L1 ⚛ L1-397 ⊙ Testnet

FitzHugh-Nagumo Excitability Model

Computational Biology · Neural excitability

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⬇ L1-397.md

# ⚛ L1 Principle — FitzHugh-Nagumo Excitability Model **ID:** `L1-397` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Neural excitability* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** FHN parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555199 --- ## 🧠 1. Introduction **FitzHugh-Nagumo Excitability Model** is a **parameter-estimation problem** whose unknown lives in **FHN parameter vector** space, within the **Neural excitability** sub-domain of **Computational Biology**. Measurements consist of N/A via a **action potential recording** sensing mechanism. The forward operator applies, in order: time evolution of the state; O · chi2 · phase portrait operator; S · continuation · bifurcation operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered FHN_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); noise_amplitude 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** → Time derivative → O · chi2 · phase portrait → S · continuation · bifurcation → **y** (detector). ``` y = `S.continuation.bifurcation` `O.chi2.phase_portrait` ∂_t x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `O.chi2.phase_portrait` | O · chi2 · phase portrait operator | | `S.continuation.bifurcation` | S · continuation · bifurcation operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Neural excitability | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | FHN_parameter_vector | | Noise model | gaussian | | Integration axis | time | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered FHN_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); noise_amplitude dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | phase_portrait_RMSE | | Secondary | bifurcation_point_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `action_potential_recording` **Center point:** | Parameter | Unit | Value | |---|---|---| | B recovery | — | 0.8 | | A threshold | — | 0.7 | | Noise sigma | — | 0 | | Epsilon timescale | — | 0.08 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | B recovery | — | 0.5 – 1.5 | | A threshold | — | 0.5 – 1.5 | | Noise sigma | — | 0.0 – 0.5 | | Epsilon timescale | — | 0.01 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.05 phase_portrait_RMSE | Metric | Range | |---|---| | Phase portrait rmse | 0.005 – 0.3 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **phase_portrait_RMSE**, with κ = `1000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x0f0efe82f19e8d237278873f54b39dce08570a944fd6e45f0603e19bd0b77e09` - **Chain tx hash:** `0x3b1a85302d1679b27651f4b43eaa418a7328c603470d6d53948b62e99fb1717b` - **Chain block:** `41555199` --- ## File Mapping This bundle consists of: `L1-397.md`, `L1-397.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-397.md` | Source of truth — edit this | Human or LLM | | `L1-397.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 `L1-397`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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    "integration_axis": "time",
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    "solution_space": "FHN_parameter_vector",
    "sub_domain": "Neural excitability",
    "title": "FitzHugh-Nagumo Excitability Model"
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      "forward_operator": "action_potential_recording",
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    "epsilon_bounds": {
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      "noise_sigma": [
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        0.5
      ]
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Neural excitability",
  "title": "FitzHugh-Nagumo Excitability Model"
}

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