FRAMOR: Variational Structure of an Information-Weighted Metric-Affine Microgeometry

This preprint develops the variational structure of FRAMOR, an information-weighted metric-affine microgeometry positioned between the earlier FRAMOR Foundations paper (https: //doi. org/10. 5281/zenodo. 18154594) and the forthcoming FRAMOR Microtheory. The goal is to formalise the covariant and dynamical ingredients from which later phenomenological modules will be built. The construction begins with an effective-information functional Iₑff, encoding coarse-grained information content, coherence, curvature response and horizon-related information. From Iₑff arise an information current KFR and a Landauer-guard energy density that describe how information change carries energetic and geometric consequences. On the geometric side the work employs a general metric-affine Lagrangian Lgeo (g, S), where the affine connection contains torsion and nonmetricity. This keeps the formulation compatible with metric-affine gravity while allowing controlled deformations of general relativity. The full action combines Lgeo with an information-interaction sector and a Landauer-type term that penalizes variation of Iₑff along timelike congruences. A key result is a FRAMOR balance law derived from diffeomorphism invariance and generalized Bianchi identities. The usual covariant conservation of the total stress-energy tensor gains an additional information-driven contribution, leading to an entropic Bianchi-type consistency relation linking horizon information, an effective Planck scale, the information current and the Landauer-guard density. Using this structure the paper constructs non-singular FRAMOR core configurations in which a strongly information-coupled interior behaves effectively like a de Sitter region with emergent scale LambdaL = 8 pi G epsilon₀. The Raychaudhuri-Landauer subsystem provides a stable attractor mechanism, replacing curvature singularities with finite-radius cores. At cosmological scales a minimal FRW reduction is introduced in which the FRAMOR energy density rhoFR evolves according to a relaxation-type equation. This generates a time-dependent effective cosmological term in a simple covariant setting and forms the basis for later phenomenological modules developed in the forthcoming FRAMOR microtheory. An appendix outlines a four-mode Bose–Einstein condensate analogue-gravity proposal intended to illustrate how structural elements of the effective-information functional and Landauer-guard sector could be realised in a controllable laboratory setting. Overall, this Variational Structure preprint provides the covariant and variational infrastructure linking FRAMOR Foundations to the upcoming FRAMOR microtheory, where the microscopic origin of Iₑff, the core dynamics and the phenomenological windows will be developed in detail.