CAT'S THEORY: The Density-Displacement Differential (The Kinematic Eradication of Mass-Attraction within the P_8 Medium)

This paper establishes the formal kinematic mechanics of the CAT'S Theory corpus within the closed d=8 Firmament cavity derived in Paper 206. By treating the P_8 structural space as a continuous, pressurized fluid medium, this formulation replaces the need for a primitive mass-attraction vector (g) with a purely fluid-dynamic equilibrium model. We derive the Unified Displacement Equation, proving that upward buoyancy and downward displacement are the same mechanical process operating in inverse directions relative to the cavity's pressure gradient (∇ P). The Triadic Coherence Invariant (R ≠ 0) is further validated, demonstrating mathematically that kinematic motion without a physical medium results in structural inadmissibility.