HDC-CBC/ER ER = ERP: An Effective Geometric Interpretation of the Correlational Structure

Preface — HDC–CBC/ER This document forms part of the Supplementary Structural & Interpretative Program (SSIP) of the HDC–CBC / CBCₜ framework. Its purpose is not to introduce new dynamics, new degrees of freedom, nor to modify the formal structure of the model, but to clarify the interpretative status of a possible geometric reading of the non-local correlational structure already present in the framework. The motivation for this volume arises from conceptual dialogue with the equivalence ER = EPR, formulated in its modern version by Maldacena and Susskind within the holographic AdS/CFT context. In that framework, the relation between quantum entanglement and geometric connectivity rests upon an exact duality between theories defined in different dimensions. This construction, rigorous and well delimited, has opened a broad debate regarding the role of geometry in the description of non-local structures. The present work is not situated in that context. HDC–CBC is not a holographic framework, does not presuppose Anti-de Sitter space, does not introduce boundary theories or exact dualities, and does not identify quantum states with geometries. Consequently, this volume does not propose a cosmological extension of ER = EPR, nor a reinterpretation of the AdS/CFT formalism. However, the HDC–CBC framework incorporates, from its fundamental formulation, a non-local correlational structure, integrated in a covariant, stable manner compatible with relativistic causality. This structure is present in the quantum, relativistic, and tensorial regimes of the model, and has clear physical manifestations, particularly in gravitational propagation and in the historical memory of space-time. In light of this formal closure, the objective of this SSIP is to address a subsequent and strictly interpretative question: whether such correlational structure admits an effective geometric reading, internal to the HDC–CBC framework and compatible with general relativity, without introducing new physics nor compromising the ontology of the model. This volume proposes that such a reading may be formulated through the equivalence ER = ERP, where ERP designates an Effective Relational Projection: an effective and non-ontological geometric projection of the correlational structure of the vacuum. The use of geometric language here is strictly auxiliary and controlled, and does not imply the existence of physical bridges nor fundamental connectivity of space-time. ER = ERP does not constitute an additional hypothesis of the HDC–CBC framework nor an extension of CBCₜ. It introduces no new parameters, does not modify the variational principle, nor alter the correlational dynamics already established. Its validity depends entirely on the prior consistency of the HDC–CBC corpus, as developed in volumes Q, R, P, T, O, N, and in the Ω synthesis. This text must be read in continuity with other SSIP works of the project, in particular HDC–CBC/I and HDC–CBC/CM, and not as a foundational document. Its function is to clarify and delimit, not to expand. It offers a sober and precise geometric reading framework that allows dialogue with the language introduced by ER = EPR without abandoning the principles nor the limits proper to HDC–CBC / CBCₜ.