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Calculus Invariance
HomeProblem
MOO InvarianceFoundationsLoop Corrections
OverviewValidation Resultsk(L) Formula
Symbolic (10/10)GUD BenchmarksNegative Results (H0/S8)Spectral Gap VerifiedLog-Space Verified
Generator Discovery3D BH/NS Mergers3D Galaxy N-body3D Vortex Rings3D Plasma3D SPH Fluid3D QuantumConsumer HardwareChaos PreservationCrack Tip SingularityTurbulence VortexMolecular DynamicsRadiation Transport
CFD: Shock TubeQFT AmplitudesNumerical RelativityQuantum GeometryDual MOO Synergy
IntroductionThe BridgeCore Mathematics12-Year JourneyProofsTextbook
PapersArchiveSource Code
HomeProblem
MOO InvarianceFoundationsLoop Corrections
OverviewValidation Resultsk(L) Formula
Symbolic (10/10)GUD BenchmarksNegative Results (H0/S8)Spectral Gap VerifiedLog-Space Verified
Generator Discovery3D BH/NS Mergers3D Galaxy N-body3D Vortex Rings3D Plasma3D SPH Fluid3D QuantumConsumer HardwareChaos PreservationCrack Tip SingularityTurbulence VortexMolecular DynamicsRadiation Transport
CFD: Shock TubeQFT AmplitudesNumerical RelativityQuantum GeometryDual MOO Synergy
IntroductionThe BridgeCore Mathematics12-Year JourneyProofsTextbook
PapersArchiveSource Code

Demos

Interactive simulations and model-discovery demos for the calculus invariance framework. The corrected demo track leads with coordinate/generator selection and then shows where CASCADE-style transformed search is useful near hard regions.

Generator Discovery Lab

New

Coordinate selection, sparse dynamics, reaction log coordinates, and constraint-preserving GlobalMOO wrappers.

3D BH/NS Mergers

3D

Merger-inspired singularity-adjacent visualization with CASCADE controls.

3D Galaxy N-body

3D

Explore orbital structure and scale-dependent numerical behavior.

3D Vortex Rings

3D

Fluid vortex interaction demo with numerical stability controls.

3D Plasma

3D

Plasma field visualization for nonlinear simulation behavior.

3D SPH Fluid

3D

Particle-fluid simulation for discontinuity and shock-like behavior.

3D Quantum

3D

Quantum tunneling visualization with numerical trade-off controls.

Crack Tip Singularity

2D

Fracture mechanics benchmark near a 1/sqrt(r) stress field.

Turbulence Vortex

2D

Vortex-core benchmark for singularity-adjacent search.

Molecular Dynamics

2D

Lennard-Jones close-encounter simulation and stability comparison.

Radiation Transport

2D

Inverse-square intensity benchmark near point sources.

Consumer Hardware

Applied

Applied optimization demo for hardware trade-offs.

Chaos Preservation

Dynamics

Compare coordinate choices on chaotic system diagnostics.

Calculus Invariance Framework by David Youssef | Numerical Methods Research

GitHubSource CodeResults