L1 ⚛ L1-052 ⊙ Testnet

Brachytherapy Dose Imaging

Medical Imaging · Sealed-source close-range radiotherapy dose

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⬇ L1-052.md

# ⚛ L1 Principle — Brachytherapy Dose Imaging **ID:** `L1-052` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Sealed-source close-range radiotherapy dose* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D dose distribution > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553386 --- ## 🧠 1. Introduction **Brachytherapy Dose Imaging** is a **linear inverse problem** whose unknown lives in **3D dose distribution** space, within the **Sealed-source close-range radiotherapy dose** sub-domain of **Medical Imaging**. Measurements consist of photons collected by an optical detector via a **brachytherapy dose** sensing mechanism. The forward operator applies, in order: L · sealed gamma source operator; L · inverse square decay operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Existence of the recovered 3D dose distribution 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 ~= 10); source_position_error dominates the stability cliff; tissue_heterogeneity 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 · sealed gamma source → L · inverse square decay → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.inverse_square_decay` `L.sealed_gamma_source` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.sealed_gamma_source` | L · sealed gamma source operator | | `L.inverse_square_decay` | L · inverse square decay operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Sealed-source close-range radiotherapy dose | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 3D_dose_distribution | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3.2 | ## 📡 4. Measurement Model Existence of the recovered 3D dose distribution 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 ~= 10); source_position_error dominates the stability cliff; tissue_heterogeneity 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:** `brachytherapy` · **Forward operator:** `brachytherapy_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 128 | | Snr db | dB | 30 | | N sources | — | 20 | | Applicator motion | — | 0 | | Tissue heterogeneity | — | 0.05 | | Source position error | — | 0 | | Inter source shielding | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 32 – 512 | | Snr db | dB | 15.0 – 40.0 | | N sources | — | 1 – 100 | | Applicator motion | — | 0.0 – 3.0 | | Tissue heterogeneity | — | 0.0 – 0.3 | | Source position error | — | 0.0 – 3.0 | | Inter source shielding | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x2cd9e3e7a6e5c0552a4dff75b2e087f4c04267894a9e40b85c5a655c075f2695` - **Chain tx hash:** `0xcb383f9ba0b815746310aeba284073d60ee5f5a8d89ee7d7dc601b8442600839` - **Chain block:** `41553386` --- ## File Mapping This bundle consists of: `L1-052.md`, `L1-052.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-052.md` | Source of truth — edit this | Human or LLM | | `L1-052.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 `L1-052`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-052.md).
Regenerate L1-052.json so every field matches the Markdown.
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L2-052-001 Brachytherapy Dose Imaging Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553386,
  "chain_hash": "0x2cd9e3e7a6e5c0552a4dff75b2e087f4c04267894a9e40b85c5a655c075f2695",
  "chain_tx_hash": "0xcb383f9ba0b815746310aeba284073d60ee5f5a8d89ee7d7dc601b8442600839",
  "domain": "Medical Imaging",
  "hardness_fn": {
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    "kappa": 200,
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    "type": "epsilon_fn"
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    "regime": "Existence of the recovered 3D dose distribution 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 ~= 10); source_position_error dominates the stability cliff; tissue_heterogeneity 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": {
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    "difficulty_delta": 3,
    "domain": "Medical Imaging",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
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      "L.inverse_square_decay",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "brachytherapy_dose",
    "solution_space": "3D_dose_distribution",
    "sub_domain": "Sealed-source close-range radiotherapy dose",
    "title": "Brachytherapy Dose Imaging"
  },
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      "inter_source_shielding",
      "applicator_motion",
      "source_position_error",
      "tissue_heterogeneity",
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      "applicator_motion"
    ],
    "allowed_problem_classes": [
      "brachytherapy"
    ],
    "center_spec": {
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      "forward_operator": "brachytherapy_forward",
      "input_format": "measurement_only",
      "omega": {
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        "source_position_error": 0.0,
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      ]
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      "N_sources": [
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        100
      ],
      "SNR_dB": [
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        40.0
      ],
      "W": 128,
      "Z": [
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        512
      ],
      "applicator_motion": [
        0.0,
        3.0
      ],
      "inter_source_shielding": [
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        0.3
      ],
      "source_position_error": [
        0.0,
        3.0
      ],
      "tissue_heterogeneity": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Sealed-source close-range radiotherapy dose",
  "title": "Brachytherapy Dose Imaging"
}

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