L1 ⚛ L1-500 ⊙ Testnet

Optimal Experimental Design

Optimization · Information-theoretic design

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⬇ L1-500.md

# ⚛ L1 Principle — Optimal Experimental Design **ID:** `L1-500` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Optimization — *Information-theoretic design* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** experiment design vector > **📡 Carrier:** N/A · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555318 --- ## 🧠 1. Introduction **Optimal Experimental Design** is a **nonlinear inverse problem** whose unknown lives in **experiment design vector** space, within the **Information-theoretic design** sub-domain of **Optimization**. Measurements consist of N/A via a **fisher information optimization** sensing mechanism. The forward operator applies, in order: adds a prior term that biases the solution toward smoothness/sparsity; O · d optimality · criterion operator; S · gradient · update operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered experiment_design_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); prior_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → O · d optimality · criterion → S · gradient · update → **y** (detector). ``` y = `S.gradient.update` `O.d_optimality.criterion` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `O.d_optimality.criterion` | O · d optimality · criterion operator | | `S.gradient.update` | S · gradient · update operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Optimization | | Sub domain | Information-theoretic design | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | experiment_design_vector | | Noise model | gaussian | | Integration axis | parameter_space | | Difficulty delta | 5 | | L dag | 2.8 | ## 📡 4. Measurement Model Existence of the recovered experiment_design_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); prior_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | D_optimality_criterion | | Secondary | parameter_estimation_RMSE | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `fisher_information_optimization` **Center point:** | Parameter | Unit | Value | |---|---|---| | P parameters | — | 5 | | Sigma2 noise | — | 0.1 | | N experiments | — | 20 | | Nonlinearity level | — | 0.5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | P parameters | — | 2 – 20 | | Sigma2 noise | — | 0.01 – 1.0 | | N experiments | — | 5 – 100 | | Nonlinearity level | — | 0.1 – 2.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.80 D_optimality_criterion | Metric | Range | |---|---| | D optimality criterion | 0.3 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **D_optimality_criterion**, with κ = `1000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe56535577bd0cb33edad3f534ebd44c2540e17ec7040920c32b7456bfe695242` - **Chain tx hash:** `0xd0e0e30d2fee837aedd2225cb2239be38be2f079c300dec27c8e15a0eec5a7f0` - **Chain block:** `41555318` --- ## File Mapping This bundle consists of: `L1-500.md`, `L1-500.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-500.md` | Source of truth — edit this | Human or LLM | | `L1-500.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 `L1-500`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "status": "testnet",
  "sub_domain": "Information-theoretic design",
  "title": "Optimal Experimental Design"
}

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