L1 ⚛ L1-527 ⊙ Testnet

Knee / Hip Osteoarthritis Kellgren-Lawrence Grading (PWDR)

Medical Imaging · Joint-space-narrowing + osteophyte recovery from radiograph with KL-grade categorical readout

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⬇ L1-527.md

# ⚛ L1 Principle — Knee / Hip Osteoarthritis Kellgren-Lawrence Grading (PWDR) **ID:** `L1-527` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Joint-space-narrowing + osteophyte recovery from radiograph with KL-grade categorical readout* > **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D kl grade > **📡 Carrier:** x_ray · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41552307 --- ## 🧠 1. Introduction **Knee / Hip Osteoarthritis Kellgren-Lawrence Grading (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D kl grade** space, within the **Joint-space-narrowing + osteophyte recovery from radiograph with KL-grade categorical readout** sub-domain of **Medical Imaging**. Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **radiograph with kl grading** sensing mechanism. The forward operator applies, in order: polyenergetic X-ray emission spectrum; line-integral projection through an attenuation map; L · joint space measurement operator; L · osteophyte detection operator; L · kl grade classifier operator; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson counting noise. Existence inherited from L1-031. Uniqueness conditional on consistent weight-bearing positioning. Stability dominated by manual_grader_inter_rater_kappa (~0.55-0.75 typical). Joint Hadamard well-posedness established by Kellgren-Lawrence 1957 (foundational), Altman 1986 (ACR criteria), Tiulpin 2018 (deep learning KL grading benchmark), Norman 2019 (DeepKnee multi-task). ## ⚙ 2. Forward Model Physical chain: **x** → X-ray source → Attenuation projection → L · joint space measurement → L · osteophyte detection → L · kl grade classifier → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.kl_grade_classifier` `L.osteophyte_detection` `L.joint_space_measurement` ∫µ dl I₀(E) x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.xray_source` | Polyenergetic x-ray emission spectrum | | `L.attenuation_projection` | Line-integral projection through an attenuation map | | `L.joint_space_measurement` | L · joint space measurement operator | | `L.osteophyte_detection` | L · osteophyte detection operator | | `L.kl_grade_classifier` | L · kl grade classifier operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Joint-space-narrowing + osteophyte recovery from radiograph with KL-grade categorical readout | | Carrier | x_ray | | Problem class | linear_inverse_with_categorical_readout | | Solution space | 1D_kl_grade | | Noise model | poisson | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 4.6 | ## 📡 4. Measurement Model Existence inherited from L1-031. Uniqueness conditional on consistent weight-bearing positioning. Stability dominated by manual_grader_inter_rater_kappa (~0.55-0.75 typical). Joint Hadamard well-posedness established by Kellgren-Lawrence 1957 (foundational), Altman 1986 (ACR criteria), Tiulpin 2018 (deep learning KL grading benchmark), Norman 2019 (DeepKnee multi-task). | Metric | Value | |---|---| | Metric | categorical_accuracy | | Secondary | weighted_kappa_kl | ## 📏 5. Operating Range (Ω) **Center problem class:** `knee_oa_kl_pwdr` · **Forward operator:** `knee_oa_kl_pwdr_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2500 | | W | px | 3000 | | Kvp | — | 70 | | Mas | — | 8 | | View | — | AP_standing | | Snr db | dB | 30 | | Rotation artifact | — | 0 | | Pixel resolution um | µm | 100 | | Weight bearing state | — | full_weight_bearing | | Joint positioning error | — | 0 | | Early oa subtle features | — | 0 | | Incidental chondrocalcinosis | — | 0 | | Manual grader inter rater kappa | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 1024 – 4096 | | W | px | 1024 – 4096 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.75_accuracy | Metric | Range | |---|---| | Categorical accuracy | 0.4 – 0.95 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **categorical_accuracy**, with κ = `60` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x834bbc0720c68442634f1d5ccb322f4ffe34fa07be0a49ab65614c7603438180` - **Chain tx hash:** `0xae0ea400a76e4c1d324b588975e4f0e1ad3df0d6808c279fa24b68e442e06a24` - **Chain block:** `41552307` --- ## File Mapping This bundle consists of: `L1-527.md`, `L1-527.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-527.md` | Source of truth — edit this | Human or LLM | | `L1-527.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 `L1-527`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-527.md).
Regenerate L1-527.json so every field matches the Markdown.
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L2-527-001 Knee / Hip Osteoarthritis Kellgren-Lawrence Grading (PWDR) — Spec Skeleton

