We propose that Time is not a fundamental dimension, but an emergent thermody-namic phase transition describing the decay of the non-associative Sedenion Bulk (S) intothe associative Octonionic Vacuum (O). Within the framework of Axiomatic PhysicalHomeostasis (APH), we identify the “Present” not as a coordinate, but as the activeComputational Shockwave of this Cayley-Dickson cascade. We derive the fundamentalunit of time, the Geometric Chronon (τAP H ), as a function of the local Associator Haz-ard A and the vacuum stiffness β ≈ 1.91. We demonstrate that General Relativistic timedilation arises as a Computational Viscosity effect: regions of high geometric torsion(mass) impose a higher processing load on the vacuum, effectively slowing the local clock.Finally, we prove that the Arrow of Time is unidirectional because the renormalization groupflow of the vacuum geometry is strictly contractive, minimizing the non-associative defectof the universe.