The Chronon Decay: Deriving the Arrow of Time as the Topological Relaxation of the Sedenion Bulk

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) into
the associative Octonionic Vacuum (O). Within the framework of Axiomatic Physical
Homeostasis (APH), we identify the “Present” not as a coordinate, but as the active
Computational Shockwave of this Cayley-Dickson cascade. We derive the fundamental
unit 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 time
dilation 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 group
flow of the vacuum geometry is strictly contractive, minimizing the non-associative defect
of the universe.