# ⚛  L1 Principle — Age-Related Macular Degeneration OCT Grading (PWDR)

**ID:** `L1-530` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Medical Imaging — *Macular layer + drusen + fluid recovery from OCT with AREDS / AMD-stage categorical readout*
> **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D amd stage
> **📡 Carrier:** photon · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553374

---

## 🧠 1. Introduction

**Age-Related Macular Degeneration OCT Grading (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D amd stage** space, within the **Macular layer + drusen + fluid recovery from OCT with AREDS / AMD-stage categorical readout** sub-domain of **Medical Imaging**.

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

The forward operator applies, in order: L · oct acquisition operator; L · layer segmentation operator; L · drusen detection operator; L · fluid detection operator; L · ga segmentation operator; L · amd stage classifier operator; pixel-level spatial averaging on the detector.

Observations are corrupted by additive Gaussian noise. Existence inherited from L1-042. Uniqueness conditional on adequate OCT image quality (signal strength index > 6/10 typical). Stability dominated by patient_motion + shadowing_artifact. Joint Hadamard well-posedness established by AREDS Research Group 2001 (foundational), Beckman 2013 (consensus classification), Schmidt-Erfurth 2018 (OCT in AMD review), De Fauw 2018 (DeepMind referrable disease classification benchmark).

## ⚙ 2. Forward Model

Physical chain: **x** → L · oct acquisition → L · layer segmentation → L · drusen detection → L · fluid detection → L · ga segmentation → L · amd stage classifier → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.amd_stage_classifier` `L.ga_segmentation` `L.fluid_detection` `L.drusen_detection` `L.layer_segmentation` `L.oct_acquisition` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.oct_acquisition` | L · oct acquisition operator |
| `L.layer_segmentation` | L · layer segmentation operator |
| `L.drusen_detection` | L · drusen detection operator |
| `L.fluid_detection` | L · fluid detection operator |
| `L.ga_segmentation` | L · ga segmentation operator |
| `L.amd_stage_classifier` | L · amd stage classifier operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Medical Imaging |
| Sub domain | Macular layer + drusen + fluid recovery from OCT with AREDS / AMD-stage categorical readout |
| Carrier | photon |
| Problem class | linear_inverse_with_categorical_readout |
| Solution space | 1D_amd_stage |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 5.6 |

## 📡 4. Measurement Model

Existence inherited from L1-042. Uniqueness conditional on adequate OCT image quality (signal strength index > 6/10 typical). Stability dominated by patient_motion + shadowing_artifact. Joint Hadamard well-posedness established by AREDS Research Group 2001 (foundational), Beckman 2013 (consensus classification), Schmidt-Erfurth 2018 (OCT in AMD review), De Fauw 2018 (DeepMind referrable disease classification benchmark).

| Metric | Value |
|---|---|
| Metric | categorical_accuracy |
| Secondary | sensitivity_for_referable_AMD |

## 📏 5. Operating Range (Ω)

**Center problem class:** `amd_oct_pwdr` · **Forward operator:** `amd_oct_pwdr_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 512 |
| W | px | 512 |
| Z | — | 128 |
| Snr db | dB | 30 |
| Media opacity | — | 0 |
| Wavelength nm | nm | 850 |
| Patient motion | — | 0 |
| Macular centration | — | 0 |
| Shadowing artifact | — | 0 |
| Axial resolution um | µm | 5 |
| Lateral resolution um | µm | 15 |
| Vitreous floater artifact | — | 0 |
| Manual grader inter rater kappa | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 1024 |
| W | px | 128 – 1024 |
| Z | — | 32 – 512 |

## 🎯 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:** `0xd82995adf798cc5feb705e3a2ffecbe73c89608810271eb2ec27fef476e0d9aa`
- **Chain tx hash:** `0xa068758abb70617ff5e1056181bc24c7f3cb4ea230f73b5ce303903bcf6e3b00`
- **Chain block:** `41553374`

---

## File Mapping

This bundle consists of: `L1-530.md`, `L1-530.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-530.md` | Source of truth — edit this | Human or LLM |
| `L1-530.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 `L1-530`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._