Wilson primes in nature

This research note proposes Petersen's hypothesis: no naturally occurring physicalor biological process has an intrinsic generating mechanism in which theWilson-prime condition plays an essential role in determining observablebehaviour. It specifies operational criteria for a credible naturalcounterexample and excludes fitted numerical coincidences, arbitrary encodings,unit-dependent digit matches, and deliberately programmed generators.The note reports limited background numerical exploration using the accompanyingWilson Ratio Scout 1.0.0 software and datasets. The exploration does not establishthe universal hypothesis. Comparison searches find no demonstrated Wilson-specificphysical relationship within the tested families. The paper makes no claim of aproved theorem, peer review, established priority, or recognition as a major openproblem. Relevant earlier literature, objections to the criteria, and mechanisticcounterexamples are invited.AI assistance is disclosed in the paper. Source code, tests, search settings,comparison results, and high-precision numerical candidates are supplied with it.