Parameter-Free SymPy Verification of the Cosmological Constant from First Principles in the CSU Framework

This supplementary software package contains the complete symbolic validation suite for the Chrono-Singularity Unification (CSU) framework's derivation of the cosmological constant. Written in Python and utilizing the SymPy library for rigorous symbolic mathematics, the script (validate_cosmological_constant_symbolic.py) computationally verifies the framework's parameter-free derivations.

The package mathematically validates the "Dual Pathway" convergence, confirming that both the Information-Theoretic pathway (via binary quantization and CFT trace anomaly) and the Topological pathway (via Gauss-Bonnet Euler characteristic and Riemann zeta Casimir energy) independently converge to the exact vacuum spectral weight of wvac=25/12w_{vac} = 25/12wvac=25/12. Furthermore, it computationally verifies the derivation of the dark energy density (ΩΛ=25/36\Omega_\Lambda = 25/36ΩΛ=25/36), the dimensionless cosmological constant (ΞΛ\Xi_\LambdaΞΛ), the equation of state (w=−1w = -1w=−1), and the proposed resolution to the Hubble tension. The included documentation and code provide a fully reproducible, parameter-free verification of the mathematical claims made in the main and supplementary CSU papers.