The Synchronization Bath: Phase, Rate, and the Geometry of Contact in Five-Dimensional Fluid Spacetime

▼About this document Paper III modelled dark matter as ordinary matter displaced along bulk time beyond an electromagnetic window |Δt| < τ_e, and left two questions open: how visible matter remains visible, and what the exchange of photons between clocks actually accomplishes. We answer both from the mechanical floor of the framework, with no fitted parameter. (i) Phase additivity gives the fractional pull-back of a clock offset per completed absorption, g = E_γ/(E_abs + E_γ), and a power formulation of the maintenance condition. (ii) The receiver's w-t orbit of radius w_0 = ħ/2mc has a time-direction diameter w_τ = ħ/mc², with the universal invariant w_τ ω = 1; the electron's orbit is tangent to the photon layer w = w_max (the photon-contact condition of Paper I), contact is a binary overlap of the arriving stamp with this one-cycle disk, and the edge of the window is exact. Paper III's τ_e is thereby derived. Lawful rate differences enter the arriving photon and the receiver's clock in common mode, so matter born inside the window remains inside indefinitely. (iii) Clock rates are integer-quantised, ω = n m_0 c²/ħ, which forbids continuous drift; the sharpness of Lyman-alpha absorption lines is the astronomical record of this quantisation. (iv) Kick ⇒ handshake ⇒ shared layer, with inter-layer motion forbidden, makes layer membership a property fixed at birth and makes the registered null of recoil detection for displaced matter (P-11) an exact zero rather than a weak coupling. (v) A clock is a double broadcaster: its phase travels only on detached real quanta (layer-selective: electromagnetic synchronisation), its rate leaks as the w-terrain (layer-blind: gravity), and it has no noise. This two-broadcast theorem identifies the decomposition of clock observables with the classification of forces, and is witnessed by optical-lattice-clock comparisons that resolve millimetre gravitational redshifts while phase-stitching the clocks. (vi) Collisions transfer no stamp (detachment criterion; pressure broadening matches the collision rate to order of magnitude), phonons carry stamps with fidelity exp(−d/ℓ) fixed by the measured mean free path, and the length of a photon wave train enters absorption rates but never the window. The census of synchronisation margins concludes that no maintained phase lock exists anywhere: visibility is a qualification fixed at birth, contact is an event, and synchronisation is the sum of the pushes those events leave. We state the sharpened relations to Papers I-III, the falsification conditions (a layer-selective gravity; any confirmed recoil detection), and record the post-registration corrections made in the course of this work.