We study exact witness architectures, sentences or semantic classes equipped with distinguished exact witness channels. The main theorem is a selection jump: for every decidable local verifier, any nonempty stagewise-local success class is automatically $Pi^0_2$-complete. Thus a single successful seed already forces maximal stagewise complexity. Around this theorem we prove three further barrier layers. Finite stagewise prefixes are uniformly insufficient, and undecidable co-c.e. witness architectures admit no decidable one-shot positive certifier and no exact-domain compiler. Same-theory adequacy along a universal $Pi_1$ embedding yields full $Pi_1$ reflection, ruling out internal exact certification in consistent recursively axiomatizable extensions of $ISone$. Finally, an arithmetic exact terminality predicate exists on a truth-faithfully embedded fragment exactly when the fragment truth set is arithmetical, yielding Tarski and diagonal barriers. For fixed propositions with exact two-sided decidable witness packages, these results assemble into a bridge trichotomy: isolated extensional bridges are vacuous, effective bridge classes are empty or $Pi^0_2$-complete, and assertion-enriched resolver layers are truth-universal.