Representational Incompleteness: No Self-Modeling System Can Capture Its Own Diagonal — A Machine-Checked Barrier with Six Closed Escape Routes
Year: 2026
Type: preprint
Abstract: Any system that models itself — any s : A -> A -> B whatsoever — is necessarily incomplete with respect to its own diagonal behavior: the function a |-> f(s a a) is never equal to any row s a0 of the self-model, for every fixed-point-free f : B -> B and every a0 in A. No surjective self-model of this kind can exist. This paper proves six "no-escape" routes are formally closed as machine-checked Lean 4 theorems: no surjection, no injective tower, no idempotent loop, no parametric evaluator, no diagonal row, and no representational bypass. The topological complement proves the Mobius strip is not homeomorphic to the closed cylinder, the orientability boundary of the representational incompleteness thesis.
Author: Spivack, Nova
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166320406
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