On a Spectral Invariant of the GCA COMP Operator Related to Prime and Composite Numbers

This work presents an exploratory investigation of the COMP (geometric complement) operator within the framework of the Geometric Composition Algebra (GCA). A spectral statistical invariant, defined as an averaged ratio of geometric norms after application of COMP to all configurations associated with an integer, is introduced and studied. Extensive numerical experiments reveal a robust statistical separation between prime and composite integers, without relying on explicit factorization. Although this invariant does not constitute a primality test, it highlights a persistent geometric signature correlated with multiplicative structure. A theoretical explanation of this phenomenon is currently under development.