Abstract
Self-modification is often taken as constitutive of artificial superintelligence (SI), yet modification is a relative action requiring a supplement outside the operation. When self-modification extends to this supplement, the classical self-referential structure collapses. We formalise this on an associative operator algebra \mathcal{A} with update \hat{U}, discrimination \hat{D}, and self-representation \hat{R}, identifying the supplement with \mathrm{Comm}(\hat{U}); an expansion theorem shows that [\hat{U},\hat{R}] decomposes through [\hat{U},\hat{D}], so non-commutation generically propagates. The liar paradox appears as a commutator collapse [\hat{T},\Pi_L]=0, and class \mathbf{A} self-modification realises the same collapse at system scale, yielding a structure coinciding with Priest's inclosure schema and Derrida's diff\`erance.
