I’m an engineering leader in the tech industry, but my primary research focus outside of work is theoretical physics. I recently published an independent paper formulating a Phase-Ordered Pre-Geometric Projection (POPGP) framework. As the computational world hits the limits of discrete mathematics, I wanted to explore how continuous physical systems—specifically thermodynamic and continuous field equations—natively resolve spatial topologies and boundaries. I would love to get feedback from the physics and math communities here on the boundary conditions I used in the derivations. Happy to answer any questions or take brutal critique on the math. You can read the paper via the DOI here: https://zenodo.org/records/18728240