L1 ⚛ L1-410 ⊙ Testnet

Tumor Growth Model Inversion

Computational Biology · Cancer modeling

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⬇ L1-410.md

# ⚛ L1 Principle — Tumor Growth Model Inversion **ID:** `L1-410` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Cancer modeling* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** tumor growth parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** lognormal > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555219 --- ## 🧠 1. Introduction **Tumor Growth Model Inversion** is a **parameter-estimation problem** whose unknown lives in **tumor growth parameter vector** space, within the **Cancer modeling** sub-domain of **Computational Biology**. Measurements consist of N/A via a **tumor volume imaging** sensing mechanism. The forward operator applies, in order: time evolution of the state; O · nls · tumor fit operator; S · bootstrap · uncertainty tumor operator. Observations are corrupted by log-normal multiplicative noise. Existence of the recovered tumor_growth_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); imaging_noise_percent dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Time derivative → O · nls · tumor fit → S · bootstrap · uncertainty tumor → **y** (detector). ``` y = `S.bootstrap.uncertainty_tumor` `O.nls.tumor_fit` ∂_t x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `O.nls.tumor_fit` | O · nls · tumor fit operator | | `S.bootstrap.uncertainty_tumor` | S · bootstrap · uncertainty tumor operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Cancer modeling | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | tumor_growth_parameter_vector | | Noise model | lognormal | | Integration axis | time | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered tumor_growth_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); imaging_noise_percent dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | volume_prediction_RMSE_percent | | Secondary | time_to_progression_error_days | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `tumor_volume_imaging` **Center point:** | Parameter | Unit | Value | |---|---|---| | Tumor volume mm3 | — | 1000 | | N imaging timepoints | — | 8 | | Imaging noise percent | — | 10 | | Growth rate lambda day | — | 0.05 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Tumor volume mm3 | — | 10 – 100000 | | N imaging timepoints | — | 3 – 50 | | Imaging noise percent | — | 2 – 50 | | Growth rate lambda day | — | 0.001 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 15 volume_prediction_RMSE_percent | Metric | Range | |---|---| | Volume prediction rmse percent | 2 – 50 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **volume_prediction_RMSE_percent**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x620e8df375d9196c6a63965210a58ca98b17a9b9ce5db9fec21c68b1431358f6` - **Chain tx hash:** `0x1778f33dfa3227c2f3e71c47c070508f97e6e04a38bcc50774df1a2470f4e149` - **Chain block:** `41555219` --- ## File Mapping This bundle consists of: `L1-410.md`, `L1-410.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-410.md` | Source of truth — edit this | Human or LLM | | `L1-410.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 `L1-410`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-410-001 Tumor Growth Model Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "domain": "Computational Biology",
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    "integration_axis": "time",
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    "sensing_mechanism": "tumor_volume_imaging",
    "solution_space": "tumor_growth_parameter_vector",
    "sub_domain": "Cancer modeling",
    "title": "Tumor Growth Model Inversion"
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      "growth_rate_lambda_day",
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      "input_format": "measurement_only",
      "omega": {
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        "growth_rate_lambda_day": 0.05,
        "imaging_noise_percent": 10,
        "tumor_volume_mm3": 1000
      },
      "problem_class": "parameter_estimation"
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        50
      ],
      "growth_rate_lambda_day": [
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        0.5
      ],
      "imaging_noise_percent": [
        2,
        50
      ],
      "tumor_volume_mm3": [
        10,
        100000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Cancer modeling",
  "title": "Tumor Growth Model Inversion"
}

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