Direct Self-Semantic Fixed Points: Intrinsic Diagonal Claims Against Final Internal Self-Theories Paper 52 of the NEMS Suite
Year: 2026
Type: preprint
Abstract: Paper 51 proved that no sufficiently expressive diagonally capable reflexive system can internally contain a final theory of its own realized semantics . That theorem was established by reducing the final self-theory to a total decider and importing the SelectorStrength barrier. The present paper upgrades the result into an intrinsic theorem: we construct the contradiction directly inside the self-semantic framework itself. We introduce semantic negation on claims, a self-reference frame for code-level fixed points, and anti-verdict claims of the form "(T) does not say yes on (c)." Under these hypotheses, we prove that there exists a fixed-point code (d) such that (\Decode(d)) is semantically equivalent to the anti-yes claim for (T) on (d). A putative final self-theory must then correctly settle this fixed-point claim; a case split on its verdict yields contradiction in every branch. The result is therefore self-generated by the self-semantic framework rather than only by reduction to external barrier machinery. We derive direct no-weak-self-erasure and no-strong-self-erasure corollaries. The development is mechanized in Lean 4 as the SemanticSelfReference library in reflexive-closure-lean. The direct theorem is bridged back to the general self-reference calculus of Paper 26. Primary Lean anchors: self_semantic_fixed_point_exists, direct_no_final_self_theory (). Trust boundary. Checked in reflexive-closure-lean with dependencies on nems-lean; kernel + pin + imports as usual. Narrative claims about "intrinsicity" are conceptual, not separate theorem declarations.
Author: Spivack, Nova
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7150164660
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