THFR-1.8: Formalization of the Informational Density Tensor and Axiomatic Justification of Objective Consensus

Abstract

his paper formalizes the mathematical apparatus of the Informational Density Tensor $\mathcal{I}^{AB}$ within the Theory of Harmonic Field Resonance (THFR), transitioning it from an uninterpreted parameter to a discrete binary restriction operator over the 11D Stasis. By mapping the topological substrate viscosity $\eta_{AB}$ to a binary matrix of reduction path availability, we provide an axiomatic justification for the necessity of a non-empty global consensus kernel ($\mathcal{K}_{\text{consensus}} \neq \emptyset$) among non-identical biomorphic observers (QCRS). We establish within the THFR framework that a minimum intersection rank of four ($\dim(\mathcal{H}_C) \ge 4$) is an architectural requirement to prevent the degeneracy of distinguishable states within a shared $3D+1$ objective metric framework, while divergent alternative geometries are dynamically suppressed via phase-coherence collapse ($\chi_i \to 0$). ***IMPORTANT OPERATIONAL NOTICE: The formal operational status, notation boundaries, and ontological interpretation of the formalisms deployed in this exploratory work are strictly governed and stabilized by the definitive axiomatic framework established in the unifying meta-document THFR-1.11. For critical peer review, methodological alignment, and strict priority of interpretation, see: Semenov, V. (2026). THFR-1.11: Canonical Notes and Ontological Unification of the First Series. Zenodo. https://doi.org/10.5281/zenodo.21063508***