9a87fd25b2`
- **Chain block:** `41554001`

---

## File Mapping

This bundle consists of: `L1-253.md`, `L1-253.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-253.md` | Source of truth — edit this | Human or LLM |
| `L1-253.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 `L1-253`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._