L1 ⚛ L1-512 ⊙ Testnet

PillCam-SPECTRA Bleeding-Region Detection (PWDR)

Medical Imaging · Capsule-endoscopic bleeding / polyp / mucosal-anomaly classification via thresholded chromophore recovery

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⬇ L1-512.md ⬇ L1-512.json

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You are helping me submit a MODIFICATION of L1-512 (PillCam-SPECTRA Bleeding-Region Detection (PWDR)) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-512.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-512.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 = Σ_λ ∫_A dA `L.threshold_classifier` `L.chromophore_unmixing` `L.detector_response` exp(-∫µ dl) `L.diffuse_reflectance` `L.optical_source` x + n,    n ~ 𝒩(0, σ²)

world state x (2D categorical mucosal label map)

→

L · optical source `L.optical_source`

→

L · diffuse reflectance `L.diffuse_reflectance`

→

Beer-Lambert attenuation exp(-∫µ dl)

→

L · detector response `L.detector_response`

→

L · chromophore unmixing `L.chromophore_unmixing`

→

L · threshold classifier `L.threshold_classifier`

→

Spatial integration ∫_A dA

→

Spectral integration Σ_λ

→

observation y (photon detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-512.md

# ⚛ L1 Principle — PillCam-SPECTRA Bleeding-Region Detection (PWDR) **ID:** `L1-512` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Capsule-endoscopic bleeding / polyp / mucosal-anomaly classification via thresholded chromophore recovery* > **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 2D categorical mucosal label map > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553373 --- ## 🧠 1. Introduction **PillCam-SPECTRA Bleeding-Region Detection (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **2D categorical mucosal label map** space, within the **Capsule-endoscopic bleeding / polyp / mucosal-anomaly classification via thresholded chromophore recovery** sub-domain of **Medical Imaging**. Measurements consist of photons collected by an optical detector via a **diffuse reflectance capsule with threshold classifier** sensing mechanism. The forward operator applies, in order: L · optical source operator; L · diffuse reflectance operator; exponential attenuation along the propagation path; L · detector response operator; L · chromophore unmixing operator; L · threshold classifier operator; pixel-level spatial averaging on the detector; detector sums all spectral bands. Observations are corrupted by additive Gaussian noise. Existence and uniqueness inherited from L1-511 analytical core; threshold function is piecewise-constant and Lipschitz-continuous on the underlying chromophore-concentration state, so existence and uniqueness lift from continuous to discrete readout under the standard categorical-readout argument (PWM_GATE_CLASSES_AND_SCALING.md Case A). Stability inherits L1-511's kappa_eff ~ 15 plus a small additive contribution C_threshold * |threshold_calibration_uncertainty| from per-class threshold-value uncertainty. The threshold-continuity_proof in discrete_readout demonstrates that boundaries between class regions form measure-zero hyperplanes in chromophore space, so misclassification probability scales linearly with chromophore-recovery error away from the boundary. ## ⚙ 2. Forward Model Physical chain: **x** → L · optical source → L · diffuse reflectance → Beer-Lambert attenuation → L · detector response → L · chromophore unmixing → L · threshold classifier → Spatial integration → Spectral integration → **y** (detector). ``` y = Σ_λ ∫_A dA `L.threshold_classifier` `L.chromophore_unmixing` `L.detector_response` exp(-∫µ dl) `L.diffuse_reflectance` `L.optical_source` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.optical_source` | L · optical source operator | | `L.diffuse_reflectance` | L · diffuse reflectance operator | | `L.beer_lambert` | Exponential attenuation along the propagation path | | `L.detector_response` | L · detector response operator | | `L.chromophore_unmixing` | L · chromophore unmixing operator | | `L.threshold_classifier` | L · threshold classifier operator | | `int.spatial` | Pixel-level spatial averaging on the detector | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Capsule-endoscopic bleeding / polyp / mucosal-anomaly classification via thresholded chromophore recovery | | Carrier | photon | | Problem class | linear_inverse_with_categorical_readout | | Solution space | 2D_categorical_mucosal_label_map | | Noise model | gaussian | | Integration axis | spectral_spatial | | Difficulty delta | 3 | | L dag | 6.9 | ## 📡 4. Measurement Model Existence and uniqueness inherited from L1-511 analytical core; threshold function is piecewise-constant and Lipschitz-continuous on the underlying chromophore-concentration state, so existence and uniqueness lift from continuous to discrete readout under the standard categorical-readout argument (PWM_GATE_CLASSES_AND_SCALING.md Case A). Stability inherits L1-511's kappa_eff ~ 15 plus a small additive contribution C_threshold * |threshold_calibration_uncertainty| from per-class threshold-value uncertainty. The threshold-continuity_proof in discrete_readout demonstrates that boundaries between class regions form measure-zero hyperplanes in chromophore space, so misclassification probability scales linearly with chromophore-recovery error away from the boundary. | Metric | Value | |---|---| | Metric | categorical_accuracy | | Secondary | mIoU_per_class | ## 📏 5. Operating Range (Ω) **Center problem class:** `pillcam_spectra_bleeding_pwdr` · **Forward operator:** `pillcam_spectra_pwdr_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Snr db | dB | 26 | | Tau bvf | — | 0.04 | | Tau hbo2 | — | 0.5 | | Tau edema | — | 0.45 | | N wavelengths | — | 8 | | Lambda range nm | nm | 400 – 950 | | Tau lipid polyp | — | 0.15 | | Tau total blood | — | 0.06 | | Tau scatter neop | — | 22 | | Tau scatter polyp | — | 18 | | Tau oxy ratio neop | — | 4 | | Working distance mm | mm | 2 | | Scattering anisotropy g | g | 0.85 | | Source detector distance mm | mm | 5 | | Motion induced label flicker | — | 0 | | Between region smoothing artifact | — | 0 | | Threshold calibration uncertainty | — | 0 | | Capsule orientation mucosal assignment | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 1024 | | W | px | 128 – 1024 | | Snr db | dB | 10.0 – 38.0 | | N wavelengths | — | 3 – 16 | | Motion induced label flicker | — | 0.0 – 0.4 | | Between region smoothing artifact | — | 0.0 – 0.3 | | Threshold calibration uncertainty | — | 0.0 – 0.3 | | Capsule orientation mucosal assignment | — | 0.0 – 0.4 | ## 🎯 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 = `80` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xeb1e83e6df8f26f674a4f3c080ee808696aa30e1cba1fad3f8e0044f7f4d9b85` - **Chain tx hash:** `0x3504adc2e3ab9fe2688f49a503724aa99f6d3ac7813dbb3d95122cb52d8f5485` - **Chain block:** `41553373` --- ## File Mapping This bundle consists of: `L1-512.md`, `L1-512.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-512.md` | Source of truth — edit this | Human or LLM | | `L1-512.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 `L1-512`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-512-001 PillCam-SPECTRA Bleeding-Region Detection (PWDR) — Spec Skeleton

