Phase Before Probability: Why Stable Route Combination Forces a Compositional Invariant

Phase is forced by cancellation, before probability or physics enters the story. This paper continues a constructive sequence deriving only what is logically forced once incompatible closure criteria induce non-commuting stabilization operations. When distinct stabilization routes matter, a state-only description becomes lossy, but explicit route-tracking produces unbounded descriptive growth (“route explosion”). To summarize non-equivalent routes without erasing forced distinctions, the framework is compelled to introduce a contribution carrier and a combination rule. Regrouping invariance forces associativity; null contributions force an identity element; cancellation adequacy forces inverses, pushing the…