Reconciling the Chae–Banik Tension in Wide Binaries with Density-Dependent Gravity

 significant tension has emerged in recent tests of gravity using Gaia DR3 wide binaries. While Chae (2023) reports a
gravitational anomaly consistent with MOND in systems with weak external fields, Banik et al. (2024) find strict Newtonian
behaviour in the Solar neighbourhood. We propose that this discrepancy is not methodological but physical, arising from an
environmental screening mechanism. We introduce a phenomenological density-dependent scale, 𝑎𝑒 𝑓 𝑓 (𝜌) ∝ exp(−√︁ 𝜌/𝜌𝑐𝑟𝑖𝑡 ),
consistent with scalar field frameworks stabilized by geometric Casimir energy. We demonstrate that the high-density environment
of the Banik sample (𝜌 > 𝜌𝑐𝑟𝑖𝑡 ) suppresses the anomaly, while the lower-density selection of Chae (𝜌 < 𝜌𝑐𝑟𝑖𝑡 ) allows it to
emerge. We estimate a critical transition density of 𝜌𝑐𝑟𝑖𝑡 ≈ 0.03𝑀⊙ pc−3. This single parameter unifies both datasets, resolving
the conflict without requiring dark matter in the local disk.