A Sheaf-Theoretic and Multi-Layer Formalization of Advanced Tragedy: Local Rationality, Inter-Layer Interference, and Global Obstruction

This work proposes a formal theory of advanced tragedy based on sheaf theory, bounded rationality, and multi-layer system analysis. The central thesis is that tragedy should not be understood primarily as moral failure, foolishness, or random misfortune. Instead, tragedy emerges when locally rational actions and belief structures fail to extend into globally coherent outcomes due to structural connection gaps across information layers. The framework models narrative and social systems as sheaves of local information, beliefs, and action policies. Tragic phenomena are characterized as local-to-global obstructions and can be represented through non-trivial first Čech cohomology classes. The theory integrates bounded rationality, game-theoretic coordination failures, information asymmetry, and multi-layer causality into a unified mathematical structure. The paper further introduces a taxonomy of tragedy based on value rupture, information rupture, and causality rupture, together with five phenomenological tragedy types. Literary case studies including Sophocles' Oedipus Rex and Shakespeare's Hamlet are analyzed within the proposed framework. In addition to literary analysis, the theory suggests broader applications to collective-action problems, institutional failure, economic coordination breakdowns, AI narrative generation, and the study of social systems as local-to-global obstruction structures. Keywords: tragedy theory, sheaf theory, bounded rationality, cohomology, game theory.