What question did this study set out to answer?

The research aims to advance Tetrahedral Emergent Gravity by utilizing quaternions to describe the quantum vacuum and its implications for dark matter.

June 3, 2026Open Access

Tetrahedral Emergent Gravity : The Quaternion Vacuum and the Projection Paradigm (Corrected Working Draft - June 2026)

Key Points

The research aims to advance Tetrahedral Emergent Gravity by utilizing quaternions to describe the quantum vacuum and its implications for dark matter.
Proposes a model based on unit quaternions in four-dimensional division algebra H.
Utilizes the projection π: H → R³ to derive gravitational effects perceived as dark matter.
Extends previous numerical results on galactic rotation curves for validation.
Establishes a connection between the 5-cell structure in H and the tetrahedral network in three-dimensional space.
Corrects structural and formatting issues from a previous draft while enhancing ontological foundations.

Abstract

This is a corrected and improved working draft of Tetrahedral Emergent Gravity (TEG v1.1). TEG v1.1 proposes that the quantum vacuum is fundamentally described by unit quaternions in the four-dimensional division algebra H (topologically S³). The natural projection π: H → R³ discards the scalar component, generating a gravitational shadow interpreted as dark matter. The 5-cell (4-simplex) in S³ projects naturally to the tetrahedral network (z=4) observed in three-dimensional space. This version corrects structural and formatting issues present in a previous withdrawn draft. It builds upon and extends TEG v8 by providing a deeper ontological foundation while preserving all previous numerical results on galactic rotation curves. **Status:** Working Draft - Idea preservation and priority registration. Several open problems are explicitly identified. The framework remains under active development. **Keywords:** Tetrahedral Emergent Gravity, Quaternion Vacuum, Projection Paradigm, Gravitational Shadow, Dark Matter, 5-cell, Holographic Bit, Emergent Gravity, Modified Gravity

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