L1 ⚛ L1-042 ⊙ Testnet

Optical Coherence Tomography (OCT)

Medical Imaging · Coherence-gated depth-resolved imaging

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⬇ principle.md ⬇ principle.json

Fork L1-042

⬇ L1-042.md ⬇ L1-042.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-042 (Optical Coherence Tomography (OCT)) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-042.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-042.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.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = Σ_λ S_raster `L.fourier_transform` `L.sd_oct_spectral` x + n,    n ~ 𝒩(0, σ²)

world state x (3D tissue reflectivity)

→

L · sd oct spectral `L.sd_oct_spectral`

→

L · fourier transform `L.fourier_transform`

→

Raster scan S_raster

→

Spectral integration Σ_λ

→

observation y (photon detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-042.md

# ⚛ L1 Principle — Optical Coherence Tomography (OCT) **ID:** `L1-042` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Coherence-gated depth-resolved imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D tissue reflectivity > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553358 --- ## 🧠 1. Introduction **Optical Coherence Tomography (OCT)** is a **linear inverse problem** whose unknown lives in **3D tissue reflectivity** space, within the **Coherence-gated depth-resolved imaging** sub-domain of **Medical Imaging**. Measurements consist of photons collected by an optical detector via a **oct spectral domain** sensing mechanism. The forward operator applies, in order: L · sd oct spectral operator; L · fourier transform operator; ordered pixel-by-pixel sampling; detector sums all spectral bands. Observations are corrupted by additive Gaussian noise. Existence of the recovered 3D tissue reflectivity 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 moderately conditioned (kappa_eff ~= 12); dispersion_mismatch dominates the stability cliff; motion_artifacts and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise 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** → L · sd oct spectral → L · fourier transform → Raster scan → Spectral integration → **y** (detector). ``` y = Σ_λ S_raster `L.fourier_transform` `L.sd_oct_spectral` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.sd_oct_spectral` | L · sd oct spectral operator | | `L.fourier_transform` | L · fourier transform operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Coherence-gated depth-resolved imaging | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 3D_tissue_reflectivity | | Noise model | gaussian | | Integration axis | spectral | | Difficulty delta | 3 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered 3D tissue reflectivity 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 moderately conditioned (kappa_eff ~= 12); dispersion_mismatch dominates the stability cliff; motion_artifacts and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise 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:** `oct` · **Forward operator:** `oct_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Z | — | 1024 | | Snr db | dB | 30 | | Pixel um | µm | 5 | | Lambda bw nm | nm | 50 | | Speckle noise | — | 0 | | Lambda center nm | nm | 840 | | Motion artifacts | — | 0 | | Dispersion mismatch | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 256 – 4096 | | Snr db | dB | 10.0 – 45.0 | | Pixel um | µm | 1 – 20 | | Lambda bw nm | nm | 20 – 200 | | Speckle noise | — | 0.0 – 0.3 | | Signal roll off | — | 0.0 – 0.3 | | Lambda center nm | nm | 830 – 1310 | | Motion artifacts | — | 0.0 – 0.3 | | Dispersion mismatch | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x0fceaa62df330335afa1042cca0507d44e53b368763761fe9617f6258e421264` - **Chain tx hash:** `0xff46ebfed82ede08ddedb1909b8786ac17f01b990a912684a292d6dd7f987c28` - **Chain block:** `41553358` --- ## File Mapping This bundle consists of: `L1-042.md`, `L1-042.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-042.md` | Source of truth — edit this | Human or LLM | | `L1-042.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 `L1-042`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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⌥ Hierarchy

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L2-042-001 Optical Coherence Tomography (OCT) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553358,
  "chain_hash": "0x0fceaa62df330335afa1042cca0507d44e53b368763761fe9617f6258e421264",
  "chain_tx_hash": "0xff46ebfed82ede08ddedb1909b8786ac17f01b990a912684a292d6dd7f987c28",
  "domain": "Medical Imaging",
  "hardness_fn": {
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    "kappa": 240,
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    "type": "epsilon_fn"
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  "physics_fingerprint": {
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    "sub_domain": "Coherence-gated depth-resolved imaging",
    "title": "Optical Coherence Tomography (OCT)"
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Coherence-gated depth-resolved imaging",
  "title": "Optical Coherence Tomography (OCT)"
}

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