Rational expectations are well-supported in financial markets. Evidence that traders are also rationally inattentive, however, runs through a single channel: the business cycle. Whether inattention binds independently of cyclical variation-as a primitive cognitive friction mapping objective events into subjective beliefs-remains open. We answer using NFL prediction markets: binary contracts traded on Polymarket against a cash-like safe asset, benchmarked against ESPN's continuous win probability, in an environment that trends but does not cycle. Using 2025-26 season data and a dynamic program nesting FIRE and cognitive discounting, we reject FIRE three ways: U-shaped pre-game volatility drifting with competitiveness, a persistent state-dependent wedge unaltered by concurrent market load, and precisely zero cross-game spillovers. These collapse to a cognitive discount of 80%, validated by a reinforcement-learning agent reproducing the inaction and panic-liquidation patterns. The result isolates acyclical, purely-cognitive rational inattention, locating the friction at the state-to-probability mapping rather than the attention-across-assets margin.