Holistic Approaches in Mental Health and Wellness
A Spectral Analogy Between the Birch and Swinnerton-Dyer Conjecture and Cerebrospinal Fluid Dynamics
Abstract
Chur Chin
We construct a symbolic and computational analogy between the Birch and Swinnerton-Dyer (BSD) conjecture from number theory and cerebrospinal fluid (CSF) dynamics observed in neuroanatomy. Using synthetic flow data and spectral analysis on a discretized CSF model, we define a CSF L-function LCSF(s)=∑λk –s, inspired by the Hasse–Weil L-function of elliptic curves. The function’s local minima along the critical line Re(s)=0.5 mimic the statistical behavior of Riemann zeta zeroes, aligning with the Hilbert–Pólya conjecture. Numerical simulations incorporating aqueductal stenosis demonstrate a reduction in these minima, paralleling a decrease in elliptic curve rank under constraints. This framework bridges arithmetic geometry and neurofluidic topology, providing novel perspectives in mathematical neuroscience.