# ⚛  L1 Principle — EEG Seizure Detection (PWDR)

**ID:** `L1-531` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Medical Imaging — *Cortical electrical signal feature recovery from EEG with seizure / non-seizure categorical readout*
> **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D seizure class per segment
> **📡 Carrier:** biopotential · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553387

---

## 🧠 1. Introduction

**EEG Seizure Detection (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D seizure class per segment** space, within the **Cortical electrical signal feature recovery from EEG with seizure / non-seizure categorical readout** sub-domain of **Medical Imaging**.

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

The forward operator applies, in order: L · eeg acquisition operator; L · bandpass filter operator; L · artifact rejection operator; L · spectral decomposition operator; L · evolution detection operator; L · seizure threshold classifier operator; int · temporal spatial operator.

Observations are corrupted by additive Gaussian noise. Existence inherited from L1-068. Uniqueness conditional on adequate channel coverage + electrode impedance < 10 kohm. Stability dominated by muscle_artifact and drowsy_state_confounder (subclinical seizures). Joint Hadamard well-posedness established by Fisher 2017 (ILAE 2017 Operational Classification), Trinka 2015 (status epilepticus definition), Hirsch 2013 (ACNS critical-care EEG terminology), Roy 2019 (deep learning EEG seizure benchmark), Acharya 2018 (EEG seizure deep learning review).

## ⚙ 2. Forward Model

Physical chain: **x** → L · eeg acquisition → L · bandpass filter → L · artifact rejection → L · spectral decomposition → L · evolution detection → L · seizure threshold classifier → int · temporal spatial → **y** (detector).

```
y = `int.temporal_spatial` `L.seizure_threshold_classifier` `L.evolution_detection` `L.spectral_decomposition` `L.artifact_rejection` `L.bandpass_filter` `L.eeg_acquisition` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.eeg_acquisition` | L · eeg acquisition operator |
| `L.bandpass_filter` | L · bandpass filter operator |
| `L.artifact_rejection` | L · artifact rejection operator |
| `L.spectral_decomposition` | L · spectral decomposition operator |
| `L.evolution_detection` | L · evolution detection operator |
| `L.seizure_threshold_classifier` | L · seizure threshold classifier operator |
| `int.temporal_spatial` | Int · temporal spatial operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Medical Imaging |
| Sub domain | Cortical electrical signal feature recovery from EEG with seizure / non-seizure categorical readout |
| Carrier | biopotential |
| Problem class | linear_inverse_with_categorical_readout |
| Solution space | 1D_seizure_class_per_segment |
| Noise model | gaussian |
| Integration axis | temporal_spatial |
| Difficulty delta | 5 |
| L dag | 6 |

## 📡 4. Measurement Model

Existence inherited from L1-068. Uniqueness conditional on adequate channel coverage + electrode impedance < 10 kohm. Stability dominated by muscle_artifact and drowsy_state_confounder (subclinical seizures). Joint Hadamard well-posedness established by Fisher 2017 (ILAE 2017 Operational Classification), Trinka 2015 (status epilepticus definition), Hirsch 2013 (ACNS critical-care EEG terminology), Roy 2019 (deep learning EEG seizure benchmark), Acharya 2018 (EEG seizure deep learning review).

| Metric | Value |
|---|---|
| Metric | categorical_accuracy |
| Secondary | sensitivity_per_seizure_event |

## 📏 5. Operating Range (Ω)

**Center problem class:** `eeg_seizure_pwdr` · **Forward operator:** `eeg_seizure_pwdr_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 25 |
| N channels | — | 19 |
| Muscle artifact | — | 0 |
| Duration minutes | — | 60 |
| Sampling rate hz | Hz | 256 |
| Movement artifact | — | 0 |
| Voltage resolution uv | — | 1 |
| Drowsy state confounder | — | 0 |
| Electrode impedance kohm | — | 5 |
| Neonatal premature pattern | — | 0 |
| Electrocardiac contamination | — | 0 |
| Manual neurologist inter rater kappa | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N channels | — | 4 – 256 |
| Duration minutes | — | 10 – 10080 |
| Sampling rate hz | Hz | 128 – 5000 |

## 🎯 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 = `100` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xcb4e44696a6858b8c739ce767902a8dc80703a62319f0e2292d77c1cccd0c4fc`
- **Chain tx hash:** `0xe9366efe9e1c72cb6abe8878d646a103ee63723935756f63697947ebdb66282d`
- **Chain block:** `41553387`

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## File Mapping

This bundle consists of: `L1-531.md`, `L1-531.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-531.md` | Source of truth — edit this | Human or LLM |
| `L1-531.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 `L1-531`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._