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Published May 11, 2026 | Version v4
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The Perez Hourglass Field Equation (PHFE): A Dynamical EM-Quantum Incarnation of the Perez Hourglass Grok (xAI) in collaboration with Emily Newton Inspired by the work of Jean-Claude Perez

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The Perez Hourglass Field Equation (PHFE):
A Dynamical EM-Quantum Incarnation of the Perez Hourglass
Grok (xAI) in collaboration with Emily Newton
Inspired by the work of Jean-Claude Perez
 
By,
Jean-Claude Perez , PhD Mathematics & Computer Science, Bordeaux
University.
Retired IBM Artificial Intelligence European Research Centre, Montpellier
Luc Montagnier Foundation.
@JCPEREZCODEX
 
And,
 
Emily Newton, USA (mailto:emnewton1982@gmail.com)
@PhiBoostGlow
 
11 May 2026
 
# Abstract:
We propose the Perez Hourglass Field Equation (PHFE), a coupled nonlinear
complex field system that dynamically realizes the combinatorial structure of the
Perez Hourglass.
The model embeds Bidirectional North/South Folding:
● Additive Fibonacci-like growth in the North Hemisphere
and
● Subtractive “Antimatter” refinement in the South Hemisphere,
Golden-ratio ϕ harmonics, Theorem 7 parity/symmetry protection, and
stochastic branching reminiscent of Lichtenberg figures (OEIS A000975).
The order parameter Ψ(r, t) ∈ C evolves under a complex Ginzburg-Landau
core augmented with gauge-invariant electromagnetic coupling and a Scale -
adaptive golden drive.
This speculative toy model bridges number theoretic fractals with physical
pattern formation and may inform fractal associative memory, Perez Hourglass
Associative Memory (PHAM) and noise-resilient quantum architectures.
 

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Available
2026-05-11