aprender-simulate 0.30.0

Unified Simulation Engine for the Sovereign AI Stack
Documentation 
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# Harmonic Oscillator Verification Experiment
# EDD-compliant experiment specification

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

metadata:
  name: "Harmonic Oscillator Verification"
  description: |
    Verify Störmer-Verlet integrator against analytical solution
    for simple harmonic oscillator. EDD compliance test.
  author: "PAIML Engineering"
  created: "2025-12-11"
  tags: ["physics", "verification", "edd", "harmonic", "symplectic"]

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

hypothesis:
  null_hypothesis: |
    H₀: The Störmer-Verlet integrator produces solutions that deviate
    significantly from the analytical solution x(t) = A·cos(ωt + φ)
    for the simple harmonic oscillator.
  alternative_hypothesis: |
    H₁: Numerical solution matches analytical within tolerance ε = 1e-6
    over 100 periods.
  expected_outcome: "reject"  # We expect H₀ to be FALSIFIED

reproducibility:
  seed: 42
  ieee_strict: true
  platforms:
    - "x86_64-unknown-linux-gnu"
    - "aarch64-apple-darwin"
    - "wasm32-unknown-unknown"

initial_conditions:
  state:
    x: 1.0      # Initial displacement (m)
    v: 0.0      # Initial velocity (m/s)

  parameters:
    omega: 6.283185307  # 2π rad/s (1 Hz)

  derived:
    amplitude: "sqrt(x^2 + (v/omega)^2)"
    phase: "atan2(-v/omega, x)"
    total_energy: "0.5 * omega^2 * amplitude^2"

simulation:
  time:
    start: 0.0
    end: 100.0        # 100 periods at ω = 2π
    dt: 0.001         # 1000 steps per period
    units: "s"

  integrator:
    type: "stormer_verlet"
    adaptive: false

  output:
    sample_interval: 10
    format: "parquet"
    quantities:
      - name: "t"
        description: "Simulation time"
      - name: "x"
        description: "Displacement"
      - name: "v"
        description: "Velocity"
      - name: "E"
        description: "Total energy"
      - name: "x_analytical"
        description: "Analytical solution"
      - name: "error"
        description: "Numerical - Analytical"

falsification:
  import_from_emc: true
  criteria:
    - id: "HO-FC-001"
      name: "Maximum error bound"
      condition: "max(abs(error)) < tolerance"
      tolerance: 1e-6
      severity: "critical"

    - id: "HO-FC-002"
      name: "Energy conservation"
      condition: "max(abs(E - E_initial)) / E_initial < tolerance"
      tolerance: 1e-10
      severity: "critical"

    - id: "HO-FC-003"
      name: "Period accuracy"
      condition: "|T_measured - T_expected| / T_expected < tolerance"
      tolerance: 1e-6
      severity: "major"

  jidoka:
    enabled: true
    stop_on_severity: "critical"

verification:
  analytical_solution:
    expression: "amplitude * cos(omega * t + phase)"

  metrics:
    - name: "L2_error"
      type: "l2_norm"
      expected: "< 1e-6"

    - name: "Linf_error"
      type: "linf_norm"
      expected: "< 1e-6"

    - name: "energy_drift"
      type: "conservation"
      quantity: "E"
      expected: "< 1e-10"

  convergence:
    enabled: true
    dt_sequence: [0.01, 0.005, 0.0025, 0.00125]
    expected_order: 2
    tolerance: 0.1

statistics:
  bootstrap:
    n_samples: 1000
    confidence_level: 0.95

reporting:
  format: "markdown"
  output: "reports/harmonic_oscillator_verification.md"
  include:
    - "hypothesis_test_results"
    - "convergence_plot"
    - "energy_conservation_plot"
    - "error_distribution"