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This research aims to create a real-time functional-integral framework for stochastic neural fields using the Henstock-Kurzweil integral.

August 2, 2026Open Access

Henstock–Kurzweil Path Integrals for Stochastic Neural Fields: A Machine-Verified Real-Time Framework

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Real-time framework develops a gauge integral for stochastic neural fields, highlighting cognitive transitions in biological systems.

This research aims to create a real-time functional-integral framework for stochastic neural fields using the Henstock-Kurzweil integral.
Developed a real-time gauge integral approach for stochastic neural fields.
Applied it to the subjective-centered model of Titov involving neural field dynamics.
Proved convergence of time-sliced approximants to the exact propagator satisfying the Fokker-Planck equation.
Obtain a closed-form partition function and two-point correlation for the neural field model.
Identify cognitive transition probability as a one-dimensional Gaussian tail.
Formalize all findings in the Lean 4/Mathlib framework, ensuring error-free proofs.

Berdinsky et al. (2026) studied this question.

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