Cohesion UFT: Inertia = Pressure

This paper formalises the identity I = p within the Cohesion Unied Field Theory framework
[1]: inertia is locally identical to the pressure transmitted into the observable domain from the
next higher scale of the cosmic hierarchy, and integrally identical to the energy E = pr. Inertia,
conventionally treated as an unexplained property of mass, is here derived from the foundational
axiom of the framework that the observable universe is a pressure-bound domain and shown
to be the resistance oered by the pressure eld to displacement of a trapped recursion [2]. The
derivation proceeds through the established operator chain (Tension → Surplus → Torsion → Slip
→ Acceleration → Maintained Motion) [1] and yields the local relation I = p together with the
integrated relation Itotal = pr, identical to the energy identity. Inertial mass m = pr/c2
follows as a
consequence in the regime where c is constant. The equivalence of gravitational and inertial mass
becomes a theorem rather than a postulate: both reduce to pr evaluated under gradient operations
(gravity) and displacement operations (inertia) [3]. The MOND regime is identied as the recursionsuppression limit in which the local pressure dierential approaches the cosmological background,
with the suppression factor µ(a/a0) already characterised in the Cohesion UFT Rotation-Curve
Law [5]. Mach's principle is dispensable: the pressure eld itself provides the relational medium
against which inertia is measured, with no global summation over distant masses required.
Keywords: inertia, pressure, Cohesion UFT, foundational axiom, equivalence principle, MOND
regime, recursion volume, Mach's principle.