L1 ⚛ L1-511 ⊙ Testnet

PillCam-SPECTRA Optical-Property Recovery (analytical core)

Medical Imaging · Capsule-endoscopic multispectral diffuse-reflectance optical-property recovery

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

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-511.md

# ⚛ L1 Principle — PillCam-SPECTRA Optical-Property Recovery (analytical core) **ID:** `L1-511` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Capsule-endoscopic multispectral diffuse-reflectance optical-property recovery* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D chromophore concentration > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553360 --- ## 🧠 1. Introduction **PillCam-SPECTRA Optical-Property Recovery (analytical core)** is a **linear inverse problem** whose unknown lives in **2D chromophore concentration** space, within the **Capsule-endoscopic multispectral diffuse-reflectance optical-property recovery** sub-domain of **Medical Imaging**. Measurements consist of photons collected by an optical detector via a **diffuse reflectance capsule** 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; pixel-level spatial averaging on the detector; detector sums all spectral bands. Observations are corrupted by additive Gaussian noise. Existence of recovered chromophore concentrations is guaranteed within the declared Omega bounds. Uniqueness holds under multi-wavelength acquisition with N_wavelengths >= 5 (sufficient to resolve the typical chromophore basis); single-wavelength acquisition is non-unique (cannot decompose mu_a into chromophore components). Stability is well-conditioned (kappa_eff ~ 15) — capsule_to_mucosa_distance dominates absolute-concentration bias; mucosal_curvature contributes a geometric-correction factor; scattering_anisotropy_g uncertainty contributes a scaling factor of order ~10%. Joint Hadamard well-posedness for the diffuse-reflectance forward is established by Farrell-Patterson-Wilson 1992 (foundational), Wang-Jacques 1995 (MCML), Yudovsky-Pilon 2010 (multispectral inverse), Bjorgan-Milanic-Randeberg 2014 (hyperspectral classification), and Calin-Parasca-Savastru 2014 (medical hyperspectral). ## ⚙ 2. Forward Model Physical chain: **x** → L · optical source → L · diffuse reflectance → Beer-Lambert attenuation → L · detector response → Spatial integration → Spectral integration → **y** (detector). ``` y = Σ_λ ∫_A dA `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 | | `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 multispectral diffuse-reflectance optical-property recovery | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_chromophore_concentration | | Noise model | gaussian | | Integration axis | spectral_spatial | | Difficulty delta | 3 | | L dag | 4.9 | ## 📡 4. Measurement Model Existence of recovered chromophore concentrations is guaranteed within the declared Omega bounds. Uniqueness holds under multi-wavelength acquisition with N_wavelengths >= 5 (sufficient to resolve the typical chromophore basis); single-wavelength acquisition is non-unique (cannot decompose mu_a into chromophore components). Stability is well-conditioned (kappa_eff ~ 15) — capsule_to_mucosa_distance dominates absolute-concentration bias; mucosal_curvature contributes a geometric-correction factor; scattering_anisotropy_g uncertainty contributes a scaling factor of order ~10%. Joint Hadamard well-posedness for the diffuse-reflectance forward is established by Farrell-Patterson-Wilson 1992 (foundational), Wang-Jacques 1995 (MCML), Yudovsky-Pilon 2010 (multispectral inverse), Bjorgan-Milanic-Randeberg 2014 (hyperspectral classification), and Calin-Parasca-Savastru 2014 (medical hyperspectral). | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | RMSE_per_chromophore | ## 📏 5. Operating Range (Ω) **Center problem class:** `pillcam_spectra_optical_recovery` · **Forward operator:** `diffuse_reflectance_capsule_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Snr db | dB | 26 | | Motion blur | — | 0 | | N wavelengths | — | 8 | | Lambda range nm | nm | 400 – 950 | | Mucosal curvature | — | 0 | | Working distance mm | mm | 2 | | Illumination uniformity | — | 0 | | Scattering anisotropy g | g | 0.85 | | Capsule orientation drift | — | 0 | | Capsule to mucosa distance | — | 0 | | Source detector distance mm | mm | 5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 1024 | | W | px | 128 – 1024 | | Snr db | dB | 10.0 – 38.0 | | Motion blur | — | 0.0 – 0.3 | | N wavelengths | — | 3 – 16 | | Mucosal curvature | — | 0.0 – 0.3 | | Working distance mm | mm | 0.5 – 5.0 | | Illumination uniformity | — | 0.0 – 0.4 | | Scattering anisotropy g | g | 0.7 – 0.95 | | Capsule orientation drift | — | 0.0 – 0.4 | | Capsule to mucosa distance | — | 0.0 – 0.4 | | Source detector distance mm | mm | 3.0 – 12.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `80` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x012312d456bc56bf1a0e52320db3a100003569313e9ae82eb93f91c0253d7b20` - **Chain tx hash:** `0x0f9a522bef3d15516c0a667ac47b1fa9269d5ae319486d8d0b207085a8c4855b` - **Chain block:** `41553360` --- ## File Mapping This bundle consists of: `L1-511.md`, `L1-511.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-511.md` | Source of truth — edit this | Human or LLM | | `L1-511.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 `L1-511`._ _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 (L1-511.md).
Regenerate L1-511.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 ▾

