AI Software Production Systems (ASPS) proposes that the future of enterprise software will not be defined by writing more code faster, but by the governed transformation of human intent into production-proven, legally accountable, cyber-resilient, compliant, and reversible system behavior. As autonomous AI agents move from code assistants to production actors, traditional paradigms — SDLC, Agile, DevOps, GitOps, MLOps, and Platform Engineering — leave critical gaps in trust, reversibility, and accountability that this work addresses directly. This thesis introduces two core contributions. First, the CTQOST-R optimization model, which reframes production success as correctness per unit cost and time under explicit constraints of Quality, Operability, Security, Trust, and Reversibility — elevating reversibility to a first-class engineering invariant rather than an afterthought. Second, Reversibility-by-Design, the principle that no autonomous action is promotable to production unless its reversal, compensation, containment, or safe-degradation path is defined in advance. ASPS organizes autonomous production into eleven interdependent governance domains — including Intent Governance, Context Integrity, Agent Engineering, Verification Factory, Evidence Ledger, Runtime Truth, Cybersecurity, Compliance, Legal Governance, and Economics — converging on a single objective: production trust. The framework is presented as a board-grade reference architecture for organizations adopting autonomous software production at enterprise scale, where a single weak domain lowers the trustworthiness of the entire system.