Subhalo or Future–Mass Projection? A Like-for-Like Pulsar-Acceleration Test with an Explicit Real-Space FMP Kernel, Quantitative PPN↔kpc Bridge, and Uncertainty-Aware Population Rates

Binary-pulsar accelerations have been interpreted as evidence for a local ∼ 107 M⊙ subhalo. We strengthen the like-for-like confrontation with Future–Mass Projection (FMP) by: (i) deriving a closed, numerically stable real-space kernel Γϵ(r) from ϵ(k) = ϵ0 (1+k2/k2 0 )−1 W (k) with W (k) = 1 − e−(k/kw )2 , including exact erf/erfc forms, asymptotics, and a monotonicity proof; (ii) computing a quantitative Solar-System map ϵSS(ϵ0, k0, kw) with (|β − 1|, | ˙G/G|) for concrete feasibility points; (iii) providing analytic bounds that link the required kpc-scale acceleration to PPN safety and the forecast baryon budget; (iv) specifying a reproducible Π → Meff → alos pipeline (ROI, hyperpriors, figure/table slots); (v) refactoring detection rates with a 68% band from (ρDM, fsub, ∆ ln M ). We retain the published compact/NFW subhalo evidences as benchmarks and define ready-to-populate outputs (log-evidence table, corner plots, vector-geometry comparison) for the FMP runs under the same GP likelihood.