The Inverse-Square Law at Micron Separations: What Short-Range Experiments Leave for a Torsional Force

Newton's inverse-square law has been verified directly down to separations of 55 micrometres (Kapner et al. 2007). A Yukawa force of gravitational strength and range equal to the separation would distort the force there by a fraction 0.74, and at twice its range by 0.41 - distortions the torsion-balance data exclude for the corresponding strengths, as the companion exclusion analysis tabulates. This paper works through the deviation arithmetic itself: how a Yukawa term's signature scales with separation, why experiments pattern their test masses to cancel the Newtonian term while preserving the Yukawa one, and what residual room remains for a torsional force whose range is tied to its mediator's mass. Computed, not measured.