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 Planck
Pressure (VP) hypothesis in a covariant and mathematically explicit form. Its central objective
is to determine whether gravitational and inertial phenomena can be represented within a
single constitutive framework based on the local clock field c, the metric coefficient A = c², the
normalized 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 corresponding
geodesic and hydrostatic relations, and analyzes the extent to which the same
pressure-gradient structure can account for both gravitation and inertia. The work further
formulates the relevant Killing, Komar, and energy-balance identities needed for internal
mathematical consistency. Particular attention is given to dimensional closure, compatibility
with weak-field limits, and the distinction between geometric identities and genuinely
constitutive assumptions. The main challenge addressed is the construction of a formally
closed description without introducing ad hoc sector-specific postulates. The achieved result is
a unified VP representation in which gravitational and inertial accelerations admit a common
interpretation through the clock-field and pressure-gradient structure, while the remaining open
problems are identified at the level of fully dynamical closure and broader empirical
discrimination.