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

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