Theoretical Prediction of Modular Geometry in Quantum Decoherence: A Pre-experimental Study

Takagi, Takayuki · Zenodo (CERN European Organization for Nuclear Research) · 2025

Theoretical Prediction of Modular Geometry in Quantum Decoherence 🎯 Overview We present a theoretical prediction for the behavior of quantum decoherence in GHZ states based on modular geometry. 📐 Core Hypothesis We hypothesize that the structural constant λ₃, extracted from GHZ state fidelity, follows an elliptic integral scaling: $$\lambda_3(x) = \frac{3}{8[K(\sqrt{x})]^2}$$ where: K is the complete elliptic integral of the first kind x = 1 - F is the decoherence parameter F is the GHZ state fidelity 🔺 Triangle Correspondence This function connects three fundamental domains: Domain Connection Ramanujan Modular forms and 1/π series LCFT c = -2 logarithmic conformal field theory GHZ/FSIG Quantum entanglement geometry ⭐ Key Constant In the ideal limit (x → 0), we recover the fundamental structural constant: $$\lambda_3^* = \frac{3}{2\pi^2} \approx 0.152$$ derived from the volume of the 3-sphere: Vol(S³) = 2π². 📊 Predictions We predict specific experimental values for 7 measurement points across x ∈ [0.02, 0.40]: x F λ₃ (predicted) 0.02 0.98 0.15046 0.05 0.95 0.14815 0.10 0.90 0.14423 0.15 0.85 0.14024 0.25 0.75 0.13196 0.35 0.65 0.12324 0.40 0.60 0.11869 🔬 Experimental Verification This prediction is scheduled to be tested on IBM Torino (127-qubit Heron processor) in January 2026. Model discrimination will use AIC/BIC criteria to distinguish the elliptic model from linear noise approximations. ⚠️ Version Note Version 1 (December 2025): Pre-experimental prediction Version 2 (Expected January 2026): Experimental verification 🔗 Related Works TSTT Classical-Quantum Correspondence: doi:10.5281/zenodo.17388273 TSTT Quantum Experiments V3.2: doi:10.5281/zenodo.17589109 TSTT V3.3 Soul of Formal Causation: doi:10.5281/zenodo.17620967 Structural Gravity (Galaxy Rotation): doi:10.5281/zenodo.17839846 Keywords: Quantum Information, GHZ State, Ramanujan, Modular Forms, Logarithmic CFT, Decoherence, Elliptic Integrals, IBM Quantum

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