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March 31, 20260 citationsOpen Access

The Logos Made Code: Analogical Compression and the Limits of Self-Audit

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MBMartin Brodeur

Key Points

  • This research explores the limitations of self-audit in LLMs due to the nature of analogical compression.
  • Utilized orthogonal probing to identify failures in a production system.
  • Compared failure detection rates of orthogonal probing and same-axis self-audit.
  • Applied persistent homology to analyze failure classes and identify significant topological features.
  • Structural theories like Tarski undefinability and Rice's theorem were examined.
  • Orthogonal probing discovered approximately 4-5 times more failures (80%) compared to self-audit (20%).
  • Identified 20 significant topological loops from persistent homology analysis.
  • Implemented 85 deterministic validators and 524 end-to-end tests confirming findings.

Abstract

Preprint. Orthogonal probing discovers roughly 4–5× more failures than same-axis self-audit (~80% vs ~20%) in a 350,000-line production system. We argue this asymmetry reflects a structural limit: LLMs trained via analogical compression cannot audit their own compression manifold from within. Formalized via Tarski undefinability and Rice's theorem. Persistent homology on 58 documented failure classes yields β₁ = 20 significant topological loops. Production reference implementation: 85 deterministic validators, 524 E2E tests, 8-axis probe framework.

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Cite This Study

Martin Brodeur (2026) studied this question.

synapsesocial.com/papers/69cb6589e6a8c024954b9932https://doi.org/10.5281/zenodo.19302031
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1The Logos Made Code: Analogical Compression and the Limits of Self-Audit2026
  2. 2The Logos Made Code: Semantic Manifold Coverage and the Geometry of LLM-Generated Entropy2026
  3. 3The Logos Made Code: Orthogonal Probing and the Geometry of LLM Entropy2026
  4. 4Orthogonal Probing and the Geometry of LLM Entropy: Empirical Evidence for Axis-Rotation Auditing of LLM-Generated Artifacts2026
  5. 5Orthogonal Probing and the Geometry of LLM Entropy: Empirical Evidence for Axis-Rotation Auditing of LLM-Generated Artifacts2026