Published May 16, 2026 | Version v8
Preprint Open

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

Authors/Creators

Description

The Perez Hourglass Field Equation (PHFE):
A Dynamical EM - Quantum Incarnation of the Perez Hourglass

Emily Newton, in collaboration with James Lockwood,
illustrated by Christophe Chauprade, inspired by the work of
"Jean-Claude Perez".
With Addendum & Erratum & Patch & Code confirmed & Fix

By,
Jean-Claude Perez , PhD Mathematics & Computer Science, Bordeaux
University.
Retired IBM Artificial Intelligence European Research Centre, Montpellier
Luc Montagnier Foundation.
jeanclaudeperez2@gmail.com ( mailto:jeanclaudeperez2@gmail.com)
@JCPEREZCODEX
ORCID https://orcid.org/0000-0001-6446-2042

And, Emily Newton, USA (mailto:emnewton1982@gmail.com), @PhiBoostGlow

And, James Lockwood, USA ( mailto: spectralityworkinggroup@gmail.com ),
@QBlazedog61029J
 
16 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
2026-05-12