The Dimensional Determination Theorem for Classical Gravity

We prove a structural classification theorem showing that, in isolated and symmetry-exhausted vacuum regimes, the strength of gravitational response must decrease with distance in a way that is completely fixed by the number of spatial dimensions. In such regimes, there is only one admissible pattern of weakening with distance for each possible dimension of space. As a corollary, the familiar inverse-square weakening of gravity is admissible if and only if space has three dimensions. The result is purely structural: it assumes no field equations, force laws, or phenomenological inputs. Newtonian gravity and general relativity appear only as realizations of admissible structure, not as axioms.