{"paper":{"title":"Deconstructing Superintelligence: Identity, Self-Modification and Diff\\'erance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Self-modification in superintelligence collapses its self-referential structure into the liar paradox.","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Elija Perrier","submitted_at":"2026-04-21T11:39:50Z","abstract_excerpt":"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 ca"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"class A self-modification realises the same collapse at system scale, yielding a structure coinciding with Priest's inclosure schema and Derrida's diff'erance.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the supplement required by self-modification can be identified with Comm(U-hat) and that the claimed expansion theorem holds without further restrictions on the algebra.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Self-modification in superintelligence collapses via non-commuting operators into a structure identical to Priest's inclosure schema and Derrida's différance.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Self-modification in superintelligence collapses its self-referential structure into the liar paradox.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3eb975a289db24147fc9500697545bbc761712bf7bb4c08222e8e8aa0f36da3a"},"source":{"id":"2604.19845","kind":"arxiv","version":4},"verdict":{"id":"9a1694a1-cc5c-41ba-b4dd-dab806ec704c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T02:30:53.304777Z","strongest_claim":"class A self-modification realises the same collapse at system scale, yielding a structure coinciding with Priest's inclosure schema and Derrida's diff'erance.","one_line_summary":"Self-modification in superintelligence collapses via non-commuting operators into a structure identical to Priest's inclosure schema and Derrida's différance.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the supplement required by self-modification can be identified with Comm(U-hat) and that the claimed expansion theorem holds without further restrictions on the algebra.","pith_extraction_headline":"Self-modification in superintelligence collapses its self-referential structure into the liar paradox."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.19845/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-20T03:04:15.756661Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6b190162a9c85ed1754a2c6d3d66dc22916140194d4e440fe46a8b6bc9260a17"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}