Theory of Computational Irreversibility in Self-Parameterized Function Chains

Comprehensive theory of computational irreversibility in self-parameterized function chains. This paper introduces three distinct mechanisms for irreversibility:- Computational — exponential search complexity Ω(mⁿ)- Probabilistic — recovery probability approaching zero- Absolute — mathematical impossibility through information destruction We present the concept of Tunable Complexity — a framework where inversion difficulty can be precisely controlled through system parameters (permutation complexity π, dependency depth δ, information loss λ). VERSION HISTORY:- v3 (24 January 2026): Reformatted to LaTeX, added reference to experimental validation work- v2 (04 January 2026): Initial public release RELATED WORK:The theoretical concepts introduced here are developed into a rigorous experimental framework with statistical validation in: "Nonna Functions: An Experimental Study of Information Loss and Inversion Complexity" (24 January 2026)DOI: https://doi.org/10.5281/zenodo.18361874 STATUS: Theoretical framework. Does not claim to resolve P vs NP.