From Informational Distinguishability to an Operational Test of Geometry: A Holographic Synthesis of an Emergent-Geometry Program and Yaniv Riz's Unified Informational Theory.

This work develops a quantitative bridge between Yaniv Riz's Unified Informational Theory (UiT) and holographic gravity. UiT suggests that spatial geometry reflects the capacity to distinguish configurations, while curvature modifies that capacity. On the other hand, holography (AdS/CFT) and recent work by Wang et al. show that boundary mutual information imposes bounds on bulk geometric separation, with the particular feature that classical Ryu-Takayanagi mutual information can vanish at a transition even though the geometric distance remains finite. To address this, the dimensionless diagnostic S∗QES=Ibulk/(CΔe−2ΔLren)S∗QES=Ibulk/(CΔe−2ΔLren) is introduced, where IbulkIbulk is the mutual information of quantum fields in the bulk. The paper reduces the calculation of IbulkIbulk for a free scalar field in AdS₅ to a numerical problem of Gaussian covariance matrices, explicitly deriving the mode expansions, Wightman functions, and canonical discretization required. The goal is not to prove that UiT derives holography, nor vice versa, but to formulate a falsifiable test: if the numerical result yields S∗QES≪1S∗QES≪1, this specific bridge is refuted; if it is ≳1≳1, a non-trivial quantitative correspondence would be established, requiring further theoretical interpretation. The synthesis is intentionally asymmetric: UiT provides the conceptual motivation, while holographic quantum information provides the mathematical definitions and the falsifiability criterion.