The first atoms formed approximately 380,000 years after the Big Bang, when the universe cooled enough for electrons to bind to protons. This recombination redshift z_rec is a key cosmological observable. Standard cosmology calculates it using measured atomic physics constants and a fitted cosmological model. Pentagon Physics derives z_rec = 1107 from spectral geometry alone — using only the derived values of α, m_e, and η, without fitting any cosmological parameters. The 1.6% discrepancy from Planck's measurement of z = 1090 is identified as the Hubble tension expressed as a time difference — not an error in the atomic physics.