TimeT — Document 2: Discrete Temporal Transitions in a Time-Field Framework: Definition and Analysis of the Jump Operator J

This work presents the second theoretical component of the TimeT framework, introducing and analyzing the Jump Operator J, which describes finite and localized transitions between temporal foliations generated by the scalar time field T(x). Building upon the foundations established in Document 1, this paper develops the mathematical structure of discrete temporal transitions, formulates the physical criteria for their initiation, stability, and completion, and establishes connections between time-field dynamics, causality preservation, and geometric consistency.

The document refines the phenomenological Lagrangian approach, ensures compatibility with general relativity, and outlines the physical and geometric conditions under which controlled temporal jumps may occur. This work forms the theoretical basis for subsequent experimental proposals aimed at detecting or manipulating perturbations δT(x) of the time field.