L1 ⚛ L1-513 ⊙ Testnet

Diabetic Retinopathy Grading from Fundus Imaging (PWDR)

Medical Imaging · Retinal vasculature reconstruction with diabetic retinopathy ETDRS-grade categorical readout

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⬇ L1-513.md

# ⚛ L1 Principle — Diabetic Retinopathy Grading from Fundus Imaging (PWDR) **ID:** `L1-513` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Retinal vasculature reconstruction with diabetic retinopathy ETDRS-grade categorical readout* > **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D etdrs severity grade > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553387 --- ## 🧠 1. Introduction **Diabetic Retinopathy Grading from Fundus Imaging (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D etdrs severity grade** space, within the **Retinal vasculature reconstruction with diabetic retinopathy ETDRS-grade categorical readout** sub-domain of **Medical Imaging**. Measurements consist of photons collected by an optical detector via a **fundus color photography with etdrs grading** sensing mechanism. The forward operator applies, in order: L · fundus acquisition operator; L · vessel segmentation operator; L · lesion segmentation operator; L · lesion count aggregation operator; L · etdrs threshold classifier operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Existence inherited from L1-049 fundus core. Uniqueness conditional on adequate image quality (no severe media opacity; pupil dilation enables peripheral retinal coverage); ETDRS-grade transition boundaries (the 4-2-1 rule) form measure-zero hypersurfaces in lesion-count space. Stability inherits L1-049's kappa_eff plus a small additive contribution from grader_inter_rater_variability_calibration. The threshold-continuity proof in discrete_readout demonstrates that ETDRS-grade is a well-defined function of lesion counts; misclassification probability scales linearly with lesion-count error away from the 4-2-1 hypersurface boundary. Joint Hadamard well-posedness for the coupled vasculature-reconstruction + ETDRS-threshold forward established by Wilkinson 2003 (foundational ICDR paper), Abramoff 2018 (FDA-cleared autonomous AI), Gulshan 2016 (deep-learning grading benchmarks), Ting 2017 (Asian-population validation), Bhaskaranand 2019 (real-world performance), and Solomon 2017 (DR screening guidelines). ## ⚙ 2. Forward Model Physical chain: **x** → L · fundus acquisition → L · vessel segmentation → L · lesion segmentation → L · lesion count aggregation → L · etdrs threshold classifier → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.etdrs_threshold_classifier` `L.lesion_count_aggregation` `L.lesion_segmentation` `L.vessel_segmentation` `L.fundus_acquisition` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.fundus_acquisition` | L · fundus acquisition operator | | `L.vessel_segmentation` | L · vessel segmentation operator | | `L.lesion_segmentation` | L · lesion segmentation operator | | `L.lesion_count_aggregation` | L · lesion count aggregation operator | | `L.etdrs_threshold_classifier` | L · etdrs threshold classifier operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Retinal vasculature reconstruction with diabetic retinopathy ETDRS-grade categorical readout | | Carrier | photon | | Problem class | linear_inverse_with_categorical_readout | | Solution space | 1D_etdrs_severity_grade | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 5 | ## 📡 4. Measurement Model Existence inherited from L1-049 fundus core. Uniqueness conditional on adequate image quality (no severe media opacity; pupil dilation enables peripheral retinal coverage); ETDRS-grade transition boundaries (the 4-2-1 rule) form measure-zero hypersurfaces in lesion-count space. Stability inherits L1-049's kappa_eff plus a small additive contribution from grader_inter_rater_variability_calibration. The threshold-continuity proof in discrete_readout demonstrates that ETDRS-grade is a well-defined function of lesion counts; misclassification probability scales linearly with lesion-count error away from the 4-2-1 hypersurface boundary. Joint Hadamard well-posedness for the coupled vasculature-reconstruction + ETDRS-threshold forward established by Wilkinson 2003 (foundational ICDR paper), Abramoff 2018 (FDA-cleared autonomous AI), Gulshan 2016 (deep-learning grading benchmarks), Ting 2017 (Asian-population validation), Bhaskaranand 2019 (real-world performance), and Solomon 2017 (DR screening guidelines). | Metric | Value | |---|---| | Metric | categorical_accuracy | | Secondary | weighted_kappa_etdrs | ## 📏 5. Operating Range (Ω) **Center problem class:** `diabetic_retinopathy_etdrs_pwdr` · **Forward operator:** `fundus_etdrs_pwdr_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2048 | | W | px | 2048 | | Snr db | dB | 30 | | Image quality | — | 0 | | Media opacity | — | 0 | | Pixel resolution um | µm | 5 | | Pupil dilation state | — | 1 | | Field of view degrees | — | 45 | | Peripheral field truncation | — | 0 | | Grader inter rater variability calibration | — | 0 | | Manual vs automated lesion segmentation disagreement | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 512 – 8192 | | W | px | 512 – 8192 | | Image quality | — | 0.0 – 0.5 | | Media opacity | — | 0.0 – 0.4 | | Field of view degrees | — | 30 – 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 = `100` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x2cdbd05721a0533f7f9f3b0b29ab053ec0bc9e17cf9b7914ea0fc2e2975cdd35` - **Chain tx hash:** `0xd162e26a36f9adcd19383925254a415bde3896422ea4fb0a5d9474cb1b8f1458` - **Chain block:** `41553387` --- ## File Mapping This bundle consists of: `L1-513.md`, `L1-513.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-513.md` | Source of truth — edit this | Human or LLM | | `L1-513.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 `L1-513`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-513.md).
Regenerate L1-513.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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L2-513-001 Diabetic Retinopathy Grading from Fundus Imaging (PWDR) — Spec Skeleton

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📋 JSON metadata

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    "regime": "Existence inherited from L1-049 fundus core. Uniqueness conditional on adequate image quality (no severe media opacity; pupil dilation enables peripheral retinal coverage); ETDRS-grade transition boundaries (the 4-2-1 rule) form measure-zero hypersurfaces in lesion-count space. Stability inherits L1-049\u0027s kappa_eff plus a small additive contribution from grader_inter_rater_variability_calibration. The threshold-continuity proof in discrete_readout demonstrates that ETDRS-grade is a well-defined function of lesion counts; misclassification probability scales linearly with lesion-count error away from the 4-2-1 hypersurface boundary. Joint Hadamard well-posedness for the coupled vasculature-reconstruction + ETDRS-threshold forward established by Wilkinson 2003 (foundational ICDR paper), Abramoff 2018 (FDA-cleared autonomous AI), Gulshan 2016 (deep-learning grading benchmarks), Ting 2017 (Asian-population validation), Bhaskaranand 2019 (real-world performance), and Solomon 2017 (DR screening guidelines).",
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    "title": "Diabetic Retinopathy Grading from Fundus Imaging (PWDR)"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Retinal vasculature reconstruction with diabetic retinopathy ETDRS-grade categorical readout",
  "title": "Diabetic Retinopathy Grading from Fundus Imaging (PWDR)"
}

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