VP Hypothesis: Gravity and Inertia. A Mathematical Model for the Unified Description of Gravity, Inertia, Mass, Time, and the Properties of the Medium

This work develops the “Gravity and Inertia” sector of the Universe in Terms of PlanckPressure (VP) hypothesis in a covariant and mathematically explicit form. Its central objectiveis to determine whether gravitational and inertial phenomena can be represented within asingle constitutive framework based on the local clock field c, the metric coefficient A = c², thenormalized pressure-deficit field f = 1 - A, and the Planck-pressure relation P = P¥ + PPf.The study derives the static and accelerated sectors in parallel, establishes the correspondinggeodesic and hydrostatic relations, and analyzes the extent to which the samepressure-gradient structure can account for both gravitation and inertia. The work furtherformulates the relevant Killing, Komar, and energy-balance identities needed for internalmathematical consistency. Particular attention is given to dimensional closure, compatibilitywith weak-field limits, and the distinction between geometric identities and genuinelyconstitutive assumptions. The main challenge addressed is the construction of a formallyclosed description without introducing ad hoc sector-specific postulates. The achieved result isa unified VP representation in which gravitational and inertial accelerations admit a commoninterpretation through the clock-field and pressure-gradient structure, while the remaining openproblems are identified at the level of fully dynamical closure and broader empiricaldiscrimination.