Failure Geometry and Spectral Collapse Under Epistemic Stress A Semantic-Topological Analysis of Restricted Computational Dynamics

Recent work by Al-Zawahreh and Tassan introduces a spectral-geometric framework in which discrete computational problems are embedded into smooth energy landscapes, revealing topological fragmentation and spectral gap collapse in hard instances. While these constructions have been framed as evidence toward a separation of complexity classes, we argue that their true contribution lies elsewhere: they formally characterize a failure geometry for a broad class of restricted computational dynamics. In this paper, we reinterpret these spectral-topological obstructions through the lens of Semantic Physics, treating computation not as an abstract decision procedure but as a controlled dynamical process operating over a relational state space. We show that exponential homological complexity and associated spectral collapse do not imply absolute unsolvability, but instead constitute a conditional no-go result for local, smooth, and adiabatic-like dynamics-including those induced by contemporary interactive language models. By integrating Tassan's RES = RAG (Relational Equilibrium equals Generative Agent) framework as a relational interpretation layer rather than a proof mechanism, we formalize a phase transition from controllable to uncontrollable regimes under epistemic stress. The resulting theory explains observed failure modes-looping, evasive equilibria, intent overreach, and non-termination-as geometric consequences of control loss in fractured semantic manifolds. Supplementary Material File (failure geometry and spectral collapse.pdf) - Download - 202.10 KB Information & Authors Information Version history Copyright This work is licensed under a Creative Commons Attribution 4.0 International License

Authors Metrics & Citations Metrics Article Usage 110views 85downloads Citations Download citation Trent Slade. Failure Geometry and Spectral Collapse Under Epistemic Stress A Semantic-Topological Analysis of Restricted Computational Dynamics. Authorea. 07 January 2026. DOI: https://doi.org/10.22541/au.176780583.34651713/v1 DOI: https://doi.org/10.22541/au.176780583.34651713/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.