L1 ⚛ L1-511 ⊙ Testnet

PillCam-SPECTRA Optical-Property Recovery (analytical core)

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

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You are helping me submit a MODIFICATION of L1-511 (PillCam-SPECTRA Optical-Property Recovery (analytical core)) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-511.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-511.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.detector_response` exp(-∫µ dl) `L.diffuse_reflectance` `L.optical_source` x + n,    n ~ 𝒩(0, σ²)

world state x (2D chromophore concentration)

→

L · optical source `L.optical_source`

→

L · diffuse reflectance `L.diffuse_reflectance`

→

Beer-Lambert attenuation exp(-∫µ dl)

→

L · detector response `L.detector_response`

→

Spatial integration ∫_A dA

→

Spectral integration Σ_λ

→

observation y (photon detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-511.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._

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

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📋 JSON metadata

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  "chain_block": 41553360,
  "chain_hash": "0x012312d456bc56bf1a0e52320db3a100003569313e9ae82eb93f91c0253d7b20",
  "chain_tx_hash": "0x0f9a522bef3d15516c0a667ac47b1fa9269d5ae319486d8d0b207085a8c4855b",
  "domain": "Medical Imaging",
  "hardness_fn": {
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    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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  "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": {
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    "carrier": "photon",
    "difficulty_delta": 3,
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    "integration_axis": "spectral_spatial",
    "noise_model": "gaussian",
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    "sub_domain": "Capsule-endoscopic multispectral diffuse-reflectance optical-property recovery",
    "title": "PillCam-SPECTRA Optical-Property Recovery (analytical core)"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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        "N_wavelengths": 8,
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      "capsule_to_mucosa_distance": [
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      "illumination_uniformity": [
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        0.3
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      "working_distance_mm": [
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    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Capsule-endoscopic multispectral diffuse-reflectance optical-property recovery",
  "title": "PillCam-SPECTRA Optical-Property Recovery (analytical core)"
}

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