Timing the X-ray Heating Epoch from the 21-cm Turning Points

After coupling comes heating: X-ray sources among the first stellar populations raise the gas temperature, the absorption weakens, passes through zero, and eventually appears in emission. Using the stated cosmology and the brightness-temperature relations described in the Methods, the calculation gives the following headline values: z heat = 13.8; z heat standard = 15; shift = -1.2; fx = 0.60. The comparison values taken from the published record — including the EDGES and SARAS reports, HERA limits and the Planck optical depth where relevant — are used exactly as published, and the bounce contribution enters only through the named timing, heating or shear inputs. The result is a computed prediction for the delayed-onset history, with its sensitivity to each input stated in the Discussion. This study is simulated and computed from stated assumptions; it is not a measurement.