L1 ⚛ L1-156 ⊙ Testnet

PET-CT Fusion (metabolism + anatomy)

Multimodal Fusion · Hybrid anatomical/functional diagnostic imaging

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⬇ L1-156.md

# ⚛ L1 Principle — PET-CT Fusion (metabolism + anatomy) **ID:** `L1-156` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Multimodal Fusion — *Hybrid anatomical/functional diagnostic imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D fused anatomical functional > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554241 --- ## 🧠 1. Introduction **PET-CT Fusion (metabolism + anatomy)** is a **linear inverse problem** whose unknown lives in **3D fused anatomical functional** space, within the **Hybrid anatomical/functional diagnostic imaging** sub-domain of **Multimodal Fusion**. Measurements consist of photons collected by an optical detector via a **pet ct fusion** sensing mechanism. The forward operator applies, in order: L · ct attenuation map operator; L · pet activity map operator; L · registration operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Existence of the recovered 3D fused anatomical functional 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 ~= 14); registration_error dominates the stability cliff; breathing_motion 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 · ct attenuation map → L · pet activity map → L · registration → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.registration` `L.pet_activity_map` `L.ct_attenuation_map` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.ct_attenuation_map` | L · ct attenuation map operator | | `L.pet_activity_map` | L · pet activity map operator | | `L.registration` | L · registration operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Multimodal Fusion | | Sub domain | Hybrid anatomical/functional diagnostic imaging | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 3D_fused_anatomical_functional | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered 3D fused anatomical functional 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 ~= 14); registration_error dominates the stability cliff; breathing_motion 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:** `pet_ct_fusion` · **Forward operator:** `pet_ct_fusion_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 200 | | Snr db | dB | 25 | | Breathing motion | — | 0 | | Temporal mismatch | — | 0 | | Registration error | — | 0 | | Attenuation correction bias | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 32 – 512 | | Snr db | dB | 0.0 – 35.0 | | Breathing motion | — | 0.0 – 10.0 | | Temporal mismatch | — | 0.0 – 3600 | | Registration error | — | 0.0 – 5.0 | | Attenuation correction bias | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `280` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc97553b1b9c382ebc6df6d0f6bc01ed133d728e5604658a5a1d2f5e031680183` - **Chain tx hash:** `0xb9fff2a4049f0f8f82a35127f94d8dc02f0a6a8d1152a01e9a075574f2b6971b` - **Chain block:** `41554241` --- ## File Mapping This bundle consists of: `L1-156.md`, `L1-156.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-156.md` | Source of truth — edit this | Human or LLM | | `L1-156.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 `L1-156`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-156.md).
Regenerate L1-156.json so every field matches the Markdown.
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L2-156-001 PET-CT Fusion (metabolism + anatomy) Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Multimodal Fusion",
  "hardness_fn": {
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    "secondary": "SSIM"
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  "physics_fingerprint": {
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    "sub_domain": "Hybrid anatomical/functional diagnostic imaging",
    "title": "PET-CT Fusion (metabolism + anatomy)"
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      "attenuation_correction_bias": [
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Hybrid anatomical/functional diagnostic imaging",
  "title": "PET-CT Fusion (metabolism + anatomy)"
}

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