L1 ⚛ L1-407 ⊙ Testnet

Lotka-Volterra Predator-Prey Dynamics

Computational Biology · Population dynamics

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⬇ L1-407.md

# ⚛ L1 Principle — Lotka-Volterra Predator-Prey Dynamics **ID:** `L1-407` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Population dynamics* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** LV parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** lognormal > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555218 --- ## 🧠 1. Introduction **Lotka-Volterra Predator-Prey Dynamics** is a **parameter-estimation problem** whose unknown lives in **LV parameter vector** space, within the **Population dynamics** sub-domain of **Computational Biology**. Measurements consist of N/A via a **population census survey** sensing mechanism. The forward operator applies, in order: time evolution of the state; O · nls · population fit operator; S · continuation · bifurcation LV operator. Observations are corrupted by log-normal multiplicative noise. Existence of the recovered LV_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); stochastic_demographic_noise 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 · population fit → S · continuation · bifurcation LV → **y** (detector). ``` y = `S.continuation.bifurcation_LV` `O.nls.population_fit` ∂_t x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `O.nls.population_fit` | O · nls · population fit operator | | `S.continuation.bifurcation_LV` | S · continuation · bifurcation lv operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Population dynamics | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | LV_parameter_vector | | Noise model | lognormal | | Integration axis | time | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered LV_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); stochastic_demographic_noise dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | population_trajectory_RMSE_log | | Secondary | period_amplitude_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `population_census_survey` **Center point:** | Parameter | Unit | Value | |---|---|---| | Period yr | — | 5 | | N observations | — | 50 | | Amplitude h max | — | 1000 | | Observation noise log sigma | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Period yr | — | 0.5 – 50 | | N observations | — | 10 – 300 | | Amplitude h max | — | 10 – 100000 | | Observation noise log sigma | — | 0.01 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.10 population_trajectory_RMSE_log | Metric | Range | |---|---| | Population trajectory rmse log | 0.01 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **population_trajectory_RMSE_log**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x2ddd2c04866e2278ad4c71739cb7b04448bd5d90fd7d2e384f238157a7bfd067` - **Chain tx hash:** `0xfa70a63fa21039d7210901a3a16e7df7bfa2d224f561aac8c85797e637a10da7` - **Chain block:** `41555218` --- ## File Mapping This bundle consists of: `L1-407.md`, `L1-407.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-407.md` | Source of truth — edit this | Human or LLM | | `L1-407.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 `L1-407`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "chain_hash": "0x2ddd2c04866e2278ad4c71739cb7b04448bd5d90fd7d2e384f238157a7bfd067",
  "chain_tx_hash": "0xfa70a63fa21039d7210901a3a16e7df7bfa2d224f561aac8c85797e637a10da7",
  "domain": "Computational Biology",
  "hardness_fn": {
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    "kappa": 500,
    "metric": "population_trajectory_RMSE_log",
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    "regime": "Existence of the recovered LV_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); stochastic_demographic_noise dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor.",
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  },
  "physics_fingerprint": {
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    "integration_axis": "time",
    "noise_model": "lognormal",
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      "S.continuation.bifurcation_LV"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "population_census_survey",
    "solution_space": "LV_parameter_vector",
    "sub_domain": "Population dynamics",
    "title": "Lotka-Volterra Predator-Prey Dynamics"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "period_yr",
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    "allowed_problem_classes": [
      "parameter_estimation"
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    "center_spec": {
      "epsilon_fn_center": "0.10 population_trajectory_RMSE_log",
      "forward_operator": "population_census_survey",
      "input_format": "measurement_only",
      "omega": {
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        "amplitude_H_max": 1000,
        "observation_noise_log_sigma": 0.1,
        "period_yr": 5
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    "epsilon_bounds": {
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        0.5
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    },
    "omega_bounds": {
      "N_observations": [
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        300
      ],
      "amplitude_H_max": [
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        100000
      ],
      "observation_noise_log_sigma": [
        0.01,
        1.0
      ],
      "period_yr": [
        0.5,
        50
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Population dynamics",
  "title": "Lotka-Volterra Predator-Prey Dynamics"
}

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