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This research aims to propose a unified framework for understanding matter and gravity through advanced mathematical structures.

March 15, 2026Open Access

Resonant Topological Wave Model of Matter v1.1

Key Points

This research aims to propose a unified framework for understanding matter and gravity through advanced mathematical structures.
Introduced a non-linear resonant medium framework for matter emergence as topological solitons.
Identified the vacuum with the S7 manifold, where the Standard Model gauge group naturally appears.
Explained baryons as Skyrmion-type solitons and derived proton scales from quaternionic embeddings.
Revealed dark energy as 'phase pressure' to maintain vacuum constraints.
Emergence of gravity as a metric of the wave medium helps resolve the vacuum catastrophe.

Abstract

Resonant Topological Wave Model of Matter (v1.1)This paper proposes a unified framework where matter emerges as stable topological solitons of a non-linear resonant medium. Key Scientific Breakthroughs:- Vacuum Ontology: The vacuum is identified with the S7 manifold (unit octonions), where the Standard Model gauge group SU(3)xSU(2)xU(1) emerges naturally as a symmetry subgroup.- Baryon Structure: Baryons are interpreted as Skyrmion-type solitons. The proton scale is derived from the quaternionic embedding H ⊂ O (S3 ⊂ S7).- Fermion Generations: Origin of the three generations is explained as radial excitations of the soliton state.- Dark Energy & Gravity: Dark Energy is revealed as "phase pressure" required to maintain the S7 vacuum constraint. Gravity emerges as an effective metric of the wave medium, resolving the vacuum catastrophe through coherent filtration.

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