L1 ⚛ L1-404 ⊙ Testnet

Pharmacodynamics Dose-Response Inversion

Computational Biology · Pharmacodynamics

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⬇ L1-404.md

# ⚛ L1 Principle — Pharmacodynamics Dose-Response Inversion **ID:** `L1-404` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Pharmacodynamics* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** PD parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** lognormal > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555218 --- ## 🧠 1. Introduction **Pharmacodynamics Dose-Response Inversion** is a **parameter-estimation problem** whose unknown lives in **PD parameter vector** space, within the **Pharmacodynamics** sub-domain of **Computational Biology**. Measurements consist of N/A via a **effect concentration measurement** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; O · nls · pd fit operator; S · bayesian · pd posterior operator. Observations are corrupted by log-normal multiplicative noise. Existence of the recovered PD_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); inter_individual_variability_PD 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** → Pointwise nonlinearity → O · nls · pd fit → S · bayesian · pd posterior → **y** (detector). ``` y = `S.bayesian.pd_posterior` `O.nls.pd_fit` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `O.nls.pd_fit` | O · nls · pd fit operator | | `S.bayesian.pd_posterior` | S · bayesian · pd posterior operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Pharmacodynamics | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | PD_parameter_vector | | Noise model | lognormal | | Integration axis | concentration_space | | Difficulty delta | 3 | | L dag | 2 | ## 📡 4. Measurement Model Existence of the recovered PD_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); inter_individual_variability_PD dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | EC50_RMSE_fold | | Secondary | dose_response_fit_RMSE | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `effect_concentration_measurement` **Center point:** | Parameter | Unit | Value | |---|---|---| | N hill | — | 1.5 | | Ec50 nm | nm | 100 | | N dose groups | — | 6 | | Noise cv percent | — | 20 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N hill | — | 0.5 – 5.0 | | Ec50 nm | nm | 0.1 – 1000000.0 | | N dose groups | — | 3 – 20 | | Noise cv percent | — | 5 – 100 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.5 EC50_RMSE_fold | Metric | Range | |---|---| | Ec50 rmse fold | 1.05 – 5.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **EC50_RMSE_fold**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xee72c89da66e97ecd73154e158d753de9735dce17b199c8d1c2705bf9f7b2306` - **Chain tx hash:** `0xf1404d5483048628ad972f47ef4f4a0777d7ae50c5149a0db8d6a701d545f40d` - **Chain block:** `41555218` --- ## File Mapping This bundle consists of: `L1-404.md`, `L1-404.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-404.md` | Source of truth — edit this | Human or LLM | | `L1-404.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 `L1-404`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-404-001 Pharmacodynamics Dose-Response Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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    "sub_domain": "Pharmacodynamics",
    "title": "Pharmacodynamics Dose-Response Inversion"
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        5.0
      ],
      "noise_CV_percent": [
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        100
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Pharmacodynamics",
  "title": "Pharmacodynamics Dose-Response Inversion"
}

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