L1 ⚛ L1-515 ⊙ Testnet

Mammographic Breast Density Classification BI-RADS (PWDR)

Medical Imaging · Mammographic glandular-tissue density reconstruction with BI-RADS density category readout

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You are helping me submit a MODIFICATION of L1-515 (Mammographic Breast Density Classification BI-RADS (PWDR)) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-515.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-515.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

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[PASTE THE .md HERE]

⚙ Forward Model

y = ∫_A dA `L.birads_threshold_classifier` `L.vbd_aggregation` `L.glandular_fraction_recovery` `L.dual_energy_decomposition` ∫µ dl I₀(E) x,    measurements ~ Poisson(αy)

world state x (1D birads density category)

→

X-ray source I₀(E)

→

Attenuation projection ∫µ dl

→

L · dual energy decomposition `L.dual_energy_decomposition`

→

L · glandular fraction recovery `L.glandular_fraction_recovery`

→

L · vbd aggregation `L.vbd_aggregation`

→

L · birads threshold classifier `L.birads_threshold_classifier`

→

Spatial integration ∫_A dA

→

observation y (x ray detector)

Noise: Poisson counting noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-515.md

# ⚛ L1 Principle — Mammographic Breast Density Classification BI-RADS (PWDR) **ID:** `L1-515` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Mammographic glandular-tissue density reconstruction with BI-RADS density category readout* > **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D birads density category > **📡 Carrier:** x_ray · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553360 --- ## 🧠 1. Introduction **Mammographic Breast Density Classification BI-RADS (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D birads density category** space, within the **Mammographic glandular-tissue density reconstruction with BI-RADS density category readout** sub-domain of **Medical Imaging**. Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **mammography with birads density grading** sensing mechanism. The forward operator applies, in order: polyenergetic X-ray emission spectrum; line-integral projection through an attenuation map; L · dual energy decomposition operator; L · glandular fraction recovery operator; L · vbd aggregation operator; L · birads threshold classifier operator; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson counting noise. Existence and uniqueness inherited from L1-036 mammography. Stability inherits L1-036's well-conditioned reconstruction plus a small additive contribution from compression_thickness_calibration_error (dominant systematic bias source) and age_related_density_shift. Joint Hadamard well-posedness for the coupled mammography + BI-RADS threshold forward established by Sickles E et al. (2013 BI-RADS Atlas 5th ed), Highnam R et al. (2010 Volpara volumetric density), Hartman K et al. (2013 Quantra), Yaffe MJ (2008 review of mammographic density), Boyd NF et al. (2007 density and breast cancer risk), and Pertuz S et al. (2014 automated density estimation comparison). ## ⚙ 2. Forward Model Physical chain: **x** → X-ray source → Attenuation projection → L · dual energy decomposition → L · glandular fraction recovery → L · vbd aggregation → L · birads threshold classifier → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.birads_threshold_classifier` `L.vbd_aggregation` `L.glandular_fraction_recovery` `L.dual_energy_decomposition` ∫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.dual_energy_decomposition` | L · dual energy decomposition operator | | `L.glandular_fraction_recovery` | L · glandular fraction recovery operator | | `L.vbd_aggregation` | L · vbd aggregation operator | | `L.birads_threshold_classifier` | L · birads threshold classifier operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Mammographic glandular-tissue density reconstruction with BI-RADS density category readout | | Carrier | x_ray | | Problem class | linear_inverse_with_categorical_readout | | Solution space | 1D_birads_density_category | | Noise model | poisson | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 5.8 | ## 📡 4. Measurement Model Existence and uniqueness inherited from L1-036 mammography. Stability inherits L1-036's well-conditioned reconstruction plus a small additive contribution from compression_thickness_calibration_error (dominant systematic bias source) and age_related_density_shift. Joint Hadamard well-posedness for the coupled mammography + BI-RADS threshold forward established by Sickles E et al. (2013 BI-RADS Atlas 5th ed), Highnam R et al. (2010 Volpara volumetric density), Hartman K et al. (2013 Quantra), Yaffe MJ (2008 review of mammographic density), Boyd NF et al. (2007 density and breast cancer risk), and Pertuz S et al. (2014 automated density estimation comparison). | Metric | Value | |---|---| | Metric | categorical_accuracy | | Secondary | weighted_kappa_birads | ## 📏 5. Operating Range (Ω) **Center problem class:** `mammographic_birads_density_pwdr` · **Forward operator:** `mammography_birads_pwdr_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Kvp | — | 30 | | Mas | — | 100 | | H proj | — | 3500 | | Snr db | dB | 32 | | W proj | — | 2800 | | Pixel size um | µm | 85 | | Filter material | — | Mo | | Anode target material | — | Mo | | Exposure factor drift | — | 0 | | Compression thickness mm | mm | 50 | | Age related density shift | — | 0 | | Calibration phantom uncertainty | — | 0 | | Automated vs radiologist disagreement | — | 0 | | Compression thickness calibration error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Kvp | — | 25 – 35 | | H proj | — | 1024 – 5500 | | W proj | — | 1024 – 4500 | | Pixel size um | µm | 50 – 200 | | Compression thickness mm | mm | 20 – 90 | ## 🎯 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:** `0xbc0db9931caa3bf1b6cd65d243103412660149215ca9cf038c3720ecf6ae0c52` - **Chain tx hash:** `0xa728d0236a9dc4d96f2b2a3ff9d3dd2088fa9583d6ebecfb8ca1a2803e52f838` - **Chain block:** `41553360` --- ## File Mapping This bundle consists of: `L1-515.md`, `L1-515.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-515.md` | Source of truth — edit this | Human or LLM | | `L1-515.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 `L1-515`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-515-001 Mammographic Breast Density Classification BI-RADS (PWDR) — Spec Skeleton

