PulsumSpace Test Cases: Muon Lifetime, GPS Clock Corrections, and Altitude-Dependent Time Dilation in a Field-Density Framework

Preprint version V1. This preprint presents a compact set of test-case calculations within the PulsumSpace framework. PulsumSpace describes physical space as a dynamic field medium whose local density and pulsation structure are related to measurable time and frequency effects. The purpose of this preprint is not to claim an experimental confirmation of PulsumSpace or a replacement of established relativity theory, but to show that selected relativistic benchmark cases can be reproduced numerically within a field-density interpretation. Four examples are considered: altitude-dependent clock shifts over a height difference of 3000 m, gravitational clock corrections for GPS satellites, combined altitude and velocity effects for aircraft clocks, and the lifetime extension of relativistic muons. In each case, the PulsumSpace formulation yields the same leading-order numerical values as the corresponding weak-field or special-relativistic expressions: approximately +28 ns/day for a 3000 m altitude difference, approximately +45 μs/day for the gravitational part of GPS clock correction, approximately −15 ns/day for a representative aircraft case, and a muon lifetime extension proportional to the Lorentz factor γ. These results show that the PulsumSpace density-function approach can reproduce known relativistic benchmark values in the weak-field and usual-velocity regimes. This does not by itself constitute an independent experimental confirmation of the model. Rather, it establishes a basis for further theoretical refinement and for future differential tests.