L1 ⚛ L1-364 ⊙ Testnet

N-body Gravitational Simulation

Astrophysics · Orbital dynamics

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⬇ L1-364.md

# ⚛ L1 Principle — N-body Gravitational Simulation **ID:** `L1-364` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Orbital dynamics* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 6N phase space > **📡 Carrier:** N/A · **🌫 Noise:** observation gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555176 --- ## 🧠 1. Introduction **N-body Gravitational Simulation** is a **parameter-estimation problem** whose unknown lives in **6N phase space** space, within the **Orbital dynamics** sub-domain of **Astrophysics**. Measurements consist of N/A via a **gravitational force summation** sensing mechanism. The forward operator applies, in order: F · gravity · nbody operator; S · tree · barnes hut operator; O · leapfrog · integrator operator. Observations are corrupted by observation gaussian. Existence of the recovered 6N_phase_space 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 ~= 500); initial_condition_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → F · gravity · nbody → S · tree · barnes hut → O · leapfrog · integrator → **y** (detector). ``` y = `O.leapfrog.integrator` `S.tree.barnes_hut` `F.gravity.nbody` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `F.gravity.nbody` | F · gravity · nbody operator | | `S.tree.barnes_hut` | S · tree · barnes hut operator | | `O.leapfrog.integrator` | O · leapfrog · integrator operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Orbital dynamics | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | 6N_phase_space | | Noise model | observation_gaussian | | Integration axis | time | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered 6N_phase_space 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 ~= 500); initial_condition_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | orbital_energy_conservation_relative | | Secondary | position_RMSE_AU | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `gravitational_force_summation` **Center point:** | Parameter | Unit | Value | |---|---|---| | Dt yr | — | 0.01 | | N bodies | — | 100 | | T end yr | — | 100 | | Softening au | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Dt yr | — | 0.001 – 0.1 | | N bodies | — | 10 – 10000 | | T end yr | — | 10 – 10000 | | Softening au | — | 0.01 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1e-6 orbital_energy_conservation_relative | Metric | Range | |---|---| | Orbital energy conservation relative | 1e-10 – 0.001 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **orbital_energy_conservation_relative**, with κ = `100000.0` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x63131da3973889de4d4c05e7deab5eac1b2dad7dcb58980a385f24ff7b1e1bd5` - **Chain tx hash:** `0x7da15624c8618e308950b5083db53d3625dac3b115d254c571f4138589bd2402` - **Chain block:** `41555176` --- ## File Mapping This bundle consists of: `L1-364.md`, `L1-364.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-364.md` | Source of truth — edit this | Human or LLM | | `L1-364.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 `L1-364`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "artifact_id": "L1-364",
  "chain_block": 41555176,
  "chain_hash": "0x63131da3973889de4d4c05e7deab5eac1b2dad7dcb58980a385f24ff7b1e1bd5",
  "chain_tx_hash": "0x7da15624c8618e308950b5083db53d3625dac3b115d254c571f4138589bd2402",
  "domain": "Astrophysics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 100000.0,
    "metric": "orbital_energy_conservation_relative",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "orbital_energy_conservation_relative",
    "regime": "Existence of the recovered 6N_phase_space 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 ~= 500); initial_condition_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.",
    "secondary": "position_RMSE_AU"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Astrophysics",
    "integration_axis": "time",
    "noise_model": "observation_gaussian",
    "primitives": [
      "F.gravity.nbody",
      "S.tree.barnes_hut",
      "O.leapfrog.integrator"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "gravitational_force_summation",
    "solution_space": "6N_phase_space",
    "sub_domain": "Orbital dynamics",
    "title": "N-body Gravitational Simulation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "gravitational_force_summation"
    ],
    "allowed_omega_dimensions": [
      "N_bodies",
      "dt_yr",
      "softening_AU",
      "t_end_yr"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "1e-6 orbital_energy_conservation_relative",
      "forward_operator": "gravitational_force_summation",
      "input_format": "measurement_only",
      "omega": {
        "N_bodies": 100,
        "dt_yr": 0.01,
        "softening_AU": 0.1,
        "t_end_yr": 100.0
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "orbital_energy_conservation_relative": [
        1e-10,
        0.001
      ]
    },
    "omega_bounds": {
      "N_bodies": [
        10,
        10000
      ],
      "dt_yr": [
        0.001,
        0.1
      ],
      "softening_AU": [
        0.01,
        1.0
      ],
      "t_end_yr": [
        10,
        10000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Orbital dynamics",
  "title": "N-body Gravitational Simulation"
}

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