L1 ⚛ L1-031 ⊙ Testnet

Planar X-ray Radiography

Medical Imaging · Projection X-ray diagnostic imaging

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⬇ L1-031.md

# ⚛ L1 Principle — Planar X-ray Radiography **ID:** `L1-031` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Projection X-ray diagnostic imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D attenuation projection > **📡 Carrier:** x_ray · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553371 --- ## 🧠 1. Introduction **Planar X-ray Radiography** is a **linear inverse problem** whose unknown lives in **2D attenuation projection** space, within the **Projection X-ray diagnostic imaging** sub-domain of **Medical Imaging**. Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **xray projection** sensing mechanism. The forward operator applies, in order: polyenergetic X-ray emission spectrum; exponential attenuation along the propagation path; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D attenuation projection is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 8); scatter dominates the stability cliff; patient_motion and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → X-ray source → Beer-Lambert attenuation → Spatial integration → **y** (detector). ``` y = ∫_A dA exp(-∫µ dl) I₀(E) x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.xray_source` | Polyenergetic x-ray emission spectrum | | `L.beer_lambert` | Exponential attenuation along the propagation path | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Projection X-ray diagnostic imaging | | Carrier | x_ray | | Problem class | linear_inverse | | Solution space | 2D_attenuation_projection | | Noise model | shot_poisson | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered 2D attenuation projection is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 8); scatter dominates the stability cliff; patient_motion and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `xray_radiography` · **Forward operator:** `xray_radiography_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 3072 | | W | px | 3072 | | Kvp | — | 80 | | Mas | — | 20 | | Scatter | — | 0 | | Pixel um | µm | 140 | | Patient motion | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 1024 – 4096 | | W | px | 1024 – 4096 | | Kvp | — | 30 – 150 | | Mas | — | 0.1 – 200 | | Scatter | — | 0.0 – 0.4 | | Pixel um | µm | 50 – 500 | | Tube drift | — | 0.0 – 0.1 | | Patient motion | — | 0.0 – 0.3 | | Anti scatter grid | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 34.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x53084c6e36f8b81280fe6f2ff4f6ec5554a9c02df044095bd7bf68cb077c9f1f` - **Chain tx hash:** `0xd414f0e303b7d08d47d0df33829ab71a29600c8ec547246d6647618d4e9dcd41` - **Chain block:** `41553371` --- ## File Mapping This bundle consists of: `L1-031.md`, `L1-031.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-031.md` | Source of truth — edit this | Human or LLM | | `L1-031.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 `L1-031`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-031.md).
Regenerate L1-031.json so every field matches the Markdown.
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L2-031-001 Planar X-ray Radiography Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553371,
  "chain_hash": "0x53084c6e36f8b81280fe6f2ff4f6ec5554a9c02df044095bd7bf68cb077c9f1f",
  "chain_tx_hash": "0xd414f0e303b7d08d47d0df33829ab71a29600c8ec547246d6647618d4e9dcd41",
  "domain": "Medical Imaging",
  "hardness_fn": {
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    "kappa": 160,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 2D attenuation projection is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 8); scatter dominates the stability cliff; patient_motion and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 2.5,
    "carrier": "x_ray",
    "difficulty_delta": 3,
    "domain": "Medical Imaging",
    "integration_axis": "spatial",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.xray_source",
      "L.beer_lambert",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "xray_projection",
    "solution_space": "2D_attenuation_projection",
    "sub_domain": "Projection X-ray diagnostic imaging",
    "title": "Planar X-ray Radiography"
  },
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      "patient_motion",
      "scatter",
      "patient_motion",
      "anti_scatter_grid",
      "tube_drift"
    ],
    "allowed_problem_classes": [
      "xray_radiography"
    ],
    "center_spec": {
      "epsilon_fn_center": "34.0",
      "forward_operator": "xray_radiography_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 3072,
        "W": 3072,
        "kVp": 80,
        "mAs": 20,
        "patient_motion": 0.0,
        "pixel_um": 140,
        "scatter": 0.0
      },
      "problem_class": "xray_radiography"
    },
    "epsilon_bounds": {
      "psnr_db": [
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        45.0
      ]
    },
    "omega_bounds": {
      "H": [
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        4096
      ],
      "W": [
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        4096
      ],
      "anti_scatter_grid": [
        0.0,
        0.5
      ],
      "kVp": [
        30,
        150
      ],
      "mAs": [
        0.1,
        200
      ],
      "patient_motion": [
        0.0,
        0.3
      ],
      "pixel_um": [
        50,
        500
      ],
      "scatter": [
        0.0,
        0.4
      ],
      "tube_drift": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Projection X-ray diagnostic imaging",
  "title": "Planar X-ray Radiography"
}

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