Z4DP VII: Detection of Extraterrestrial Biosignatures - Methodology of Phase Resonance Analysis and Planetary Vortices in a Superfluid Vacuum

This paper extends the Z4DP theory, which models the cosmic vacuum as an elastic superfluid continuum, by introducing an exact methodology for detecting astrobiological signatures. Standard spectroscopic methods for finding extraterrestrial life rely on chemical markers in exoplanetary atmospheres, primarily around red dwarfs (M-stars). Z4DP, in contrast, defines life as a macroscopic harmonic oscillator that actively exerts mechanical stress on the surrounding medium. This paper mathematically formalizes matter as a stationary node of dynamic equilibrium, defines the formation of a planetary vortex, and presents a computational methodology utilizing the Biological Resonance Index (IZ4DP) with the application of a topological prominence filter in the frequency spectrum (FFT). The methodology is subsequently applied to proxy data of the stable Tau Ceti system (G8V), where it successfully identifies coherent phase resonance. To verify the robustness of the algorithm, a stress test was conducted on the multi-planetary system TRAPPIST-1 (M8V). The results exactly demonstrate that the extreme eruptive activity of red dwarfs destroys the phase integrity of the continuum, making the existence of a stable biological oscillator in such systems physically impossible. The Z4DP model thus offers a fundamentally new physical approach to the search for exolife, independent of chemical markers, computationally highly efficient, and clearly favoring stable G-type stars.