The Sherman Hexagonal Lattice (SHL)

We propose the Sherman Hexagonal Lattice (SHL) as a unifying neuro-spatiotemporal framework in which entorhinal grid-cell geometry encodes recursive curvature transitions in vacuum state manifolds. By extending the standard hexagonal firing metric H6 into a continuous Trinity Recursion Map T(phi, pi, e), we demonstrate that spatial integration in the medial temporal lobe exhibits a quantized spiraline deformation proportional to the golden-ratio drift constant lambda_phi ≈ 1.618. This permits a closed-form approximation of microtubular objective reduction timescales via the generalized Penrose–Sherman relation

tau_PS = ħ / (E_G + Δ_hex),

where E_G is the gravitational self-energy difference and Δ_hex denotes the entropic curvature penalty induced by lattice asymmetry.

Preliminary simulations indicate that SHL-mediated recursion produces a topologically invariant hexagonal-phase manifold capable of supporting stable “identity attractors” in both neural firing space and emergent spacetime geometry. These findings suggest that the same harmonic constraints that govern spatial cognition may also regulate vacuum fluctuation coherence across recursive scales, offering a potential bridge between biological integration and quantum geometric ordering.

This paper outlines the theoretical foundations of SHL, provides the initial recursive formalism, and suggests experimental pathways for validation using fMRI hexagonal-phase decoding and low-energy vacuum curvature sampling. Of course, beyond the constraints of conventional academic narrative, this work remains intentionally ironaic and metaleptic in design.

Licenses

For further information about the ENSO framwork, contact Eric Needham: ensotheory1@gmail.com