# ⚛  L1 Principle — Dermoscopy Skin Lesion Malignancy Classification (PWDR)

**ID:** `L1-517` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Medical Imaging — *Cross-polarized cutaneous reflectance imaging with melanoma / nevus categorical readout*
> **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D lesion class
> **📡 Carrier:** photon · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553387

---

## 🧠 1. Introduction

**Dermoscopy Skin Lesion Malignancy Classification (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D lesion class** space, within the **Cross-polarized cutaneous reflectance imaging with melanoma / nevus categorical readout** sub-domain of **Medical Imaging**.

Measurements consist of photons collected by an optical detector via a **cross polarized dermoscopy with abcde grading** sensing mechanism.

The forward operator applies, in order: L · cross polarized illumination operator; L · diffuse reflectance operator; L · detector response operator; L · morphological feature extraction operator; L · abcde threshold classifier operator; pixel-level spatial averaging on the detector.

Observations are corrupted by additive Gaussian noise. Existence and uniqueness conditional on adequate cross-polarization (suppresses skin glare) and sufficient lesion contrast against background skin. Stability inherits sibling-core kappa_eff plus additive contribution from manual_feature_scoring_disagreement (the dominant inter-rater variability source in clinical practice). Joint Hadamard well-posedness for the coupled dermoscopy + ABCDE/7-point/Menzies threshold forward established by Stolz 1994 (foundational ABCDE), Argenziano 1998 (7-point checklist), Menzies 1996 (Menzies method), Henning 2007 (CASH algorithm), Esteva 2017 (deep-learning benchmark).

## ⚙ 2. Forward Model

Physical chain: **x** → L · cross polarized illumination → L · diffuse reflectance → L · detector response → L · morphological feature extraction → L · abcde threshold classifier → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.abcde_threshold_classifier` `L.morphological_feature_extraction` `L.detector_response` `L.diffuse_reflectance` `L.cross_polarized_illumination` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.cross_polarized_illumination` | L · cross polarized illumination operator |
| `L.diffuse_reflectance` | L · diffuse reflectance operator |
| `L.detector_response` | L · detector response operator |
| `L.morphological_feature_extraction` | L · morphological feature extraction operator |
| `L.abcde_threshold_classifier` | L · abcde threshold classifier operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Medical Imaging |
| Sub domain | Cross-polarized cutaneous reflectance imaging with melanoma / nevus categorical readout |
| Carrier | photon |
| Problem class | linear_inverse_with_categorical_readout |
| Solution space | 1D_lesion_class |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 4.9 |

## 📡 4. Measurement Model

Existence and uniqueness conditional on adequate cross-polarization (suppresses skin glare) and sufficient lesion contrast against background skin. Stability inherits sibling-core kappa_eff plus additive contribution from manual_feature_scoring_disagreement (the dominant inter-rater variability source in clinical practice). Joint Hadamard well-posedness for the coupled dermoscopy + ABCDE/7-point/Menzies threshold forward established by Stolz 1994 (foundational ABCDE), Argenziano 1998 (7-point checklist), Menzies 1996 (Menzies method), Henning 2007 (CASH algorithm), Esteva 2017 (deep-learning benchmark).

| Metric | Value |
|---|---|
| Metric | categorical_accuracy |
| Secondary | sensitivity_for_melanoma |

## 📏 5. Operating Range (Ω)

**Center problem class:** `dermoscopy_abcde_pwdr` · **Forward operator:** `dermoscopy_pwdr_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 2048 |
| W | px | 3072 |
| Snr db | dB | 32 |
| Hair artifact | — | 0 |
| Magnification | — | 20 |
| Polarization state | — | cross_polarized |
| Pixel resolution um | µm | 50 |
| Gel immersion uniformity | — | 0 |
| Photographic color calibration | — | 0 |
| Dermoscope polarization efficiency | — | 0 |
| Manual feature scoring disagreement | — | 0 |
| Lesion contrast against skin background | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 512 – 6000 |
| W | px | 512 – 6000 |
| Magnification | — | 10 – 50 |
| Pixel resolution um | µm | 20 – 200 |

## 🎯 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:** `0xeea451afa0e64d2ebb58f3b05ab68fff663dc89008dc10053c11b8e4d684fe46`
- **Chain tx hash:** `0xefea66fa44c7424ab1e07799504d3f567dce75c90d49990969d26b16b279c8f3`
- **Chain block:** `41553387`

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## File Mapping

This bundle consists of: `L1-517.md`, `L1-517.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-517.md` | Source of truth — edit this | Human or LLM |
| `L1-517.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 `L1-517`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._