L1 ⚛ L1-402 ⊙ Testnet

Pharmacokinetics Compartment Model

Computational Biology · Drug modeling

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⬇ L1-402.md

# ⚛ L1 Principle — Pharmacokinetics Compartment Model **ID:** `L1-402` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Drug modeling* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** PK parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** lognormal > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555217 --- ## 🧠 1. Introduction **Pharmacokinetics Compartment Model** is a **parameter-estimation problem** whose unknown lives in **PK parameter vector** space, within the **Drug modeling** sub-domain of **Computational Biology**. Measurements consist of N/A via a **blood concentration sampling** sensing mechanism. The forward operator applies, in order: time evolution of the state; O · nls · pk fit operator; S · bootstrap · uncertainty PK operator. Observations are corrupted by log-normal multiplicative noise. Existence of the recovered PK_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 ~= 50); inter_individual_variability 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 · pk fit → S · bootstrap · uncertainty PK → **y** (detector). ``` y = `S.bootstrap.uncertainty_PK` `O.nls.pk_fit` ∂_t x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `O.nls.pk_fit` | O · nls · pk fit operator | | `S.bootstrap.uncertainty_PK` | S · bootstrap · uncertainty pk operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Drug modeling | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | PK_parameter_vector | | Noise model | lognormal | | Integration axis | time | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered PK_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 ~= 50); inter_individual_variability dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | AUC_RMSE_percent | | Secondary | C_max_prediction_RMSE_ng_mL | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `blood_concentration_sampling` **Center point:** | Parameter | Unit | Value | |---|---|---| | Cl l hr | — | 5 | | N subjects | — | 20 | | Bioavailability f | — | 0.8 | | N samples per subject | — | 8 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Cl l hr | — | 0.1 – 100 | | N subjects | — | 5 – 200 | | Bioavailability f | — | 0.1 – 1.0 | | N samples per subject | — | 3 – 20 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 15 AUC_RMSE_percent | Metric | Range | |---|---| | Auc rmse percent | 2 – 50 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **AUC_RMSE_percent**, with κ = `1000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x63981848850c954eeb24af46eb4277af6c41b3505e5594de532a0f6c848b573a` - **Chain tx hash:** `0x2c7fe465f6445d1a0576ecbf6f3b822d5e22e9e754ae0229bfc2aac3cf5a2875` - **Chain block:** `41555217` --- ## File Mapping This bundle consists of: `L1-402.md`, `L1-402.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-402.md` | Source of truth — edit this | Human or LLM | | `L1-402.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 `L1-402`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-402.md).
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L2-402-001 Pharmacokinetics Compartment Model — Nominal + Mismatch Specs

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📋 JSON metadata

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    "title": "Pharmacokinetics Compartment Model"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Drug modeling",
  "title": "Pharmacokinetics Compartment Model"
}

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