E = pr

The Cohesion UFT pressure axiom — the observable universe is under pressure fromthe next higher scale — generates a scalable energy formula:E = prwhere p [Pa] is the pressure from the next higher scale and r [m3] is the coherence volume:the spatial extent of one complete recursion cycle. The equation is dimensionally exact:[J] = [P a] × [m3]. It is verified exactly at one scale: the electron, where p = m4ec5/ℏ3and r = λ3Cgive E = mec2exactly with no fitting. At macroscopic scales — orbital,atmospheric, stellar — the formula gives the correct dimensional energy structure andorder of magnitude, but the precise numerical coefficient requires specifying the exactgeometry of the coherence volume. The cascade conservation law is exact at all scales:at level k, rk = r0 · 3k and pk = p0/3k, so E = pkrk = p0r0 is conserved with cascaderatio 3 = κ6/κ2. The Pressurized Recursive Effect connects E = pr to the fine-structureconstant through 1/α = θφ − ∆θ = 137.029.