{
  "title": "Deterministic timebase benchmark and separate spiral geometry",
  "status": "Reproduced twelve synthetic tone calculations; no hardware, noise source or recording medium",
  "rows": {
    "tone_cases": 12,
    "spiral": 1602
  },
  "parameters": {
    "sampling_Hz": 48000,
    "duration_s": 2,
    "tone_amplitude": 0.8,
    "tones_Hz": [
      100,
      1000,
      10000
    ],
    "scanner_turns_per_s": 2,
    "endpoint_scanner_phase_deg": [
      0,
      0.1,
      1,
      10
    ],
    "one_pole_coefficient": 0.9270509391506608,
    "coefficient_frequency_parameter_Hz": 20000,
    "discard_initial_s": 0.1,
    "spiral_start_radius_m": 0.01,
    "spiral_pitch_m_per_turn": [
      0,
      0.002
    ],
    "spiral_turns": 4
  },
  "metric_definitions": {
    "fitted_tone_signal_to_residual_dB": "10log10(mean(fit\u00b2)/mean((output-fit)\u00b2)); fit is sine/cosine at original tone frequency",
    "relative_residual_RMS_percent": "100sqrt(mean((output-fit)\u00b2)/mean(fit\u00b2))",
    "correlation": "Pearson input/output correlation, phase-sensitive and not a listening score"
  },
  "checks": {
    "all_pass": true,
    "ratio_residual_identity_max_absolute_error": 5.820766091346741e-11,
    "circle_and_spiral_radius_identity": true,
    "twelve_shared_cases": true
  },
  "limits": [
    "Scanner phase accumulates linearly over the finite track, causing deterministic time stretching; it is not random jitter.",
    "Sample positions use linear interpolation with endpoint clamping; the first 0.1 s is discarded before fitting.",
    "The 20 kHz parameter sets a discrete one-pole coefficient; it is not an exact digital -3 dB cutoff.",
    "No random noise is injected. Fitted residual includes original-frequency mismatch; zero-drift tiny residuals primarily reflect numerical precision.",
    "The two residual metrics are algebraically dependent; neither is independently measured noise or harmonic distortion.",
    "The same twelve cases support recording and scanning lessons, not two independent experiments. No hardware pass/fail rate is claimed.",
    "Spiral geometry is a separate illustration, not the physical trajectory used in the timebase simulation. No spot, optics, emulsion, servo, cross-talk or medium bandwidth is modeled."
  ]
}