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📋 JSON metadata

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  "chain_block": 41553373,
  "chain_hash": "0xeb1e83e6df8f26f674a4f3c080ee808696aa30e1cba1fad3f8e0044f7f4d9b85",
  "chain_tx_hash": "0x3504adc2e3ab9fe2688f49a503724aa99f6d3ac7813dbb3d95122cb52d8f5485",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 80,
    "metric": "categorical_accuracy",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "categorical_accuracy",
    "regime": "Existence and uniqueness inherited from L1-511 analytical core; threshold function is piecewise-constant and Lipschitz-continuous on the underlying chromophore-concentration state, so existence and uniqueness lift from continuous to discrete readout under the standard categorical-readout argument (PWM_GATE_CLASSES_AND_SCALING.md Case A). Stability inherits L1-511\u0027s kappa_eff ~ 15 plus a small additive contribution C_threshold * |threshold_calibration_uncertainty| from per-class threshold-value uncertainty. The threshold-continuity_proof in discrete_readout demonstrates that boundaries between class regions form measure-zero hyperplanes in chromophore space, so misclassification probability scales linearly with chromophore-recovery error away from the boundary.",
    "secondary": "mIoU_per_class"
  },
  "physics_fingerprint": {
    "L_DAG": 6.9,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Medical Imaging",
    "integration_axis": "spectral_spatial",
    "noise_model": "gaussian",
    "primitives": [
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      "L.diffuse_reflectance",
      "L.beer_lambert",
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      "L.threshold_classifier",
      "int.spatial",
      "int.spectral"
    ],
    "problem_class": "linear_inverse_with_categorical_readout",
    "sensing_mechanism": "diffuse_reflectance_capsule_with_threshold_classifier",
    "solution_space": "2D_categorical_mucosal_label_map",
    "sub_domain": "Capsule-endoscopic bleeding / polyp / mucosal-anomaly classification via thresholded chromophore recovery",
    "title": "PillCam-SPECTRA Bleeding-Region Detection (PWDR)"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "source_detector_distance_mm",
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      "scattering_anisotropy_g",
      "SNR_dB",
      "tau_HbO2",
      "tau_BVF",
      "tau_lipid_polyp",
      "tau_scatter_polyp",
      "tau_scatter_neop",
      "tau_oxy_ratio_neop",
      "tau_total_blood",
      "tau_edema",
      "threshold_calibration_uncertainty",
      "between_region_smoothing_artifact",
      "motion_induced_label_flicker",
      "capsule_orientation_mucosal_assignment"
    ],
    "allowed_problem_classes": [
      "pillcam_spectra_bleeding_pwdr",
      "pillcam_spectra_polyp_pwdr",
      "pillcam_spectra_neoplasia_pwdr",
      "pillcam_spectra_inflammation_pwdr",
      "pillcam_spectra_combined_5class_pwdr"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.85_accuracy",
      "forward_operator": "pillcam_spectra_pwdr_forward",
      "input_format": "multispectral_capsule_frame_with_label_map",
      "omega": {
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        "N_wavelengths": 8,
        "SNR_dB": 26,
        "W": 256,
        "between_region_smoothing_artifact": 0.0,
        "capsule_orientation_mucosal_assignment": 0.0,
        "lambda_range_nm": [
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          950
        ],
        "motion_induced_label_flicker": 0.0,
        "scattering_anisotropy_g": 0.85,
        "source_detector_distance_mm": 5.0,
        "tau_BVF": 0.04,
        "tau_HbO2": 0.5,
        "tau_edema": 0.45,
        "tau_lipid_polyp": 0.15,
        "tau_oxy_ratio_neop": 4.0,
        "tau_scatter_neop": 22.0,
        "tau_scatter_polyp": 18.0,
        "tau_total_blood": 0.06,
        "threshold_calibration_uncertainty": 0.0,
        "working_distance_mm": 2.0
      },
      "problem_class": "pillcam_spectra_bleeding_pwdr"
    },
    "epsilon_bounds": {
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        0.99
      ]
    },
    "omega_bounds": {
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        1024
      ],
      "N_wavelengths": [
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        16
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      "SNR_dB": [
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        38.0
      ],
      "W": [
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        1024
      ],
      "between_region_smoothing_artifact": [
        0.0,
        0.3
      ],
      "capsule_orientation_mucosal_assignment": [
        0.0,
        0.4
      ],
      "motion_induced_label_flicker": [
        0.0,
        0.4
      ],
      "threshold_calibration_uncertainty": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Capsule-endoscopic bleeding / polyp / mucosal-anomaly classification via thresholded chromophore recovery",
  "title": "PillCam-SPECTRA Bleeding-Region Detection (PWDR)"
}

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