On the Analysis of Coexistence Relations of Envelope Surfaces

Within the envelope surface framework, particles of the same type in different environments (such as electrons on Earth and electrons on Mars) are not two independent entities, but coexistent outputs of the same parent envelope surface under the same set of generating equations at different values of the projective coupling factor x. This paper systematically analyzes the coexistence relations of envelope surfaces: defines the mathematical structure of coexistence relations, demonstrates the homology between coexistence and nesting relations, and points out that coexistence is the parallel reading of the same parent envelope surface at different x values, rather than spatially juxtaposed entities. The paper also discusses the implications of coexistence relations for the concept of "fundamental constants" — constants are not properties of the universe, but readings of the envelope surface at specific x values.