On the Informational Incoherence of Closed Timelike Curves: A Unified Analysis and Adversarial Audit

This work presents a unified theoretical investigation and adversarial audit of the physical realizability of closed timelike curves (CTCs). While certain idealized solutions to the equations of general relativity mathematically permit CTCs, their physical status has remained controversial, with debates often framed around paradoxes, engineering limitations, or unknown quantum gravity effects. Here, the problem is reframed at a deeper level: informational coherence and physical definability. The manuscript first develops a multi-layered analytical framework combining general relativistic consistency analysis, quantum evolution on CTC backgrounds, information-theoretic closure tests, and computational self-reference analysis. Across all frameworks, the presence of CTCs is shown to induce a breakdown of global state definability, observer-independent records, unitary quantum evolution, or computable dynamics. The resulting conclusion is formalized as a no-go theorem: spacetimes containing closed timelike curves cannot support a consistent, information-preserving quantum evolution. Importantly, this result does not rely on speculative quantum gravity assumptions, but emerges already at the semi-classical and information-theoretic level. To test the robustness of this conclusion, the manuscript includes a hostile adversarial audit explicitly designed to falsify the theorem. Multiple rescue strategies are examined, including finite-length Tipler-type constructions, enforcement of classical energy conditions, and quantum self-consistency models such as Deutsch closed timelike curves. Each attempted rescue fails by introducing new forms of informational underdetermination, observer-dependent contradiction, hidden retrocausality, or computational non-definability. By unifying constructive analysis with adversarial validation in a single document, this work demonstrates that closed timelike curves are not merely technologically inaccessible or paradoxical, but are fundamentally non-constructible physical objects due to unavoidable informational incoherence. The results provide a principled explanation for chronological protection rooted in information theory, and have implications for foundational physics, quantum computation, and the criteria by which mathematically permitted models are distinguished from physically realizable ones. FUSION OS INNOVATIONS