M-r* Observation: Connection between the T0 Asymptotic Limit and the Critical Radius in Information-Dynamic Theory

This note records an observational connection between two corrected results established in the IDT T0 Correction Note (DOI: 10.5281/zenodo.20523401). The two known results are: • Critical radius at d→4:r*(4) = √e, hence r*(4)² = e • Dimensional limit:lim d→4 M(d)·(4−d) = 3e/2 The M-r* Observation: lim d→4 M(d)·(4−d) = (3/2)·r*(4)² = (3/2)·e The constant e appearing in the T0 asymptotic limit is the square of the limiting critical radius. This suggests a geometric interpretation: the divergence rate of structural inertia M(d) near d=4 is controlled by the geometry of the critical radius at d=4. Status: OBSERVATION — not a proved theorem. This is a direct algebraic consequence of two independently derived Level 5 results. The deeper question — why the T0 limit coefficient equals (3/2)·r*(4)² — remains open. Falsifiability: Any future canonical derivation of M(d) and r*(d) from IDT axioms A0–A5 must reproduce lim d→4 M(d)·(4−d) = (3/2)·r*(d→4)². If future canonical derivations produce different limiting values for M(d) or r*(d), the observation is falsified. Classification:Level 4 (Observational) Related publications: DOI: 10.5281/zenodo.20523401T0 Correction Note: Asymptotic Limit r*(d) → √e and Revised C49 Divergence Analysis (V.1) DOI: 10.5281/zenodo.20635133Information-Dynamic Theory of Stable Actualization Regimes: Conceptual Overview and Mathematical Foundations (V.2) DOI: 10.5281/zenodo.18296688IDT Programme Master Archive