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📋 JSON metadata

{
  "artifact_id": "L1-527",
  "chain_block": 41552307,
  "chain_hash": "0x834bbc0720c68442634f1d5ccb322f4ffe34fa07be0a49ab65614c7603438180",
  "chain_tx_hash": "0xae0ea400a76e4c1d324b588975e4f0e1ad3df0d6808c279fa24b68e442e06a24",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 60,
    "metric": "categorical_accuracy",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "categorical_accuracy",
    "regime": "Existence inherited from L1-031. Uniqueness conditional on consistent weight-bearing positioning. Stability dominated by manual_grader_inter_rater_kappa (~0.55-0.75 typical). Joint Hadamard well-posedness established by Kellgren-Lawrence 1957 (foundational), Altman 1986 (ACR criteria), Tiulpin 2018 (deep learning KL grading benchmark), Norman 2019 (DeepKnee multi-task).",
    "secondary": "weighted_kappa_kl"
  },
  "physics_fingerprint": {
    "L_DAG": 4.6,
    "carrier": "x_ray",
    "difficulty_delta": 3,
    "domain": "Medical Imaging",
    "integration_axis": "spatial",
    "noise_model": "poisson",
    "primitives": [
      "L.xray_source",
      "L.attenuation_projection",
      "L.joint_space_measurement",
      "L.osteophyte_detection",
      "L.kl_grade_classifier",
      "int.spatial"
    ],
    "problem_class": "linear_inverse_with_categorical_readout",
    "sensing_mechanism": "radiograph_with_kl_grading",
    "solution_space": "1D_kl_grade",
    "sub_domain": "Joint-space-narrowing + osteophyte recovery from radiograph with KL-grade categorical readout",
    "title": "Knee / Hip Osteoarthritis Kellgren-Lawrence Grading (PWDR)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "knee_oa_kl_pwdr_forward",
      "hip_oa_kl_pwdr_forward",
      "oa_oarsi_pwdr_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "pixel_resolution_um",
      "kVp",
      "mAs",
      "view",
      "weight_bearing_state",
      "SNR_dB",
      "rotation_artifact",
      "joint_positioning_error",
      "manual_grader_inter_rater_kappa",
      "early_OA_subtle_features",
      "incidental_chondrocalcinosis"
    ],
    "allowed_problem_classes": [
      "knee_oa_kl_pwdr",
      "hip_oa_kl_pwdr",
      "oa_oarsi_per_compartment_pwdr"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.75_accuracy",
      "forward_operator": "knee_oa_kl_pwdr_forward",
      "input_format": "weight_bearing_radiograph_with_kl_label",
      "omega": {
        "H": 2500,
        "SNR_dB": 30,
        "W": 3000,
        "early_OA_subtle_features": 0.0,
        "incidental_chondrocalcinosis": 0.0,
        "joint_positioning_error": 0.0,
        "kVp": 70,
        "mAs": 8,
        "manual_grader_inter_rater_kappa": 0.0,
        "pixel_resolution_um": 100,
        "rotation_artifact": 0.0,
        "view": "AP_standing",
        "weight_bearing_state": "full_weight_bearing"
      },
      "problem_class": "knee_oa_kl_pwdr"
    },
    "epsilon_bounds": {
      "categorical_accuracy": [
        0.4,
        0.95
      ]
    },
    "omega_bounds": {
      "H": [
        1024,
        4096
      ],
      "W": [
        1024,
        4096
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Joint-space-narrowing + osteophyte recovery from radiograph with KL-grade categorical readout",
  "title": "Knee / Hip Osteoarthritis Kellgren-Lawrence Grading (PWDR)"
}

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