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📋 JSON metadata

{
  "artifact_id": "L1-515",
  "chain_block": 41553360,
  "chain_hash": "0xbc0db9931caa3bf1b6cd65d243103412660149215ca9cf038c3720ecf6ae0c52",
  "chain_tx_hash": "0xa728d0236a9dc4d96f2b2a3ff9d3dd2088fa9583d6ebecfb8ca1a2803e52f838",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 60,
    "metric": "categorical_accuracy",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "categorical_accuracy",
    "regime": "Existence and uniqueness inherited from L1-036 mammography. Stability inherits L1-036\u0027s well-conditioned reconstruction plus a small additive contribution from compression_thickness_calibration_error (dominant systematic bias source) and age_related_density_shift. Joint Hadamard well-posedness for the coupled mammography + BI-RADS threshold forward established by Sickles E et al. (2013 BI-RADS Atlas 5th ed), Highnam R et al. (2010 Volpara volumetric density), Hartman K et al. (2013 Quantra), Yaffe MJ (2008 review of mammographic density), Boyd NF et al. (2007 density and breast cancer risk), and Pertuz S et al. (2014 automated density estimation comparison).",
    "secondary": "weighted_kappa_birads"
  },
  "physics_fingerprint": {
    "L_DAG": 5.8,
    "carrier": "x_ray",
    "difficulty_delta": 3,
    "domain": "Medical Imaging",
    "integration_axis": "spatial",
    "noise_model": "poisson",
    "primitives": [
      "L.xray_source",
      "L.attenuation_projection",
      "L.dual_energy_decomposition",
      "L.glandular_fraction_recovery",
      "L.vbd_aggregation",
      "L.birads_threshold_classifier",
      "int.spatial"
    ],
    "problem_class": "linear_inverse_with_categorical_readout",
    "sensing_mechanism": "mammography_with_birads_density_grading",
    "solution_space": "1D_birads_density_category",
    "sub_domain": "Mammographic glandular-tissue density reconstruction with BI-RADS density category readout",
    "title": "Mammographic Breast Density Classification BI-RADS (PWDR)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "mammography_birads_pwdr_forward",
      "dbt_birads_pwdr_forward",
      "ffdm_volpara_forward",
      "ffdm_quantra_forward"
    ],
    "allowed_omega_dimensions": [
      "H_proj",
      "W_proj",
      "pixel_size_um",
      "kVp",
      "mAs",
      "compression_thickness_mm",
      "anode_target_material",
      "filter_material",
      "SNR_dB",
      "compression_thickness_calibration_error",
      "exposure_factor_drift",
      "calibration_phantom_uncertainty",
      "age_related_density_shift",
      "automated_vs_radiologist_disagreement"
    ],
    "allowed_problem_classes": [
      "mammographic_birads_density_pwdr",
      "mammographic_4cat_density_pwdr",
      "mammographic_continuous_vbd"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.85_accuracy",
      "forward_operator": "mammography_birads_pwdr_forward",
      "input_format": "ffdm_4view_with_density_label",
      "omega": {
        "H_proj": 3500,
        "SNR_dB": 32,
        "W_proj": 2800,
        "age_related_density_shift": 0.0,
        "anode_target_material": "Mo",
        "automated_vs_radiologist_disagreement": 0.0,
        "calibration_phantom_uncertainty": 0.0,
        "compression_thickness_calibration_error": 0.0,
        "compression_thickness_mm": 50,
        "exposure_factor_drift": 0.0,
        "filter_material": "Mo",
        "kVp": 30,
        "mAs": 100,
        "pixel_size_um": 85
      },
      "problem_class": "mammographic_birads_density_pwdr"
    },
    "epsilon_bounds": {
      "categorical_accuracy": [
        0.5,
        0.99
      ]
    },
    "omega_bounds": {
      "H_proj": [
        1024,
        5500
      ],
      "W_proj": [
        1024,
        4500
      ],
      "compression_thickness_mm": [
        20,
        90
      ],
      "kVp": [
        25,
        35
      ],
      "pixel_size_um": [
        50,
        200
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Mammographic glandular-tissue density reconstruction with BI-RADS density category readout",
  "title": "Mammographic Breast Density Classification BI-RADS (PWDR)"
}

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