Compensator Stress-Energy from Finite-Domain Localization: Remnant Formation and Horizon Tests

Restricting matter stress-energy to a finite spacetime domain by a smooth scalar window (x) ∈ [0,1] produces a boundary divergence (∇^μ)\,TSMμν. The contracted Bianchi identity therefore requires a compensating boundary-layer stress-energy Tᶜᵒᵐᵖμν. This paper studies when that compensator coarse-grains away and when it survives as a macroscopic remnant. A Vanishing Lemma shows that, for phase-incoherent states with finite stress-tensor correlation length, bounded boundary stress-energy, and the minimal retarded prescription, the compensator vanishes on scales L ε, recovering standard GR. A persistent remnant forms in the class analyzed here when two conditions act together: (C1) localization events exceed the causal four-volume rate λ_*() ~ ⁻⁴, invalidating the bounded-stress assumption at the aggregate scale, and (C2) the boundary is permanently, or throughout the decoherence interval relevant to remnant formation, causally inaccessible to the external coarse-graining domain. These conditions and their consequences are collected into a formal Compensator Remnant Formation Theorem. Inflationary Hubble crossing provides the main cosmological production channel: Hubble-scale coarse-graining of squeezed super-Hubble modes generates a boundary stress-energy transfer that cannot be reabsorbed during the squeezing and decoherence epoch. A conditional proposition states that under (C1) and (C2) the resulting remnant is covariantly conserved and approximately pressureless, making it a candidate seed for a gravitationally coupled dark sector. Black-hole horizons provide the clean geometric test case: the event horizon satisfies causal blocking while the ergosphere does not, and the boundary-layer profile is controlled by surface gravity κ, vanishing as the extremal limit is approached through the non-extremal family. Standard gravitational boundary constructions, namely Israel junction conditions, the membrane paradigm, dynamical horizons, and vacuum bubble walls, serve as consistency checks on the same boundary-conservation structure.