THFR-1.7: Inter-Interface Differentiation and the Model of Partial Network Consensus in the Theory of Harmonic Field Resonance

This paper formalizes the mathematical apparatus of network interaction and nomological convergence across distinct reduction interfaces under the universal minimization of a global informational mismatch functional. Within the framework of the foundational THFR series, the partial non-identity of localized qualitative layers of the Collective Invariant Field ($\text{CIF}_1 \neq \text{CIF}_2$) is addressed by introducing a phase synchronization model over their shared invariant geometric sub-spaces, establishing the formal boundaries for a stable consensus framework ($\mathcal{K}_{\text{consensus}} \equiv \text{CIF}_{\text{global}} \neq \emptyset$). ***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***