Attractor-Driven Shape Universality in a Minimal Late-Time Interacting Dark Sector

Key Points

• The research aims to identify the dynamical origins of shape universality within a minimal late-time interacting dark sector.
• Establishing attractor-driven fast–slow reduction methodology
• Utilizing numerical simulations to demonstrate shape universality
• Applying PCA (Principal Component Analysis) for dimensional reduction
• Calculating amplitude activation flow characteristics
• Mapping growth dynamics using reduced growth mappings.
• Achieved shape universality with L² residuals less than 0.5%
• PCA reduction demonstrated efficiency with a score of 98.8%
• Determined amplitude activation flow approximation at dA/dN ≃ 1.32 A^0.67
• Verified reduced growth mapping R(z) as approximately 1 − α(z)A.