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We formalise this on an associative operator algebra $\\mathcal{A}$ with update operator $\\hat U$, difference operator $\\hat D$, and self-representation operator $\\hat R$, identifying the supplement with $\\operatorname{Comm}(\\hat U)$. A propagation theorem shows $[\\hat U,\\hat R]$ decomposes through $[\\hat U,\\hat D]$, so non-commutation propagates to self-representation. The liar paradox is the rank-one case $[\\hat T,\\Pi_L]=0$, and \\emph{class $\\mathbf{A}$} systems, in which $\\hat U$ acts on $\\hat D$, reproduce it at system scale, yielding a structure coinciding with Priest's inclosure schema and Derrida's \\emph{diff\\'erance}. Our results show that the strong self-modification taken to define superintelligence may undermine the persistent identit","title":"Deconstructing Superintelligence: Identity, Self-Modification and Diff\\'erance","url":"https://arxiv.org/abs/2604.19845","vendor":"arxiv_cs_ai"},"summary":"arXiv:2604.19845v4 Announce Type: replace \nAbstract: Self-modification is routinely treated as constitutive of artificial superintelligence (\\textbf{SI}), yet modification is a relative action requiring a \\emph{supplement} outside the operation. We formalise this on an associative operator algebra $\\mathcal{A}$ with update operator $\\hat U$, difference operator $\\hat D$, and self-representation operator $\\hat R$, identifying the supplement with $\\operatorname{Comm}(\\hat U)$. A propagation theorem shows $[\\hat U,\\hat R]$ decomposes through $[\\hat U,\\hat D]$, so non-commutation propagates to self-representation. The liar paradox is the rank-one case $[\\hat T,\\Pi_L]=0$, and \\emph{class $\\mathbf{A}$} systems, in which $\\hat U$ acts on $\\hat D$, reproduce it at system scale, yielding a structure coinciding with Priest's inclosure schema and Derrida's \\emph{diff\\'erance}. 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