We present the results of 71.6 hours of observations of the Geminga pulsar (PSR J0633+1746) with the VERITAS very-high-energy gamma-ray telescope array. Data taken with VERITAS between November 2007 and February 2013 were phase-folded using a Geminga pulsar timing solution derived from data recorded by the XMM-emph{Newton} and emph{Fermi}-LAT space telescopes. No significant pulsed emission above 100 GeV is observed, and we report upper limits at the 95% confidence level on the integral flux above 135 GeV (spectral analysis threshold) of 4.0$times10^{-13}$ s$^{-1}$ cm$^{-2}$ and 1.7$times10^{-13}$ s$^{-1}$ cm$^{-2}$ for the two principal peaks in the emission profile. These upper limits, placed in context with phase-resolved spectral energy distributions determined from five years of data from the emph{Fermi}-LAT, constrain possible hardening of the Geminga pulsar emission spectra above $sim$50 GeV.
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