aprender-simulate 0.30.0

Unified Simulation Engine for the Sovereign AI Stack
Documentation 
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# Kepler Two-Body Problem Verification Experiment
# EDD-compliant experiment specification

experiment_version: "1.0"
experiment_id: "EXP-KEPLER-001"

metadata:
  name: "Kepler Two-Body Verification"
  description: |
    Verify orbital mechanics against analytical Kepler solution.
    Tests conservation of energy, angular momentum, and eccentricity.
  author: "PAIML Engineering"
  created: "2025-12-11"
  tags: ["physics", "verification", "kepler", "orbital", "celestial"]

equation_model_card:
  emc_ref: "physics/kepler_two_body"
  emc_version: "1.0.0"

hypothesis:
  null_hypothesis: |
    H₀: The numerical orbit deviates significantly from Kepler's laws:
    1. Orbits are not conic sections
    2. Equal areas are not swept in equal times
    3. T² is not proportional to a³
  alternative_hypothesis: |
    H₁: Numerical orbit satisfies all three Kepler laws within tolerance.
  expected_outcome: "reject"  # We expect H₀ to be FALSIFIED

reproducibility:
  seed: 299792458  # Speed of light (memorable seed)
  ieee_strict: true

initial_conditions:
  state:
    # Earth-like orbit around Sun-like star
    r: [1.496e11, 0.0, 0.0]      # 1 AU in meters
    v: [0.0, 2.978e4, 0.0]       # ~30 km/s

  parameters:
    mu: 1.32712440018e20          # GM_sun (m³/s²)

  derived:
    specific_energy: "-mu/(2*a)"
    angular_momentum: "norm(cross(r, v))"
    eccentricity: "sqrt(1 + 2*E*L^2/(mu^2))"
    semi_major_axis: "-mu/(2*E)"
    period: "2*pi*sqrt(a^3/mu)"

simulation:
  time:
    start: 0.0
    end: 3.1536e7                 # 1 year in seconds
    dt: 3600                      # 1 hour timestep
    units: "s"

  integrator:
    type: "stormer_verlet"
    adaptive: false

  output:
    sample_interval: 24  # Daily samples
    format: "parquet"
    quantities:
      - name: "t"
      - name: "r"
        description: "Position vector"
      - name: "v"
        description: "Velocity vector"
      - name: "E"
        description: "Specific orbital energy"
      - name: "L"
        description: "Angular momentum magnitude"
      - name: "e"
        description: "Eccentricity"
      - name: "true_anomaly"
        description: "Angle in orbit"

falsification:
  import_from_emc: true
  criteria:
    - id: "KEPLER-1"
      name: "Eccentricity conservation"
      condition: "std(e) < tolerance"
      tolerance: 1e-10
      severity: "critical"

    - id: "KEPLER-2"
      name: "Angular momentum conservation"
      condition: "max(abs(L - L_initial)) / L_initial < tolerance"
      tolerance: 1e-12
      severity: "critical"

    - id: "KEPLER-3"
      name: "Specific energy conservation"
      condition: "max(abs(E - E_initial)) / abs(E_initial) < tolerance"
      tolerance: 1e-10
      severity: "critical"

    - id: "KEPLER-4"
      name: "Period accuracy"
      condition: "|T_measured - T_expected| / T_expected < tolerance"
      tolerance: 1e-6
      severity: "major"

  jidoka:
    enabled: true
    stop_on_severity: "critical"

verification:
  kepler_laws:
    - law: 1
      description: "Orbit is ellipse with Sun at focus"
      metric: "eccentricity_constancy"

    - law: 2
      description: "Equal areas in equal times"
      metric: "areal_velocity_constancy"

    - law: 3
      description: "T² ∝ a³"
      metric: "period_semimajor_relation"

statistics:
  alpha: 0.05

reporting:
  format: "markdown"
  output: "reports/kepler_verification.md"
  include:
    - "orbit_plot"
    - "conservation_plots"
    - "kepler_law_verification"