The Metamorphosis Operator: Structural Self-Transcendence and the Transformation of First-Order Invariance

Every formal account of perspective, identity, and epistemic viability faces a foundational limit: the proto-differential architecture M₀ — formally, the structural constraint set that determines the admissible space of differentiation operations — appears to be invariant under the very operations it conditions. This paper argues that this limit is real but not absolute. We introduce the metamorphosis operator Ξ : (M₀, C_crit, s_ext) →M₀_min M₀', a formal account of structural self-transcendence under critical collapse conditions. We develop a hierarchical invariance structure (M₀, M₀_min, M₋₁, M₋∞) and analyze four failure modes of Ξ: Rigidity Lock, Entropic Death, Isolation Lock, and Pathological Recrystallization. The paper provides formal desiderata D1–D5 for AGI systems capable of genuine structural self-transcendence, and concludes: Identity is not the preservation of M₀ but the persistence of the minimal continuity kernel M₀_min through structural transformation.