The Tsirelson--Interpretation Isomorphism: A Geometric and Information-Theoretic Unification of Quantum Correlation Bounds and Interpretation Reversal Criticality

The Tsirelson–Interpretation Isomorphism Overview We establish a geometric isomorphism between the Tsirelson bound of quantum correlations (|S|ₘax = 2√2) and the interpretation reversal index (Iₘax = 1) from the Judge-Shift Diagnostic Framework. Key Results Geometric Isomorphism: I = |S| / (2√2) Fisher Information Divergence: IF (I) = 1/ (1−I²) → ∞ as I → 1 Coordinate-Invariant Criticality: The divergence certifies the boundary as physical, not definitional Core Equations I = sin (2θ) I = |S| / (2√2) IF (I) = 1 / (1 - I²) Significance The result identifies a shared geometric boundary rather than a numerical coincidence. The Tsirelson bound and interpretation reversal criticality are the same constraint expressed in different coordinates. Files File Description paper3ₜsirelsonᵢsomorphism. pdf Main manuscript (10 pages) paper3ₜsirelsonᵢsomorphism. tex LaTeX source figure1ᵢsomorphism. pdf I–S isomorphism diagram figure2fisher. pdf Fisher information divergence figure3ₚhaseₛpace. pdf Phase space structure Related Works Judge-Shift Diagnostic Framework TSTT Quantum Experiments V3. 2 TSTT Quantum Experiments V3. 1 Keywords Tsirelson bound, CHSH inequality, Information geometry, Fisher information, Criticality, Boundary theorem, Interpretation reversal Author Takayuki Takagi Independent Researcher, Higashimatsuyama, Saitama, Japan ORCID: 0009-0003-5188-2314