The Geometry-Attached Time Era: From Human Intuition to Modern Mathematics

This monograph introduces geometry-attached time as a framework for systems in which admissible geometry may degrade, fragment, or disappear under hazard or regime change. It shows that equations, dynamics, and intelligence can remain formally well defined while meaningful evolution becomes impossible due to the loss of admissible geometry. Geometry-attached time reframes such failures as geometric rather than dynamic, clarifying the boundary of validity of classical theories across mathematics, physics, control, and learning.