# ⚛  L1 Principle — ECG Arrhythmia Classification (PWDR)

**ID:** `L1-528` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Signal Processing — *Cardiac electrical signal feature recovery with arrhythmia categorical readout*
> **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D arrhythmia class per beat
> **📡 Carrier:** biopotential · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555318

---

## 🧠 1. Introduction

**ECG Arrhythmia Classification (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D arrhythmia class per beat** space, within the **Cardiac electrical signal feature recovery with arrhythmia categorical readout** sub-domain of **Signal Processing**.

Measurements consist of biopotential signals recorded at the body surface via a **ecg with aami classifier** sensing mechanism.

The forward operator applies, in order: L · ecg acquisition operator; L · bandpass filter operator; L · blind source separation operator; L · r peak detection operator; L · qrs feature extraction operator; L · aami threshold classifier operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Existence inherited from L1-388. Uniqueness conditional on adequate SNR (typical 20-30 dB) and clean lead placement. Stability dominated by motion_artifact_wearable for consumer ECG. Joint Hadamard well-posedness established by Pan-Tompkins 1985 (foundational R-peak detection), AAMI 1998 EC57 standard, Hannun 2019 (deep-learning ECG arrhythmia detection at cardiologist level), Attia 2019 (Apple Heart Study), Perez 2019 (smartwatch AF screening).

## ⚙ 2. Forward Model

Physical chain: **x** → L · ecg acquisition → L · bandpass filter → L · blind source separation → L · r peak detection → L · qrs feature extraction → L · aami threshold classifier → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.aami_threshold_classifier` `L.qrs_feature_extraction` `L.r_peak_detection` `L.blind_source_separation` `L.bandpass_filter` `L.ecg_acquisition` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.ecg_acquisition` | L · ecg acquisition operator |
| `L.bandpass_filter` | L · bandpass filter operator |
| `L.blind_source_separation` | L · blind source separation operator |
| `L.r_peak_detection` | L · r peak detection operator |
| `L.qrs_feature_extraction` | L · qrs feature extraction operator |
| `L.aami_threshold_classifier` | L · aami threshold classifier operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Signal Processing |
| Sub domain | Cardiac electrical signal feature recovery with arrhythmia categorical readout |
| Carrier | biopotential |
| Problem class | linear_inverse_with_categorical_readout |
| Solution space | 1D_arrhythmia_class_per_beat |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 3 |
| L dag | 5.9 |

## 📡 4. Measurement Model

Existence inherited from L1-388. Uniqueness conditional on adequate SNR (typical 20-30 dB) and clean lead placement. Stability dominated by motion_artifact_wearable for consumer ECG. Joint Hadamard well-posedness established by Pan-Tompkins 1985 (foundational R-peak detection), AAMI 1998 EC57 standard, Hannun 2019 (deep-learning ECG arrhythmia detection at cardiologist level), Attia 2019 (Apple Heart Study), Perez 2019 (smartwatch AF screening).

| Metric | Value |
|---|---|
| Metric | categorical_accuracy |
| Secondary | F1_per_AAMI_class |

## 📏 5. Operating Range (Ω)

**Center problem class:** `ecg_aami_pwdr` · **Forward operator:** `ecg_aami_pwdr_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 25 |
| N leads | — | 12 |
| Baseline wander | — | 0 |
| Muscle artifact | — | 0 |
| Duration seconds | — | 10 |
| Sampling rate hz | Hz | 500 |
| Lead placement error | — | 0 |
| Voltage resolution uv | — | 5 |
| Motion artifact wearable | — | 0 |
| Powerline interference 60hz | — | 0 |
| Manual cardiologist disagreement | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N leads | — | 1 – 12 |
| Duration seconds | — | 5 – 86400 |
| Sampling rate hz | Hz | 100 – 1000 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.85_accuracy

| Metric | Range |
|---|---|
| Categorical accuracy | 0.5 – 0.99 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **categorical_accuracy**, with κ = `80` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x369ae3694ab4576b30e9f7bc59c096d848afea584fc1266052cf08c41a746bbd`
- **Chain tx hash:** `0xf548171affb46d1d2dedd4cc0b77fdb4f50b6d681b4f20d3f2d6fd3d8eca73c4`
- **Chain block:** `41555318`

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## File Mapping

This bundle consists of: `L1-528.md`, `L1-528.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-528.md` | Source of truth — edit this | Human or LLM |
| `L1-528.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 `L1-528`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._