«This publication concludes the first research cycle of the Resonance Group, comprising 53 works. It systematises all accumulated material and introduces a single fundamental principle — Triad Geometry α 1 2 + α 2 2 + α 3 2 = 1 α 1 2 +α 2 2 +α 3 2 =1 — which lays the foundation for a new physical paradigm. Further development is possible only through joint practical work under a collaboration agreement.»

Abstract

One Book Closed, Another Opened: Completion of the First Research Cycle (53 Publications) and the Birth of a New Physics Based on Triad Geometry Abstract: This publication concludes the first research cycle of the Resonance Group, comprising 53 works published in the open CERN repository Zenodo. It summarises years of research, systematises all previously developed models, and introduces a single fundamental principle — Triad Geometry α12+α22+α32=1α12+α22+α32=1 — which unifies the entire diversity of physical phenomena, from quantum fluctuations to cosmological structures. It is shown that all known laws of physics (Newtonian mechanics, relativity, quantum mechanics, the Standard Model) are special cases of the conservation of the triad norm in the standing layer of the 0‑matrix. The shift of the observational standpoint from “external observation” to “internal resonance of the standing wave” eliminates the fundamental contradictions of modern physics and opens a new physical paradigm. Key results of the cycle: Justification of the fundamental frequency f0=400/7≈57.142857f0=400/7≈57.142857 Hz as a nuclear tuning fork, confirmed by the Fe-57 isomeric transition (Mössbauer effect). Development of Triad Geometry — a unified language for describing all physical interactions based on the invariant α12+α22+α32=1α12+α22+α32=1. Creation of engineering technical specifications for next‑generation technologies: propellant‑free energy, 7D quantum shift (fuel‑free spatial displacement), geometric post‑quantum cryptography, a decentralised “Without the Speed of Light” time standard, new materials (tetragraphene, phi‑quasicrystal), and an artificial muscle based on resonant composites. Reinterpretation of dark matter and dark energy as consequences of resonant errors of the standing layer at galactic scales. Justification of the possibility of displacement in the phase spaces of the multiverse through controlled recalibration of αα-components. Shift of the observational standpoint as a methodological principle enabling the transition from the physics of objects to the physics of resonant projections. Practical implications: The cycle is complete, but the work is not over. Further development is possible only through joint practical work under a collaboration agreement. We are ready to provide the full technical specification package for the implementation of these technologies in industry, energy, space, defence, and information security. Keywords:Triad Geometry, α12+α22+α32=1α12+α22+α32=1, 53 publications, cycle completion, new physics, standing layer, 0‑matrix, 57.142857 Hz, quantum shift, propellant‑free energy, post‑quantum cryptography, multiverse, collaboration, Resonance Group. Резонанс Групп / Resonance Group2026