L1 ⚛ L1-402 ⊙ Testnet

Pharmacokinetics Compartment Model

Computational Biology · Drug modeling

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Layer template

⬇ principle.md ⬇ principle.json

Fork L1-402

⬇ L1-402.md ⬇ L1-402.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-402 (Pharmacokinetics Compartment Model) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-402.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-402.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = `S.bootstrap.uncertainty_PK` `O.nls.pk_fit` ∂_t x

world state x (PK parameter vector)

→

Time derivative ∂_t

→

O · nls · pk fit `O.nls.pk_fit`

→

S · bootstrap · uncertainty PK `S.bootstrap.uncertainty_PK`

→

observation y (N/A detector)

Noise: log-normal multiplicative noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ 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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L2-402-001 Pharmacokinetics Compartment Model — Nominal + Mismatch Specs

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📋 JSON metadata

{
  "artifact_id": "L1-402",
  "chain_block": 41555217,
  "chain_hash": "0x63981848850c954eeb24af46eb4277af6c41b3505e5594de532a0f6c848b573a",
  "chain_tx_hash": "0x2c7fe465f6445d1a0576ecbf6f3b822d5e22e9e754ae0229bfc2aac3cf5a2875",
  "domain": "Computational Biology",
  "hardness_fn": {
    "delta": 3,
    "kappa": 1000,
    "metric": "AUC_RMSE_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "AUC_RMSE_percent",
    "regime": "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.",
    "secondary": "C_max_prediction_RMSE_ng_mL"
  },
  "physics_fingerprint": {
    "L_DAG": 2.5,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Computational Biology",
    "integration_axis": "time",
    "noise_model": "lognormal",
    "primitives": [
      "D.time",
      "O.nls.pk_fit",
      "S.bootstrap.uncertainty_PK"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "blood_concentration_sampling",
    "solution_space": "PK_parameter_vector",
    "sub_domain": "Drug modeling",
    "title": "Pharmacokinetics Compartment Model"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "blood_concentration_sampling"
    ],
    "allowed_omega_dimensions": [
      "N_subjects",
      "N_samples_per_subject",
      "CL_L_hr",
      "bioavailability_F"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "15 AUC_RMSE_percent",
      "forward_operator": "blood_concentration_sampling",
      "input_format": "measurement_only",
      "omega": {
        "CL_L_hr": 5.0,
        "N_samples_per_subject": 8,
        "N_subjects": 20,
        "bioavailability_F": 0.8
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "AUC_RMSE_percent": [
        2,
        50
      ]
    },
    "omega_bounds": {
      "CL_L_hr": [
        0.1,
        100
      ],
      "N_samples_per_subject": [
        3,
        20
      ],
      "N_subjects": [
        5,
        200
      ],
      "bioavailability_F": [
        0.1,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Drug modeling",
  "title": "Pharmacokinetics Compartment Model"
}

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