Addresses Decay: A Diffusion Bound on the Holding Time of a Phase Destination

A phase left alone does not stay put; coupled to any environment, it diffuses. This paper derives the holding requirement that follows. With phase diffusion constant D, free diffusion exhausts the 0.0667 rad budget in 2224 s at D = 1e-6 rad^2/s, in 2.224e+05 s at D = 1e-8, and in 2.224e+07 s at D = 1e-10. A restoring structure with relaxation time tau_r saturates the spread at sqrt(D tau_r), so indefinite holding within budget requires tau_r <= 4.449e+05 s at D = 1e-8, with the required relaxation time scaling inversely with D. The bound converts an abstract stability question into a specification pair: measure the diffusion, and the holder's required stiffness in time follows. A coordinate with no restoring structure at all has a finite address lifetime at every nonzero diffusion rate. Computed; not measured. SIMULATED, NOT MEASURED.