SPECTRAL GEOMETRY, NON-HERMITIAN TRANSPORT, AND THE MODAL DISCIPLINE OF OBJECTIVITY: a critical–propositional analysis of Francis Procaccia's Dynamically Regulated Spectral-Geometric Transport in Higher-Order Non-Hermitian Systems in confrontation with the axioms, phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras of the Theory of Objectivity

This article presents a critical–propositional analysis of Francis Procaccia’s Dynamically Regulated Spectral-Geometric Transport in Higher-Order Non-Hermitian Systems (2026), published on Zenodo under DOI https://doi.org/10.5281/zenodo.20150287, in dialogue with the Theory of Objectivity.

The analysis examines Procaccia’s unified framework for higher-order spectral geometry, dynamical stiffness regulation, and non-Hermitian Floquet transport near exceptional points. Special attention is given to the parent wave equation, the stability bound, the effective metric tensor derived from the Hessian of the spectral relation, the biorthogonal Berry curvature, the no-go theorem for symmetric driving, and the proposed mechanism of geometric transport regulated by the auxiliary field .

From the perspective of the Theory of Objectivity, the article investigates possible compatibilities and tensions between Procaccia’s model and the modal axioms of TO, especially the axioms of boundary, relational uniqueness, composition, observation, and transcendent substance. The study also articulates the analyzed paper with TO’s phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras.

The central conclusion is that Procaccia’s work does not constitute a cosmogonic theory and does not replace the complete cosmogonic theorem of the Theory of Objectivity. However, it offers a significant operational bridge with contemporary physics by showing how emergent geometry, spectral boundaries, asymmetry, relational information, dynamic regulation, and global conservation may produce observable physical effects in constituted systems.

The article assigns Procaccia’s paper a dialogue score of 7.7/10 with the Theory of Objectivity, recognizing its strong formal and operational compatibility with several TO concepts while also identifying important limits regarding ontology, cosmic origin, modal necessity, and the identification of transcendent information as atomic radiation.

This analytical text received analytical support from ChatGPT.

Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva; Francis Procaccia; spectral geometry; non-Hermitian systems; Floquet transport; exceptional points; Berry curvature; modal ontology; phenomenic elements; Inducer Effects; cosmogonic theorem; cosmological Eras; emergent geometry; relational information; atomic radiation; dynamical regulation.