L2-511-001 PillCam-SPECTRA Optical-Property Recovery (analytical core) — Spec Skeleton

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-511",
  "chain_block": 41553360,
  "chain_hash": "0x012312d456bc56bf1a0e52320db3a100003569313e9ae82eb93f91c0253d7b20",
  "chain_tx_hash": "0x0f9a522bef3d15516c0a667ac47b1fa9269d5ae319486d8d0b207085a8c4855b",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 80,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of recovered chromophore concentrations is guaranteed within the declared Omega bounds. Uniqueness holds under multi-wavelength acquisition with N_wavelengths \u003e= 5 (sufficient to resolve the typical chromophore basis); single-wavelength acquisition is non-unique (cannot decompose mu_a into chromophore components). Stability is well-conditioned (kappa_eff ~ 15) \u2014 capsule_to_mucosa_distance dominates absolute-concentration bias; mucosal_curvature contributes a geometric-correction factor; scattering_anisotropy_g uncertainty contributes a scaling factor of order ~10%. Joint Hadamard well-posedness for the diffuse-reflectance forward is established by Farrell-Patterson-Wilson 1992 (foundational), Wang-Jacques 1995 (MCML), Yudovsky-Pilon 2010 (multispectral inverse), Bjorgan-Milanic-Randeberg 2014 (hyperspectral classification), and Calin-Parasca-Savastru 2014 (medical hyperspectral).",
    "secondary": "RMSE_per_chromophore"
  },
  "physics_fingerprint": {
    "L_DAG": 4.9,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Medical Imaging",
    "integration_axis": "spectral_spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.optical_source",
      "L.diffuse_reflectance",
      "L.beer_lambert",
      "L.detector_response",
      "int.spatial",
      "int.spectral"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "diffuse_reflectance_capsule",
    "solution_space": "2D_chromophore_concentration",
    "sub_domain": "Capsule-endoscopic multispectral diffuse-reflectance optical-property recovery",
    "title": "PillCam-SPECTRA Optical-Property Recovery (analytical core)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "diffuse_reflectance_capsule_forward",
      "monte_carlo_capsule_forward",
      "diffusion_approximation_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_wavelengths",
      "lambda_range_nm",
      "source_detector_distance_mm",
      "working_distance_mm",
      "scattering_anisotropy_g",
      "SNR_dB",
      "capsule_to_mucosa_distance",
      "mucosal_curvature",
      "illumination_uniformity",
      "motion_blur",
      "capsule_orientation_drift"
    ],
    "allowed_problem_classes": [
      "pillcam_spectra_optical_recovery",
      "pillcam_spectra_chromophore_unmixing",
      "pillcam_spectra_spatial_perfusion"
    ],
    "center_spec": {
      "epsilon_fn_center": "28.0",
      "forward_operator": "diffuse_reflectance_capsule_forward",
      "input_format": "multispectral_capsule_frame",
      "omega": {
        "H": 256,
        "N_wavelengths": 8,
        "SNR_dB": 26,
        "W": 256,
        "capsule_orientation_drift": 0.0,
        "capsule_to_mucosa_distance": 0.0,
        "illumination_uniformity": 0.0,
        "lambda_range_nm": [
          400,
          950
        ],
        "motion_blur": 0.0,
        "mucosal_curvature": 0.0,
        "scattering_anisotropy_g": 0.85,
        "source_detector_distance_mm": 5.0,
        "working_distance_mm": 2.0
      },
      "problem_class": "pillcam_spectra_optical_recovery"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        128,
        1024
      ],
      "N_wavelengths": [
        3,
        16
      ],
      "SNR_dB": [
        10.0,
        38.0
      ],
      "W": [
        128,
        1024
      ],
      "capsule_orientation_drift": [
        0.0,
        0.4
      ],
      "capsule_to_mucosa_distance": [
        0.0,
        0.4
      ],
      "illumination_uniformity": [
        0.0,
        0.4
      ],
      "motion_blur": [
        0.0,
        0.3
      ],
      "mucosal_curvature": [
        0.0,
        0.3
      ],
      "scattering_anisotropy_g": [
        0.7,
        0.95
      ],
      "source_detector_distance_mm": [
        3.0,
        12.0
      ],
      "working_distance_mm": [
        0.5,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Capsule-endoscopic multispectral diffuse-reflectance optical-property recovery",
  "title": "PillCam-SPECTRA Optical-Property Recovery (analytical core)"
}

🎁

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.