Universal Topological Convergence: A Z30 Modular Partition of the Cosmic Energy Budget Derived from Heterotic String Compactification

Standard \( \Lambda \)CDM cosmology successfully parameterizes the universe but lacks a first-principles derivation for its energy density components (\( \Omega_c, \Omega_b, \Omega_\Lambda \)). Following recent work on arithmetic interferometry and topological phase structures, we propose the hypothesis of \( \textit{Universal Topological Convergence} \). We postulate that the modular properties of the finite field \( \mathbb{Z}_{30} \) govern stability across scales from quantum to cosmological. We derive a modified Einstein-Hilbert action where the cosmic energy budget is partitioned by algebraic topology: Dark Matter corresponds to the stable coprime generators (\( \phi(30)/30 \approx 26.67\% \)), Baryonic Matter to the surface gauge coupling (\( 2\pi\alpha_{\text{eff}} \approx 4.9\% \)), and Dark Energy to the modular residue (\( \approx 68.43\% \)). We validate this model against Planck 2018 data (agreement \( <0.4\sigma \) across all components) and perform a rigorous \( \chi^2 \) analysis using the Pantheon Sample of 1048 Type Ia Supernovae. The topological model achieves a superior fit (\( \chi^2_{\text{Z30}} = 1040.49 \) vs \( \chi^2_{\Lambda\text{CDM}} = 1041.36 \)) while using fewer free parameters, yielding a decisively better Bayesian Information Criterion (\( \Delta\text{BIC} = -7.87 \)). This suggests that the universe operates as a base-30 modular system where the cosmic composition emerges from string-theoretic number theory rather than environmental fine-tuning.