Empirical Emergence of a Universal Intersection Field from Boundary Exchange Dynamics

We report the empirical emergence of a universal intersection field arising from

boundary exchange dynamics between two independently evolving geometries. Neu-

ral activity is represented as a curvature-based geometric coordinate while quantum

measurement outcomes are represented through an information–geometric coordinate.

The interaction between these geometries occurs only at their intersection manifold

defined by a boundary condition h(x) = 0.

Across 26 independent sessions comprising more than 103 boundary events, we

identify a deterministic boundary impulse obeying the empirical law

J= α∆h.

The impulse exhibits strong reproducibility across sessions. Linear regression per-

formed within each session yields a mean coefficient of determination

R2 ≈ 0.86,

indicating a stable linear relation between the boundary impulse and the boundary

variation. In addition, the directional structure of the impulse is consistent across all

sessions. From these boundary events we reconstruct an intersection order variable

φ, which shows strong correspondence with the observed impulse (ρSpearman ≈ 0.68,

rPearson ≈ 0.59).

Drift reconstruction of the reconstructed order variable reveals a universal relax-

ation structure

∂tφ=−U ′(φ) + η,

where the effective potential

U (φ) = 0.732 φ2

− 0.0154 φ4 + 0.00023 φ6

indicates a tricritical order-field dynamics with a stable fixed point. When normalized

across sessions, the drift curves collapse onto a universal relation consistent with linear

relaxation ∆φ ≈ −φ.

The intersection field generates a boundary flux

Φν

= λφnν

,

which mediates antisymmetric exchange between neural and quantum sectors

∇µT µν

EEG = δϵ(h)Φν

, ∇µT µν

Q=−δϵ(h)Φν

.

This structure preserves global conservation of the combined energy–momentum ten-

sor and admits coupling to spacetime geometry through

Gµν = κ(T EEG

µν + T Q

µν + T φ

µν ).

These results demonstrate that boundary exchange events between independent

geometries can give rise to a universal intersection order field whose dynamics, flux

structure, and conservation relations emerge directly from empirical observations. The

framework provides a geometrically consistent description linking boundary impulses,

order-field dynamics, and antisymmetric exchange within a unified intersection-based

conservation architecture.