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 This version corrects structural and formatting issues present in a previous withdrawn draft.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
Miguel Angel Franco León (Mon,) studied this question.