{
  "status": "Synthetic software checks only",
  "boundary": "Open-open acoustic cavity; ideal closed-closed has the same frequency formula. Closed-open requires (2n-1)*v/(4L).",
  "model": "f=n*v/[2*(L+Delta)]; Delta is the total end correction",
  "likelihood": "Independent Gaussian frequency errors with small length errors propagated to frequency; includes log variance. No correlated calibration, exact latent-length likelihood, humidity or temperature model.",
  "nominal_demo": {
    "speed_with_end_correction_m_s": 343.0294078469534,
    "total_end_correction_m": -7.987884675494938e-05,
    "zero_correction_speed_m_s": 343.13124711318915,
    "nll_with_end_correction": 7.98943946947247,
    "nll_zero_correction": 8.100753368141422,
    "bounds": {
      "speed_m_s": [
        250,
        450
      ],
      "end_correction_m": [
        -0.05,
        0.05
      ]
    }
  },
  "noiseless_8mm_positive_control": {
    "speed_with_end_correction_m_s": 343.20000000251264,
    "total_end_correction_m": 0.008000000000828733,
    "zero_correction_speed_m_s": 330.3874215461037,
    "nll_with_end_correction": -1.5706030955280612,
    "nll_zero_correction": 2574.0924638090983,
    "bounds": {
      "speed_m_s": [
        250,
        450
      ],
      "end_correction_m": [
        -0.05,
        0.05
      ]
    }
  },
  "note": "A frequency-axis intercept is not an end-correction parameter. A transformed plot n/(2f) versus L has slope 1/v and intercept Delta/v, with errors on both axes. Reference v is illustrative near room temperature, not a calibrated universal constant.",
  "profile_uncertainty": {
    "total_end_correction_m": [
      -0.00041166205913469034,
      0.00025194896895290586
    ],
    "speed_m_s": [
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      343.48949461206064
    ],
    "nominal_level": 0.95,
    "nll_increase_threshold": 1.920729410347062,
    "method": "Separate one-parameter profile likelihood intervals; nuisance parameter reoptimized; asymptotic chi-square(1), not joint 95% coverage.",
    "limitations": "Conditional on supplied independent Gaussian errors and linearized length uncertainty; 12 synthetic rows. No empirical coverage validation or shared calibration/systematic-error budget. Negative fitted correction is a diagnostic of noise, not a negative physical opening length.",
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}