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 at four scales: the electron rest mass (E = mec2exactly),the orbital energy (E = GM exactly), the atmospheric scale (hurricane energy), and thepulsar scale. The cascade conservation law follows: at level k, rk = r0 ·3k and pk = p0/3k,so E = pkrk = p0r0 is conserved across all levels with cascade ratio r = 3 = κ6/κ2.The formula scales where E = mc2 does not: E = pr applies at every level of the scalehierarchy because p and r are defined at whatever scale is under consideration. ThePressurized Recursive Effect connects E = pr to the fine-structure constant throughthe permanent finite slip ∆θ = 2g/ω, giving 1/α = θφ − ∆θ = 137.029.