NOVA: Fundamental Limits of Knowledge Discovery Through AI

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arXiv:2605.15219v3 Announce Type: replace Abstract: Can AI systems discover new knowledge through iterative self-improvement, and at what cost? We introduce NOVA, which models the ``generate, verify, accumulate, retrain'' loop as an adaptive sampling process over a knowledge space. We give sufficient conditions for accumulated genuine knowledge to cover a finite domain and show how violations produce contamination, forgetting, exploration failure, and acceptance failure. We then analyze how adaptive generation arises from recursive retraining. In an explicit distribution-level model where accepted artifacts influence the next generator, we identify a recursive-feedback phase transition. Unanchored feedback can lock generation onto early accepted artifacts and leave initially reachable valid artifacts undiscovered with positive probability. Anchoring updates to a persistent base distribution prevents unbounded distortion and guarantees continued exposure. Under imperfect verification, we identify a contamination trap: as easy knowledge is exhausted, even small false-positive rates can admit invalid artifacts faster than genuine discoveries. We show that Good--Turing estimation is a local batch-diversity diagnostic, not an estimator of the historically undiscovered valid mass governing long-term progress. Under a Zipf tail with exponent $\alpha>1$, the cumulative generation cost of obtaining $D$ distinct genuine discoveries satisfies $R_{\rm cum}(D)=\Theta(c_{\rm gen}D^\alpha)$. When the valid base distribution has such a tail, anchored retraining preserves the exposure …

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