This paper introduces a foundational framework that reinterprets the position of quantum correlations within the space of possible physical theories. Rather than treating the Tsirelson bound ($2\sqrt{2}$) merely as a physical restriction, this work demonstrates that it emerges naturally as the unique global optimum for systems maximizing their persistence in environments of unbounded complexity. By integrating Information Causality (IC) with the Variational Principle of Persistence (VPP), we provide a unified information-geometric explanation for why quantum correlations occupy their precise position between classical and no-signaling theories. Key Contributions & Highlights: The Quantum Boundary as a Persistence Optimum: We prove that for task distributions with unbounded support, the maximum survival probability combined with informational benefit sharply isolates $\rho = 2\sqrt{2}$ as the optimal state within the IC-constrained RAC framework. Exact Benefit–Metric Correspondence: We establish a direct identity linking the curvature of the informational benefit function to the classical Fisher information of the effective binary symmetric channel ($G'' = \mathcal{I}_F / \ln 2$). This reveals that IC is equivalent to the stability of the Fisher–Rao metric pullback under protocol concatenation, with the Tsirelson bound as the critical eigenvalue. Generalized Systemic Reduction Paradox (SRP): We identify a new optimization mechanism — a generalization of the SRP introduced in our prior VPP work — where the optimal state does not arise from classical diminishing returns (concave benefit vs. convex cost), but from a strictly convex benefit colliding with a hard viability wall, producing a corner optimum at the constraint boundary. Structural Necessity of Shannon Entropy: We demonstrate that Shannon entropy is the unique measure compatible with the concatenated RAC structure, grounded in its exclusive satisfaction of the strong chain rule. Alternatives such as Rényi entropy inherently fail to reproduce the correct quantum bounds. Significance: This manuscript bridges device-independent quantum foundations with information geometry and viability theory, offering a mathematical derivation of the Tsirelson bound as the optimal operational regime for compositional information processing under IC — within the CHSH scenario. Extensions to the full quantum correlation set remain an open question explicitly acknowledged in the paper. Reproducibility Package A reproducibility package accompanying this manuscript is available as a supplementary file. It includes a Jupyter/Colab notebook (ic_figures_colab_v3.ipynb) that reproduces Fig. 2 (Itotal vs. concatenation depth and viability horizon nmax vs. ρ) using high-precision arithmetic (mpmath, 80 decimal places) to avoid numerical cancellation near the Tsirelson point. The package also includes four CSV files containing the numerical data underlying Figs. 3–5. The notebook runs end-to-end on Google Colab with no manual configuration required.