# ⚛  L1 Principle — FDTD — finite-difference time-domain Maxwell

**ID:** `L1-234` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Electromagnetics — *Yee-grid explicit FDTD*
> **🎯 Problem class:** forward · **🧮 Solution space:** 3D E H field spacetime
> **📡 Carrier:** em · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553987

---

## 🧠 1. Introduction

**FDTD — finite-difference time-domain Maxwell** is a **forward-model simulation** whose unknown lives in **3D E H field spacetime** space, within the **Yee-grid explicit FDTD** sub-domain of **Electromagnetics**.

Measurements consist of electromagnetic field measurements via a **near field probes** sensing mechanism.

The forward operator applies, in order: L · yee grid update operator; L · pml absorb operator; L · source inject 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 · yee grid update → L · pml absorb → L · source inject → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.source_inject` `L.pml_absorb` `L.yee_grid_update` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.yee_grid_update` | L · yee grid update operator |
| `L.pml_absorb` | L · pml absorb operator |
| `L.source_inject` | L · source inject operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Electromagnetics |
| Sub domain | Yee-grid explicit FDTD |
| Carrier | em |
| Problem class | forward |
| Solution space | 3D_E_H_field_spacetime |
| 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:** `fdtd` · **Forward operator:** `fdtd_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 256 |
| W | px | 256 |
| Z | — | 128 |
| Dt fs | — | 1 |
| Snr db | dB | 30 |
| N samples | — | 2000 |
| Pml error | — | 0 |
| Dispersion error | — | 0 |
| Grid aniso error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 64 – 2048 |
| W | px | 64 – 2048 |
| Z | — | 32 – 1024 |
| Dt fs | — | 0.01 – 1000 |
| Snr db | dB | 0 – 40 |
| N samples | — | 100 – 100000 |
| Pml error | — | 0.0 – 0.2 |
| Dispersion error | — | 0.0 – 0.2 |
| Grid aniso error | — | 0.0 – 0.1 |

## 🎯 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 = `300` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xb05b69946152894d0562cf92ee6b9e93fa41b0db402a549fa3072367b256f224`
- **Chain tx hash:** `0x9b1fab6c7e685e8c74648e83c47ae5545e2d1227a5004b97666c2242effc6b3f`
- **Chain block:** `41553987`

---

## File Mapping

This bundle consists of: `L1-234.md`, `L1-234.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-234.md` | Source of truth — edit this | Human or LLM |
| `L1-234.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 `L1-234`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._