Closure, Circulation, and the Assertion of Space: A Vector-Integral Foundation of Mass in Closed Surface Theory

This paper reformulates the origin of mass and space from the standpoint of closed surface theory, using vector calculus and surface integrals. It posits that mass is not a fundamental substance but arises from incomplete vector interference over closed surfaces—specifically, when the line integral of a vector field over a loop does not vanish (∮A ≠ 0). In this framework, space is asserted only where vector closure fails, while complete interference (∮A = 0) corresponds to vacuum. The theory distinguishes between scalar fields (distributed patterns on equipotential surfaces) and vector fields (normal directional force flows), and offers a unified geometric model in which mass, volume, and space emerge from the degree and direction of interference imbalance. This approach provides a mathematically rigorous yet intuitively visualizable structure that connects mass generation to topological and geometric properties of physical fields. Author: Tetsuo Konno(今野哲夫) https://orcid.org/0009-0002-1842-7865