What question did this study set out to answer?

To develop a method for measuring semantic stability in AI communication using the TRS v2.3 framework.

January 14, 2026Open Access

Semantic Relativity Theory v2.3: Topological Stability through Euler-CHORDS++ Integration

Key Points

To develop a method for measuring semantic stability in AI communication using the TRS v2.3 framework.
Integrated Euler topological invariants with CHORDS++ framework.
Evaluated 303 instances of 101 texts using 3 large language models (LLMs).
Calculated Euler characteristic to quantify stability.
Euler characteristic values between 2 and 6 indicated differences in text stability.
Stable texts had χ=2 and comprised 55% of evaluations, while collapsing architectures had χ=6 at 23%.
The study established IRP-χ coupling for predicting semantic mass and strength.

Abstract

Semantic Relativity Theory posits meaning as field phenomenon exhibiting observer- dependent curvature in AI-mediated communication. While prior iterations established conceptual foundations, operational measurement remained limited to basal structural assessment. This paper presents TRS v2.3, integrating Euler topological invariants with CHORDS++ multidimensional framework to quantify semantic stability. The evolution from CHORDS/CS through CHORDS+ revealed critical limitation: high-scoring texts collapsed under paraphrastic stress, indicating measurement captured surface adequacy but not architectural resilience. CHORDS++ resolution—decomposing dimensions into basal, structural, and expressive subfactors with curvature and tension metrics—enables Euler characteristic (χ) calculation as stability indicator. Empirical validation across 303 evaluations (101 texts × 3 LLMs) demonstrates χ ∈ 2,6 discriminates stable (χ=2, 55%) from collapsing architectures (χ=6, 23%). Integration with Intent Resistance Parameter (IRP) establishes predictive framework: IRP-χ coupling quantifies semantic mass and gravitational field strength. TRS v2.3 closes measurement gap between theoretical predictions and empirical validation, providing operational toolset for AI content assessment, editorial quality assurance, and cross-model stability analysis

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