GenOS Gives AI Coding Workflows a Formal Criterion for When It Is Safe to Swap a Prompt, Contract, or Generator

arXiv 2608.03588·low signalXBlueskyLinkedInCopy link

Treating each layer of an agentic coding workflow as a Markov kernel with observer-relative equivalence at each interface, GenOS proves that equivalence-compatible kernels descend to quotient classes and that quotienting commutes with distributional extension and sequential composition — so equivalent prompts induce equal probabilities for all downstream equivalence-closed events, including verified commit. It also establishes workflow bisimulation, guarded-commit safety under sound validation, and an additive robustness bound attributing approximation error to individual pipeline layers. An executable insertion-sort audit over 121 inputs plus 20,000 randomized finite-kernel trials violated no exact or approximate law; compatibility is framed as a measurable property to test, not an assumption about model behavior.