# ⚛  L1 Principle — Glaucoma Optic-Disc Cupping Classification (PWDR)

**ID:** `L1-529` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Medical Imaging — *Optic disc + cup segmentation from fundus with cup-to-disc-ratio glaucoma readout*
> **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D glaucoma severity
> **📡 Carrier:** photon · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553360

---

## 🧠 1. Introduction

**Glaucoma Optic-Disc Cupping Classification (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D glaucoma severity** space, within the **Optic disc + cup segmentation from fundus with cup-to-disc-ratio glaucoma readout** sub-domain of **Medical Imaging**.

Measurements consist of photons collected by an optical detector via a **fundus with glaucoma grading** sensing mechanism.

The forward operator applies, in order: L · fundus acquisition operator; L · disc cup segmentation operator; L · cdr measurement operator; L · isnt rule check operator; L · rnfl defect detection operator; L · glaucoma severity classifier operator; pixel-level spatial averaging on the detector.

Observations are corrupted by additive Gaussian noise. Existence inherited from L1-049. Uniqueness conditional on adequate disc visibility (no media opacity). Stability dominated by physiologic_cupping_variant (large physiologic cups can mimic glaucoma) and tilted_disc_anatomy. Joint Hadamard well-posedness established by Bourne 2016 (ICO Glaucoma Guidelines), Spaeth 2002 (Disc Damage Likelihood Scale), Jonas 1989 (foundational neuroretinal rim morphometry), Li 2018 (deep learning glaucoma detection benchmark).

## ⚙ 2. Forward Model

Physical chain: **x** → L · fundus acquisition → L · disc cup segmentation → L · cdr measurement → L · isnt rule check → L · rnfl defect detection → L · glaucoma severity classifier → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.glaucoma_severity_classifier` `L.rnfl_defect_detection` `L.isnt_rule_check` `L.cdr_measurement` `L.disc_cup_segmentation` `L.fundus_acquisition` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.fundus_acquisition` | L · fundus acquisition operator |
| `L.disc_cup_segmentation` | L · disc cup segmentation operator |
| `L.cdr_measurement` | L · cdr measurement operator |
| `L.isnt_rule_check` | L · isnt rule check operator |
| `L.rnfl_defect_detection` | L · rnfl defect detection operator |
| `L.glaucoma_severity_classifier` | L · glaucoma severity classifier operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Medical Imaging |
| Sub domain | Optic disc + cup segmentation from fundus with cup-to-disc-ratio glaucoma readout |
| Carrier | photon |
| Problem class | linear_inverse_with_categorical_readout |
| Solution space | 1D_glaucoma_severity |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 5.6 |

## 📡 4. Measurement Model

Existence inherited from L1-049. Uniqueness conditional on adequate disc visibility (no media opacity). Stability dominated by physiologic_cupping_variant (large physiologic cups can mimic glaucoma) and tilted_disc_anatomy. Joint Hadamard well-posedness established by Bourne 2016 (ICO Glaucoma Guidelines), Spaeth 2002 (Disc Damage Likelihood Scale), Jonas 1989 (foundational neuroretinal rim morphometry), Li 2018 (deep learning glaucoma detection benchmark).

| Metric | Value |
|---|---|
| Metric | categorical_accuracy |
| Secondary | sensitivity_for_advanced_glaucoma |

## 📏 5. Operating Range (Ω)

**Center problem class:** `glaucoma_disc_pwdr` · **Forward operator:** `glaucoma_disc_pwdr_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 2048 |
| W | px | 2048 |
| Snr db | dB | 30 |
| Image quality | — | 0 |
| Rgb calibration | — | 0 |
| Pallor mimicker | — | 0 |
| Pixel resolution um | µm | 5 |
| Tilted disc anatomy | — | 0 |
| Field of view degrees | — | 30 |
| Physiologic cupping variant | — | 0 |
| Peripapillary atrophy overlap | — | 0 |
| Manual grader inter rater kappa | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 512 – 4096 |
| W | px | 512 – 4096 |

## 🎯 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:** `0xe7aef74be727afd2ae3572ec25bb1d6fe089484fae36b603285d906a4e4c1305`
- **Chain tx hash:** `0x4ae9e22989c9201a9492a07a2434377889e0a6f3a33067f3cc42df72fb8bc3c3`
- **Chain block:** `41553360`

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## File Mapping

This bundle consists of: `L1-529.md`, `L1-529.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-529.md` | Source of truth — edit this | Human or LLM |
| `L1-529.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 `L1-529`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._