L1 ⚛ L1-526 ⊙ Testnet

Bone Fracture Detection from Radiograph (PWDR)

Medical Imaging · Cortical bone discontinuity recovery from X-ray with fracture categorical readout

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-526.md

# ⚛ L1 Principle — Bone Fracture Detection from Radiograph (PWDR) **ID:** `L1-526` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Cortical bone discontinuity recovery from X-ray with fracture categorical readout* > **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D fracture class with AO OTA > **📡 Carrier:** x_ray · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553387 --- ## 🧠 1. Introduction **Bone Fracture Detection from Radiograph (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D fracture class with AO OTA** space, within the **Cortical bone discontinuity recovery from X-ray with fracture categorical readout** sub-domain of **Medical Imaging**. Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **radiograph with fracture classifier** sensing mechanism. The forward operator applies, in order: polyenergetic X-ray emission spectrum; line-integral projection through an attenuation map; L · cortical edge detection operator; L · fragment segmentation operator; L · fracture classifier operator; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson counting noise. Existence inherited from L1-031. Uniqueness conditional on adequate views. Stability dominated by overlapping_structures and growth_plate_confounder (pediatric). Joint Hadamard well-posedness established by Müller AO 1996 (foundational classification), Lindsey 2018 (deep learning fracture detection benchmark), Rajpurkar 2017 (CheXNet), Olczak 2017 (Stockholm fracture deep learning). ## ⚙ 2. Forward Model Physical chain: **x** → X-ray source → Attenuation projection → L · cortical edge detection → L · fragment segmentation → L · fracture classifier → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.fracture_classifier` `L.fragment_segmentation` `L.cortical_edge_detection` ∫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.cortical_edge_detection` | L · cortical edge detection operator | | `L.fragment_segmentation` | L · fragment segmentation operator | | `L.fracture_classifier` | L · fracture classifier operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Cortical bone discontinuity recovery from X-ray with fracture categorical readout | | Carrier | x_ray | | Problem class | linear_inverse_with_categorical_readout | | Solution space | 1D_fracture_class_with_AO_OTA | | Noise model | poisson | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 4.6 | ## 📡 4. Measurement Model Existence inherited from L1-031. Uniqueness conditional on adequate views. Stability dominated by overlapping_structures and growth_plate_confounder (pediatric). Joint Hadamard well-posedness established by Müller AO 1996 (foundational classification), Lindsey 2018 (deep learning fracture detection benchmark), Rajpurkar 2017 (CheXNet), Olczak 2017 (Stockholm fracture deep learning). | Metric | Value | |---|---| | Metric | categorical_accuracy | | Secondary | sensitivity_for_displaced | ## 📏 5. Operating Range (Ω) **Center problem class:** `fracture_xray_pwdr` · **Forward operator:** `fracture_pwdr_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2500 | | W | px | 3000 | | Kvp | — | 65 | | Mas | — | 6 | | Snr db | dB | 30 | | View count | — | 2 | | Anatomic region | — | wrist | | Rotation artifact | — | 0 | | Pixel resolution um | µm | 100 | | Overlapping structures | — | 0 | | Growth plate confounder | — | 0 | | Soft tissue swelling obscuring | — | 0 | | Manual radiologist disagreement | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 1024 – 4096 | | W | px | 1024 – 4096 | | View count | — | 1 – 4 | ## 🎯 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 = `60` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x06849a8d91dddbb63ca0bd3a1c05c2aec15383b0ef105e58a3a52eae7eb8d4fa` - **Chain tx hash:** `0x9a7916d79c210232418a539e6ad45df627f016fa3cc4aaccafb2143505e3c4c5` - **Chain block:** `41553387` --- ## File Mapping This bundle consists of: `L1-526.md`, `L1-526.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-526.md` | Source of truth — edit this | Human or LLM | | `L1-526.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 `L1-526`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-526.md).
Regenerate L1-526.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.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-526-001 Bone Fracture Detection from Radiograph (PWDR) — Spec Skeleton

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-526",
  "chain_block": 41553387,
  "chain_hash": "0x06849a8d91dddbb63ca0bd3a1c05c2aec15383b0ef105e58a3a52eae7eb8d4fa",
  "chain_tx_hash": "0x9a7916d79c210232418a539e6ad45df627f016fa3cc4aaccafb2143505e3c4c5",
  "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 adequate views. Stability dominated by overlapping_structures and growth_plate_confounder (pediatric). Joint Hadamard well-posedness established by M\u00fcller AO 1996 (foundational classification), Lindsey 2018 (deep learning fracture detection benchmark), Rajpurkar 2017 (CheXNet), Olczak 2017 (Stockholm fracture deep learning).",
    "secondary": "sensitivity_for_displaced"
  },
  "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.cortical_edge_detection",
      "L.fragment_segmentation",
      "L.fracture_classifier",
      "int.spatial"
    ],
    "problem_class": "linear_inverse_with_categorical_readout",
    "sensing_mechanism": "radiograph_with_fracture_classifier",
    "solution_space": "1D_fracture_class_with_AO_OTA",
    "sub_domain": "Cortical bone discontinuity recovery from X-ray with fracture categorical readout",
    "title": "Bone Fracture Detection from Radiograph (PWDR)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "fracture_pwdr_forward",
      "fracture_AO_OTA_pwdr_forward",
      "fracture_pediatric_pwdr_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "pixel_resolution_um",
      "kVp",
      "mAs",
      "anatomic_region",
      "view_count",
      "SNR_dB",
      "rotation_artifact",
      "overlapping_structures",
      "growth_plate_confounder",
      "soft_tissue_swelling_obscuring",
      "manual_radiologist_disagreement"
    ],
    "allowed_problem_classes": [
      "fracture_xray_pwdr",
      "fracture_AO_OTA_grading_pwdr",
      "fracture_pediatric_pwdr"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.85_accuracy",
      "forward_operator": "fracture_pwdr_forward",
      "input_format": "multi_view_radiograph_with_fracture_label",
      "omega": {
        "H": 2500,
        "SNR_dB": 30,
        "W": 3000,
        "anatomic_region": "wrist",
        "growth_plate_confounder": 0.0,
        "kVp": 65,
        "mAs": 6,
        "manual_radiologist_disagreement": 0.0,
        "overlapping_structures": 0.0,
        "pixel_resolution_um": 100,
        "rotation_artifact": 0.0,
        "soft_tissue_swelling_obscuring": 0.0,
        "view_count": 2
      },
      "problem_class": "fracture_xray_pwdr"
    },
    "epsilon_bounds": {
      "categorical_accuracy": [
        0.5,
        0.99
      ]
    },
    "omega_bounds": {
      "H": [
        1024,
        4096
      ],
      "W": [
        1024,
        4096
      ],
      "view_count": [
        1,
        4
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Cortical bone discontinuity recovery from X-ray with fracture categorical readout",
  "title": "Bone Fracture Detection from Radiograph (PWDR)"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.