empirical purely numerical simulations understood

The gap

Supporting evidence — 5 representative gaps

• The Qur'an and Mathematics: The Dimension of Tawhid and Knowledge in the Perspective of Afzalur Rahman (2026) · doi

  Therefore, future research should focus on empirical investigations of value-based STEM pedagogy, interdisciplinary collaboration between Qur’anic scholars and scientists, and historical analyses of knowledge transmission in Islamic civilization. As a result, mathematics is not understood as a purely abstract or value-neutral discipline, but as a reflective science that reveals order, balance, and harmony as manifestations of divine unity.

  Keywords: value future focus empirical investigations based stem pedagogy interdisciplinary collaboration anic scholars scientists historical analyses
• Some new results on the security number in the Cartesian product of graphs (2026) · doi

  No computational or empirical validation is provided; the results are purely theoretical with proof-based verification rather than experimental or algorithmic testing.

  Keywords: computational empirical validation provided purely theoretical proof based verification rather experimental algorithmic testing
• Stability and Coexistence in an Improved Three-Species Predator–Prey System with Logistic Growth and Nonlinear Interactions (2026) · doi

  The model has only been validated through numerical simulations; empirical validation with real-world ecological data from actual lion, leopard, and hare populations is needed.

  Keywords: model validated numerical simulations empirical validation real world ecological actual lion leopard hare populations needed
• Riemannian Geometry in Multiplicative Analysis: Curvature, Connections, and Isomorphic Structures (2026) · doi

  No numerical validation or empirical testing of the theoretical results is provided; the paper remains purely theoretical.

  Keywords: theoretical numerical validation empirical testing provided remains purely
• Nonregular McKean–Vlasov Equations and Calibration Problem in Local Stochastic Volatility Models (2026) · doi

  No numerical experiments, simulations, or empirical validation of the theoretical results are presented in the provided excerpt.

  Keywords: numerical experiments simulations empirical validation theoretical presented provided excerpt