L1 ⚛ L1-528 ⊙ Testnet

ECG Arrhythmia Classification (PWDR)

Signal Processing · Cardiac electrical signal feature recovery with arrhythmia categorical readout

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⬇ L1-528.md

# ⚛ 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` --- ## 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._

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Read the attached Markdown (L1-528.md).
Regenerate L1-528.json so every field matches the Markdown.
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L2-528-001 ECG Arrhythmia Classification (PWDR) — Spec Skeleton

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📋 JSON metadata

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  "domain": "Signal Processing",
  "hardness_fn": {
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    "kappa": 80,
    "metric": "categorical_accuracy",
    "type": "epsilon_fn"
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    "regime": "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).",
    "secondary": "F1_per_AAMI_class"
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  "physics_fingerprint": {
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    "carrier": "biopotential",
    "difficulty_delta": 3,
    "domain": "Signal Processing",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
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      "L.bandpass_filter",
      "L.blind_source_separation",
      "L.r_peak_detection",
      "L.qrs_feature_extraction",
      "L.aami_threshold_classifier",
      "int.temporal"
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    "problem_class": "linear_inverse_with_categorical_readout",
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    "solution_space": "1D_arrhythmia_class_per_beat",
    "sub_domain": "Cardiac electrical signal feature recovery with arrhythmia categorical readout",
    "title": "ECG Arrhythmia Classification (PWDR)"
  },
  "size_tiers": {
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    "allowed_omega_dimensions": [
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      "lead_placement_error",
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    ],
    "allowed_problem_classes": [
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      "input_format": "ecg_signal_with_per_beat_label",
      "omega": {
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        "baseline_wander": 0.0,
        "duration_seconds": 10,
        "lead_placement_error": 0.0,
        "manual_cardiologist_disagreement": 0.0,
        "motion_artifact_wearable": 0.0,
        "muscle_artifact": 0.0,
        "powerline_interference_60Hz": 0.0,
        "sampling_rate_Hz": 500,
        "voltage_resolution_uV": 5
      },
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    },
    "epsilon_bounds": {
      "categorical_accuracy": [
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        0.99
      ]
    },
    "omega_bounds": {
      "N_leads": [
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      ],
      "duration_seconds": [
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      ],
      "sampling_rate_Hz": [
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        1000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Cardiac electrical signal feature recovery with arrhythmia categorical readout",
  "title": "ECG Arrhythmia Classification (PWDR)"
}

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