L1 ⚛ L1-044 ⊙ Testnet

Magnetic Resonance Spectroscopy (MRS)

Medical Imaging · Proton chemical-shift tissue metabolite spectroscopy

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⬇ L1-044.md

# ⚛ L1 Principle — Magnetic Resonance Spectroscopy (MRS) **ID:** `L1-044` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Proton chemical-shift tissue metabolite spectroscopy* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 1D metabolite spectrum > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553385 --- ## 🧠 1. Introduction **Magnetic Resonance Spectroscopy (MRS)** is a **linear inverse problem** whose unknown lives in **1D metabolite spectrum** space, within the **Proton chemical-shift tissue metabolite spectroscopy** sub-domain of **Medical Imaging**. Measurements consist of radio-frequency electromagnetic waves via a **mrs chemical shift** sensing mechanism. The forward operator applies, in order: Bloch-equation tip of the magnetisation vector; L · chemical shift encode operator; D · fid acquisition operator; detector sums all spectral bands. Observations are corrupted by additive Gaussian noise. Existence of the recovered 1D metabolite spectrum 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 ~= 15); B0_shim dominates the stability cliff; water_suppression_imperfection 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** → RF excitation pulse → L · chemical shift encode → D · fid acquisition → Spectral integration → **y** (detector). ``` y = Σ_λ `D.fid_acquisition` `L.chemical_shift_encode` B₁(t) x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.rf_excitation` | Bloch-equation tip of the magnetisation vector | | `L.chemical_shift_encode` | L · chemical shift encode operator | | `D.fid_acquisition` | D · fid acquisition operator | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Proton chemical-shift tissue metabolite spectroscopy | | Carrier | radio_wave | | Problem class | linear_inverse | | Solution space | 1D_metabolite_spectrum | | Noise model | gaussian | | Integration axis | spectral | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered 1D metabolite spectrum 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 ~= 15); B0_shim dominates the stability cliff; water_suppression_imperfection 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:** `mrs` · **Forward operator:** `mrs_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N avg | — | 128 | | Te ms | ms | 30 | | Tr ms | ms | 2000 | | Snr db | dB | 10 | | B0 shim | — | 0 | | N samples | — | 2048 | | Lipid contamination | — | 0 | | Water suppression imperfection | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N avg | — | 16 – 2048 | | Te ms | ms | 10 – 500 | | Tr ms | ms | 500 – 10000 | | Snr db | dB | 0.0 – 30.0 | | B0 shim | — | 0.0 – 0.2 | | N samples | — | 512 – 8192 | | Short t2 signals | — | 0.0 – 0.3 | | Lipid contamination | — | 0.0 – 0.5 | | Water suppression imperfection | — | 0.0 – 0.3 | ## 🎯 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 = `300` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x506214b0a18b9f43f347ba6be778bb17c7785b21a7713d1f5000414d866d8a05` - **Chain tx hash:** `0x1067900ea6b77824cf468127217f947d62d5cea6c28c50e527ea15391a09ab7f` - **Chain block:** `41553385` --- ## File Mapping This bundle consists of: `L1-044.md`, `L1-044.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-044.md` | Source of truth — edit this | Human or LLM | | `L1-044.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 `L1-044`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-044.md).
Regenerate L1-044.json so every field matches the Markdown.
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L2-044-001 Magnetic Resonance Spectroscopy (MRS) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553385,
  "chain_hash": "0x506214b0a18b9f43f347ba6be778bb17c7785b21a7713d1f5000414d866d8a05",
  "chain_tx_hash": "0x1067900ea6b77824cf468127217f947d62d5cea6c28c50e527ea15391a09ab7f",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 5,
    "kappa": 300,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 1D metabolite spectrum 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 ~= 15); B0_shim dominates the stability cliff; water_suppression_imperfection 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.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "radio_wave",
    "difficulty_delta": 5,
    "domain": "Medical Imaging",
    "integration_axis": "spectral",
    "noise_model": "gaussian",
    "primitives": [
      "L.rf_excitation",
      "L.chemical_shift_encode",
      "D.fid_acquisition",
      "int.spectral"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "mrs_chemical_shift",
    "solution_space": "1D_metabolite_spectrum",
    "sub_domain": "Proton chemical-shift tissue metabolite spectroscopy",
    "title": "Magnetic Resonance Spectroscopy (MRS)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "mrs_forward"
    ],
    "allowed_omega_dimensions": [
      "N_samples",
      "TR_ms",
      "TE_ms",
      "N_avg",
      "SNR_dB",
      "B0_shim",
      "water_suppression_imperfection",
      "lipid_contamination",
      "B0_shim",
      "water_suppression_imperfection",
      "lipid_contamination",
      "short_T2_signals"
    ],
    "allowed_problem_classes": [
      "mrs"
    ],
    "center_spec": {
      "epsilon_fn_center": "18.0",
      "forward_operator": "mrs_forward",
      "input_format": "measurement_only",
      "omega": {
        "B0_shim": 0.0,
        "N_avg": 128,
        "N_samples": 2048,
        "SNR_dB": 10,
        "TE_ms": 30,
        "TR_ms": 2000,
        "lipid_contamination": 0.0,
        "water_suppression_imperfection": 0.0
      },
      "problem_class": "mrs"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        45.0
      ]
    },
    "omega_bounds": {
      "B0_shim": [
        0.0,
        0.2
      ],
      "N_avg": [
        16,
        2048
      ],
      "N_samples": [
        512,
        8192
      ],
      "SNR_dB": [
        0.0,
        30.0
      ],
      "TE_ms": [
        10,
        500
      ],
      "TR_ms": [
        500,
        10000
      ],
      "lipid_contamination": [
        0.0,
        0.5
      ],
      "short_T2_signals": [
        0.0,
        0.3
      ],
      "water_suppression_imperfection": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Proton chemical-shift tissue metabolite spectroscopy",
  "title": "Magnetic Resonance Spectroscopy (MRS)"
}

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