Bounded Gödelian Language Models: Proof-Carrying, Survival-Satisficing Evolutionary Self-Adaptation

Worked for 34s This paper introduces bounded Gödelian language models: self-adapting systems that can propose persistent changes to their own weights, tools, inference procedures, and meta-learning mechanisms while remaining subject to externally verified governance. The framework combines proof-carrying invariants, survival-satisficing and risk-aware selection, evolutionary archives, and candidate-conditional anytime-valid statistics so that utility gains cannot compensate for violations of viability, shutdown compliance, reversibility, or operational constraints. By adapting SEAL-style self-edits into a certified multi-generation process and providing formal lineage guarantees, implementation sketches, and a reproducible calibration study, the work offers a mathematically auditable path toward safer recursive language-model self-improvement without claiming classical Gödel-machine global optimality.