Does Collatz need all primes (an adelic obstruction)?

Speculative — an open question, not a coordinate.

The question. Whether the difficulty of the Collatz (3n+1) problem is an adelic obstruction — that no single prime's information suffices and the map must be understood at all places at once.

Discriminator (the gate). Is there genuine local-to-global structure to the 3n+1 map — a real obstruction living in the product over p-adic places, with a theorem — or is "needs all primes" a suggestive restatement of "it is hard"? A real instance would exhibit the map as a compatible family over the places with a global constraint the local pieces cannot see. Until then, a question.