The Advaithian Operator: Terminal Erasure and the Unverifiability of Victory in Sleep-Onset Contests

We study contests in which the winning condition is a state whose attainment destroys the winner's capacity to observe it. The canonical example is the sleep race: two agents compete to fall asleep first. We formalize such settings as terminal-erasure games and introduce the Advaithian operator Ж, which maps a world and a time to the outcome verified by some agent at that time, or to ⊥ if none is. Under three axioms (terminal erasure, opacity and onset blindness) we prove that Ж = ⊥ throughout the contest: no individual agent can verify the winner, and even the pooled information of all participants cannot. Rational credence in victory nevertheless decays as ½e−λt, never reaching 0 or 1. We derive a closed form for the cheapest repair, periodic heartbeat logging, whose failure probability is exactly tanh(λδ/2), and prove a report-irrelevance theorem: any prize mechanism based only on the players' own reports selects the true winner with probability 1/n. We then test these predictions computationally with learning agents that are never shown the theory. Across 20 independently seeded runs, Q-learning reporters reach 49.9% ± 0.9% accuracy without records and 89.7% ± 0.5% with logs (predicted 50% and 89.73%); a bandit agent recovers the cost-optimal heartbeat interval; and a Monte Carlo watchdog learns a credence-based failure rule within one step of the exhaustive optimum in 49 of 50 runs. AI-use statement: the research question, the sleep-race thought experiment and the Advaithian operator are the author's own. The author used Claude (Anthropic), an AI assistant, extensively to formalize the proofs, write and run the simulation code, produce the figures and draft the text.