L1 ⚛ L1-065 ⊙ Testnet

Functional Near-Infrared Spectroscopy (fNIRS)

Medical Imaging · Wearable NIR hemodynamic brain monitoring

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⬇ L1-065.md

# ⚛ L1 Principle — Functional Near-Infrared Spectroscopy (fNIRS) **ID:** `L1-065` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Wearable NIR hemodynamic brain monitoring* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D brain hbt dynamics > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41552303 --- ## 🧠 1. Introduction **Functional Near-Infrared Spectroscopy (fNIRS)** is a **linear inverse problem** whose unknown lives in **2D brain hbt dynamics** space, within the **Wearable NIR hemodynamic brain monitoring** sub-domain of **Medical Imaging**. Measurements consist of photons collected by an optical detector via a **near infrared diffusion** sensing mechanism. The forward operator applies, in order: L · nir source operator; L · diffusion propagation operator; D · nir detector operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D brain hbt dynamics 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); scalp_blood_flow_contamination dominates the stability cliff; 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 · nir source → L · diffusion propagation → D · nir detector → Temporal integration → **y** (detector). ``` y = ∫_t dt `D.nir_detector` `L.diffusion_propagation` `L.nir_source` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.nir_source` | L · nir source operator | | `L.diffusion_propagation` | L · diffusion propagation operator | | `D.nir_detector` | D · nir detector operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Wearable NIR hemodynamic brain monitoring | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_brain_hbt_dynamics | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered 2D brain hbt dynamics 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); scalp_blood_flow_contamination dominates the stability cliff; 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:** `fnirs` · **Forward operator:** `fnirs_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 20 | | Motion | — | 0 | | N sources | — | 16 | | Lambda nm | nm | 760 – 850 | | N detectors | — | 16 | | Sampling hz | Hz | 10 | | Ambient light | — | 0 | | Optode coupling | — | 1 | | Scalp blood flow contamination | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0.0 – 35.0 | | Motion | — | 0.0 – 0.5 | | N sources | — | 4 – 128 | | N detectors | — | 4 – 128 | | Sampling hz | Hz | 1 – 100 | | Ambient light | — | 0.0 – 0.3 | | Optode coupling | — | 0.3 – 1.0 | | Scalp blood flow contamination | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 18.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `280` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc4a6b1fbbbcd64467eb4307fba13ce02574d34192ce2a2e8d911a768e7dccce2` - **Chain tx hash:** `0x5ce8c4393b083051f2123d64bb6899c0e9c1aac48912f60c1383f319dc66f4e3` - **Chain block:** `41552303` --- ## File Mapping This bundle consists of: `L1-065.md`, `L1-065.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-065.md` | Source of truth — edit this | Human or LLM | | `L1-065.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 `L1-065`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-065-001 Functional Near-Infrared Spectroscopy (fNIRS) Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Medical Imaging",
  "hardness_fn": {
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    "kappa": 280,
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    "integration_axis": "temporal",
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        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Wearable NIR hemodynamic brain monitoring",
  "title": "Functional Near-Infrared Spectroscopy (fNIRS)"
}

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