GlobalMOO + Meta-Calculus

Expanding Search Spaces for Pareto-Optimal Discovery

David Youssef | December 2024

VALIDATED

CASCADE Singularity Advantage

61.9%

Win Rate

CASCADE enables access to "danger zones" near physics singularities where standard MOO fails. 21-simulation proof across 10 physics domains.

13/21

Wins

93.4%

Best Gain

1/r, 1/r^2

Singularities

k=-1

Optimal

View CASCADE proof →

The Core Thesis

Meta-calculus reparameterizes the search space, enabling exploration of Pareto-optimal regions near singularities that classical methods cannot access.

Classical: Avoids singularities (numerical overflow)

CASCADE: D*[1/r] = -1 (constant) - no divergence!

Key Discoveries

CASCADESingularity Access (13/21 wins)

93.4% closer on crack tip | 83.6% on radiation | 70.9% on gravity

DOMAINS10 Physics Domains Tested

Cosmology, Fracture, Climate, Turbulence, Fusion, Molecular, CFD, QFT, GR, Quantum

OPTIMAL kk=-1.0 for power-law singularities

k=-0.5 for sqrt | k=0 when no singularity | Bigeometric calculus regularizes

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