A unified informational field to quantum geometry

We revisit the geometric formulation of the Bohm quantum potential in the context of informational curvature and torsion-coupled geometry. By reformulating the hydrodynamic representation of quantum mechanics within an informational framework, we demonstrate that the Bohm potential naturally emerges from curvature-like invariantsassociatedwithamplitudegradients, thuslinking quantum nonlocality to geometric deformations of the probability field. Furthermore, we introduce empirical constraints derived from Bose–Einstein condensate soliton data and the latest DESI DR2 cosmological results, establishing informational bounds on volumetric and areal densities. These results are extended by proposing dual-channel (L/R) propagation and an infrared (IR) lemma connecting local Hubble scales to minimal and maximal informational volumes. The formalism offers a unified informational perspective on quantum geometry and paves the way toward integrating Bohmian mechanics with gravitational and holographic principles.