Two-Energy Theory (TDE 7.1) Operator Quantization, Vacuum Structure and Resonance Spectrum

This record releases TDE 7.1 as a historical working document representing a development stage of the Two-Energy Theory (TDE).TDE 7.1 focuses on an operator-level formalism: quantization of the resonance phase, vacuum structure, and a draft resonance spectrum (“phasons”). Throughout the TDE development series, mathematics has been used primarily as an exploratory tool—to probe whether the conceptual core can be expressed consistently in equations without immediate, obvious contradictions, and to test whether meaningful regularities emerge. Method transparency: in this version, derivations and calculations were generated and checked with the assistance of AI tools (ChatGPT), based on my conceptual framework, assumptions, and iterative interpretive decisions. The goal was not to claim validation, but to obtain a coherent formal scaffold that helps evaluate: whether dependencies and patterns appear, whether the parametrization is sensible, whether there are signs of data-fitting, and whether the conceptual core remains stable under quantum (operator) formulations. This release is intended to: preserve and timestamp the development path of TDE, enable independent technical review and criticism of the formalism, support conceptual understanding by showing how a formal representation was explored. Status: historical / working material. No claim of experimental confirmation is made. Disclaimer: as I am not a mathematician or professional theoretical physicist, this formalism may contain errors, simplifications, or elements requiring substantial correction. Its main value is to document the exploration process; it may help more experienced researchers formulate correct, closed equations (or clearly identify where and why a given formal direction fails).