The Blended Time Paradox is what Gamanian scholars referred to an impossibility in the timers on the lab equipment left by the away team when they visited during the planet's medieval period. This impossibility is caused by the fact that the timers relied on the Earth's core to keep correct time, and when brought to the coreless ring planet they went haywire.
The Professor gave a list of the times before and after the moment of alteration to Oscar Shelton when he, James Zanasiu, Roy Hawkeye, Josephine Smithson, and Lockdown visited his house, the Union headquarters. This gave Shelton the information he needed to calculate the exact value of a t-coordiante. (Card of Ten)