Persistent Theories under Bounded Revision: Representation, permanent constraints, and effective generation

Which theories can remain true through an unending sequence of local revisions? These two working papers study persistence when each step changes only a bounded number of primitive facts. Persistent Theories under Bounded Revision classifies computable propositional persistence through Σ₂⁰ complexity and finite connectivity. It gives polynomial interpolation, productive target generation, and exact certificates for arbitrary permanent cores. Implication cores with computable finite forward closures admit an explicit budget formula; periodic backward systems with finite additional constraints admit a decision procedure. Decidable cores can nevertheless impose arbitrarily large additional computability costs. Quantified Persistence under Bounded Revision studies truth carried by moving witnesses. It classifies named monadic targets, treats interacting predicates and relations inside fixed finite blocks, and determines sharp transport budgets through finite type graphs. For uniformly limit-computable sentence truth, it proves a sharp Σ₃⁰ persistence bound and classifies prescribed complete targets in a fixed computable forest: enumerable color profiles at budget 1, and Π₂⁰ profiles for computable histories at budget 2. Every Σ₃⁰ positive trace can also be prescribed with one edit. The proofs combine recurrence, finite graph geometry, computable approximation, counting normal forms, and witness transport. The main paper contains the finite-coordinate foundations; the companion supplies the additional semantic arguments. Remaining questions concern broader core decision criteria, productive generation from weaker presentations, incomplete multitype targets below the uniform budget threshold, and general prescribed first-order theories. Complete sources and supplementary finite verification code accompany both papers.