L1 ⚛ L1-068 ⊙ Testnet

Electroencephalography (EEG)

Medical Imaging · Scalp-electrode electric field brain imaging

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⬇ L1-068.md

# ⚛ L1 Principle — Electroencephalography (EEG) **ID:** `L1-068` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Scalp-electrode electric field brain imaging* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 4D cortical current > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553386 --- ## 🧠 1. Introduction **Electroencephalography (EEG)** is a **nonlinear inverse problem** whose unknown lives in **4D cortical current** space, within the **Scalp-electrode electric field brain imaging** sub-domain of **Medical Imaging**. Measurements consist of radio-frequency electromagnetic waves via a **eeg scalp array** sensing mechanism. The forward operator applies, in order: D · scalp electrode array operator; L · inverse source localization operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered 4D cortical current is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 25); electrode_contact dominates the stability cliff; muscle_artifact and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → D · scalp electrode array → L · inverse source localization → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.inverse_source_localization` `D.scalp_electrode_array` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.scalp_electrode_array` | D · scalp electrode array operator | | `L.inverse_source_localization` | L · inverse source localization operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Scalp-electrode electric field brain imaging | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 4D_cortical_current | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered 4D cortical current is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 25); electrode_contact dominates the stability cliff; muscle_artifact and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `eeg` · **Forward operator:** `eeg_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N time | — | 10000 | | Snr db | dB | 15 | | N channels | — | 64 | | Sampling hz | Hz | 1000 | | Muscle artifact | — | 0 | | Electrode contact | — | 1 | | Volume conduction | — | 0.3 | | Reference electrode bias | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N time | — | 1000 – 1000000 | | Snr db | dB | 0.0 – 30.0 | | N channels | — | 8 – 256 | | Sampling hz | Hz | 100 – 10000 | | Muscle artifact | — | 0.0 – 0.5 | | Electrode contact | — | 0.3 – 1.0 | | Volume conduction | — | 0.1 – 0.5 | | Reference electrode bias | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 13.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x99f5eb1849b47675ea4148b13a605712b7c71b9e046b7c1e53f8bfd267c99b90` - **Chain tx hash:** `0x8b2aa5074dcb57afd17a9dcee416c16351090c1fbdaeab45e79b9624ad24a803` - **Chain block:** `41553386` --- ## File Mapping This bundle consists of: `L1-068.md`, `L1-068.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-068.md` | Source of truth — edit this | Human or LLM | | `L1-068.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 `L1-068`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-068.md).
Regenerate L1-068.json so every field matches the Markdown.
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L2-068-001 Electroencephalography (EEG) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_hash": "0x99f5eb1849b47675ea4148b13a605712b7c71b9e046b7c1e53f8bfd267c99b90",
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  "domain": "Medical Imaging",
  "hardness_fn": {
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    "metric": "PSNR_dB",
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    "secondary": "SSIM"
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  "physics_fingerprint": {
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    "carrier": "radio_wave",
    "difficulty_delta": 5,
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    "integration_axis": "temporal",
    "noise_model": "gaussian",
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      "L.inverse_source_localization",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "eeg_scalp_array",
    "solution_space": "4D_cortical_current",
    "sub_domain": "Scalp-electrode electric field brain imaging",
    "title": "Electroencephalography (EEG)"
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      "reference_electrode_bias",
      "electrode_contact",
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      "volume_conduction",
      "reference_electrode_bias"
    ],
    "allowed_problem_classes": [
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      "input_format": "measurement_only",
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      ],
      "SNR_dB": [
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      ],
      "electrode_contact": [
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        1.0
      ],
      "muscle_artifact": [
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        0.5
      ],
      "reference_electrode_bias": [
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        0.3
      ],
      "sampling_Hz": [
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        10000
      ],
      "volume_conduction": [
        0.1,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Scalp-electrode electric field brain imaging",
  "title": "Electroencephalography (EEG)"
}

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