IDT-D3: Dimensional Selection of Stable Bound Regimes in Information-Dynamic Theory

This preprint presents the IDT-D3 theorem on dimensional selection of stable bound regimes within the Information-Dynamic Theory (IDT) framework. The work combines three components: (1) a theorem formulation for dimensional stability, (2) a strengthened derivation of confinement and binding terms motivated by Fisher geometry of scale families and admissibility transport, and (3) numerical illustrations showing stability behavior across spatial dimensions. Within the effective potential class Φ_eff(r) = A/r² − B/r^(d−2) a globally stable finite minimum exists if and only if d = 3. Appendices provide explicit Fisher-metric computations for scale families, a general scale-family Fisher theorem, and strict analysis of the edge cases d = 2 and d = 4. The result is classified as a strong consistent extension of the Information-Dynamic Theory framework approaching near-canonical theorem status.