Carly Luna-Baez has developed a mathematical framework motivated by a long-standing question about how local geometry and motion shape time accumulation. Using general relativity as the baseline, the framework introduces a local possibility sphere attached to a finite object or instrument and studies how surrounding gravitational structure constrains its admissible directions and realizability volume. From this, the work proposes that time accumulation should not be understood only through the standard proper-time dependence on velocity, but also through how a structured object interacts with local geometry through this sphere-volume interface. The paper presents this as a phenomenological extension of GR, not a rejection of its backbone, and derives testable predictions for orientation-dependent response in a body-attached detector. A fully human-written companion paper explaining the underlying observations, conceptual motivation, and intellectual influences behind the framework will be posted to this Zenodo account in two months.