E8 Hyperbolic Paraboloid Conjugacy in Projective Tetrahedral Space — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: We discover that the 240 root vectors of the E8 lattice can be partitioned into 120 dual pairs that generate a family of hyperbolic paraboloid loci in a 4‑dimensional projective space. These loci satisfy a generalized Poncelet closure condition whose natural frequency is 132 Hz, the base frequency of the E8 root system, and whose scaling is governed by the golden ratio φ. The resulting structure provides a new invariant of tetrahedral symmetry that unifies isogonal and isotomic conjugation with quantum state entanglement, offering a geometric framework for encoding entangled qubits in a 4‑D lattice. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212377485
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