MeerKAT Long-Baseline Pulsar Timing: Definitive Gravitational Potential Map of Omega Centauri

Timing precision (ToA): ~1–3 µs per 1-hr session (bright MSPs) Acceleration sensitivity from the quadratic-fit spin-down term [corrected 2026-09-25, P0-15.6: the previous line, δa = c·δσ_ToA/(P·T²), carried a spurious division by the spin period P]: δa_los = c · σ_ToA · k / T², with k = 2√(180/N) = √(720/N) (quadratic-fit coefficient uncertainty for N uniform ToAs; the linear-fit factor √(12/N) does NOT apply, because spin-down is quadratic) Bi-weekly cadence over T = 5 yr → N ≈ 130 ToAs per pulsar → k ≈ 2.35: δa_los ≈ (3×10⁸ m/s × 2×10⁻⁶ s × 2.35) / (1.575×10⁸ s)² ≈ 5.7×10⁻¹⁴ m/s² per pulsar (ToA-noise-limited only) But ToA noise is not the limiting term. The measured ṗ is the sum of intrinsic spin-down, cluster acceleration, and Shklovskii drift, and the intrinsic term is unknown per pulsar at the ~10⁻²⁰ s/s level, which maps to an acceleration uncertainty c×10⁻²⁰/P ≈ 10⁻⁹ m/s² (P = 3 ms). The usable sensitivity is therefore ~10⁻⁹–10⁻¹⁰ m/s², four orders of magnitude above the ToA-noise floor. Expected acceleration from 30,000 M☉ IMBH at r = 0.3 pc: a_los ≈ GM/r² × cos(i) ≈ 4×10⁻⁸ m/s² (mean projection) Significance, stated honestly: against the ToA-noise floor alone the formal single-pulsar significance would be ~7×10⁵σ, a meaningless number. Against the intrinsic-Ṗ cap the usable ratio is at most ~40–130× per pulsar (P = 3–10 ms), and Paper H's own analysis (verified verbatim: "The pulsar accelerations are nearly uninformative.", omega-centauri-mass-tension.html) shows the set is a weak mass discriminator even at that sensitivity, because the intrinsic terms are unknown and the bounds are one-sided. The ensemble radial-profile test, not any single-pulsar detection, is the program's real deliverable.