Minimum Description Length Unsupervisedly Separates Law-Grade from Statistical-Grade Knowledge in a Self-Improving Science Agent - and Reveals 86% of Its Own Discoveries Are Statistical

Wenbin Mao, Pei Zou

AI systems that discover scientific relations now generate candidate "laws" at scale, but the bottleneck has shifted from generation to vetting: which candidates deserve belief? We show that a deployed self-improving science agent - one that has admitted 252 relations through held-out prediction courts - already computes the quantity that answers this question: the Minimum Description Length compression ratio used for model selection doubles, when read under discrete accounting, as an unsupervised epistemic grader. The compression-ranked top band of the agent's ledger recovers exactly the canonical laws among its discoveries (vis-viva across seven planets, Balmer/Rydberg) plus cross-measurement identities - enrichment $p=3.6\times10^{-12}$ under a hypergeometric test - with zero counterexamples and physically coherent band structure. The same lens retroactively reveals that 86% of the ledger compresses nothing ($\mathrm{cr}\approx 1$): the agent had been recording statistical regularities, including a learned predictor with held-out $R^2=0.541$ admitted through the prediction gate, under a narrative of compression as the unified value of knowledge - a narrative that was never…