L1 ⚛ L1-407 ⊙ Testnet

Lotka-Volterra Predator-Prey Dynamics

Computational Biology · Population dynamics

⬇ Download bundle 🚀 Submit to mainnet — earn 5% royalty

🎁 Contribute & earn PWM

Improve L1-407 — submit with or without uploading. Accepted submissions earn the 1/16 modify share of A(t).

✨ Submit without uploading free check · 1×

One click — no files, no typing. We submit a check of L1-407 for you; it goes through review and earns the 1/16 share once. One free no-upload Principle per account.

You'll be asked to log in first — then it's one click, no files.

⬆ Or submit by uploading your files

Upload your .md + .json as a modification of L1-407. Unlimited.

🛠 Helper: build your files in ChatGPT / Gemini / Claude

Layer template

⬇ principle.md ⬇ principle.json

Fork L1-407

⬇ L1-407.md ⬇ L1-407.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-407 (Lotka-Volterra Predator-Prey Dynamics) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-407.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-407.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.continuation.bifurcation_LV` `O.nls.population_fit` ∂_t x

world state x (LV parameter vector)

→

Time derivative ∂_t

→

O · nls · population fit `O.nls.population_fit`

→

S · continuation · bifurcation LV `S.continuation.bifurcation_LV`

→

observation y (N/A detector)

Noise: log-normal multiplicative noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ 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._

💬

Ask the PWM AI agent AI

Ask about this Lotka-Volterra Predator-Prey Dynamics — or how to improve it & earn PWM

Free to search; log in to chat with the agent & earn PWM. How it works ↗

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Digital Twin 1 child ▾

L2-407-001 Lotka-Volterra Predator-Prey Dynamics — Nominal + Mismatch Specs

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-407",
  "chain_block": 41555218,
  "chain_hash": "0x2ddd2c04866e2278ad4c71739cb7b04448bd5d90fd7d2e384f238157a7bfd067",
  "chain_tx_hash": "0xfa70a63fa21039d7210901a3a16e7df7bfa2d224f561aac8c85797e637a10da7",
  "domain": "Computational Biology",
  "hardness_fn": {
    "delta": 3,
    "kappa": 500,
    "metric": "population_trajectory_RMSE_log",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "population_trajectory_RMSE_log",
    "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.",
    "secondary": "period_amplitude_error"
  },
  "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.population_fit",
      "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": {
    "allowed_forward_operators": [
      "population_census_survey"
    ],
    "allowed_omega_dimensions": [
      "N_observations",
      "amplitude_H_max",
      "period_yr",
      "observation_noise_log_sigma"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.10 population_trajectory_RMSE_log",
      "forward_operator": "population_census_survey",
      "input_format": "measurement_only",
      "omega": {
        "N_observations": 50,
        "amplitude_H_max": 1000,
        "observation_noise_log_sigma": 0.1,
        "period_yr": 5
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "population_trajectory_RMSE_log": [
        0.01,
        0.5
      ]
    },
    "omega_bounds": {
      "N_observations": [
        10,
        300
      ],
      "amplitude_H_max": [
        10,
        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"
}

🎁

Earn PWM by promoting this to mainnet

• PWM emission on accept — your share of A(t) (1/16 modify · 3/16 new)
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Go to submit ↑

How: use the “Contribute & earn PWM” panel at the top — either Submit without uploading (one click) or upload your files. Then the review runs and, on accept, it’s promoted to mainnet.