Analysis of Isolation Relations of Envelope Surfaces

Within the envelope surface framework, nesting relations define the vertical transmission between hierarchies, and coexistence relations define the horizontal parallel outputs of the same parent envelope surface at different values of the environmental coupling factor x. This paper defines a third relation of envelope surfaces — isolation: when two child envelope surfaces respectively belong to different coexistent parent envelope surfaces, they have no direct nesting or coexistence relation between them, and can only be compared indirectly through a common parent envelope surface. Isolation is not physical separation, but categorical isolation at the reading hierarchy. This paper clarifies: isolation describes not "different readings of the same particle in different environments," but "different objects on different reading branches" — they share the same name, but have different origins and belong to different reading branches. This paper provides the definition, mathematical expression, relationship with nesting/coexistence, and discusses the physical implications and testable predictions of isolation relations. Keywords: envelope surface, isolation relation, nesting, coexistence, reading hierarchy, categorical isolation