Macroscopic Observable Stability for Cutoff Coulomb BBGKY Defects in a Scale-Separated Observation Topology

For a cutoff-regularized Coulomb BBGKY hierarchy at a fixed reduced level s, this preprint proves that a pair-diagonal singular residual can be macroscopically harmless in a scale-separated observation topology. The topology tests residuals against weighted C^2 symbols with observation resolution δ, while the microscopic cutoff scale is ε. The main estimate has the form ||R_N,ε^(s)||_obs,s,δ ≤ C_s (m_N + B_N ε/δ + K_tail,N + K_model,N), where m_N is a weighted monopole budget, B_N ε/δ is a localized first-moment budget, and K_tail,N and K_model,N are explicit tail and model-error budgets. Normalized macroscopic density, current, and localized kinetic-energy observables are continuous in this topology with constants independent of the total particle number N; this independence follows from an explicit marginal-normalization identity. The paper also records a non-triviality diagnostic showing that the topology still detects residual components with macroscopic scale-δ projections. The framework is deliberately finite-level and conditional. It separates purely symbolic scale separation from operator-level quantization compatibility by carrying an optional remainder budget Q_N(δ, ħ_N). It also provides a conservative interface through which weighted higher-correlation or feedback models may supply the required monopole, tail, and model-error budgets. The result is not a full cutoff-free Coulomb closure theorem: trace norm, energy norm, pointwise microscopic density control, full hierarchy closure, and automatic operator-level convergence are explicitly excluded.