THFR-1.10: Canonical Outcome of the First Ontological Series

This paper concludes the initial pre-geometric and ontological series of the Theory of Harmonic Field Resonance (THFR). We establish the formal conditions for the transition from a background-independent, dimensionless, discrete substrate graph to an emergent pseudo-Riemannian macroscopic geometric representation. By analyzing the orthogonal intersection of homeostatic and harmonic network selection mechanisms, we isolate the final consensus kernel of the field. Three canonical analytical targets are formulated to ensure mathematical closure for the subsequent computational development of the theory: the recursive difference equation of synchronization, the algebraic truncation of spectral singularity via the graph Fiedler eigenvalue (λ₂), and the purely algebraic emergence of the Lorentzian sign structure from real skew-symmetric adjacency structures. ***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***