Three Spectral Results for the Dimensional Stability Problem in IDT

This preprint establishes three analytical results (C47–C49) within Information-Dynamic Theory (IDT), connecting dimensional stability, spectral soft modes, and divergence of physical time. The work provides a closed theoretical chain:Φ → λ → M → t The results show that:- bound states exist for 2 < d < 4,- a soft mode appears at d = 4,- structural inertia diverges as M(d) ~ 1/(4−d),leading to time freezing at d = 4. Together with the previously established D3 result, this yields a selection mechanism for d = 3. Experimental validation is proposed via a separate protocol based on the test:τ · f_g(P)^2 = const.