Energy Calibration Cross-Check: How a Fourteen Percent Scale Shift Moves the Measured Flux

Ultra-high-energy cosmic-ray energies are assigned by two techniques, fluorescence calorimetry and surface-detector estimation, whose cross-calibration carries a systematic scale uncertainty of order fourteen percent. Because the spectrum falls steeply, a scale shift moves the measured flux far more than it moves the energies. For an integral spectral index of 1.7 in the ankle region, a fourteen percent upward scale shift multiplies the flux above a fixed threshold by 8.003e-01; in the suppression region, where the integral index steepens to 3.2, the same shift multiplies the flux by 6.575e-01, and a twenty-one percent inter-experiment scale offset, of the size discussed between the two major observatories, multiplies it by 5.434e-01. Conversely, shifting the scale down raises the inferred flux by up to 1.620e+00. Much of the apparent disagreement between published spectra in the suppression region is therefore calibration arithmetic rather than sky, and any framework comparison, including density-bound tests, must be made after the scales are aligned. Simulated and computed; not a measurement.