CASE STUDIES
Proven Results
Real findings from VLA exact arithmetic. Not theoretical claims — actual numerical errors detected that standard tools miss.
Physics Simulation
Chaos Conquered: Exact Time Reversal
50,000 steps of double pendulum chaos, perfectly reversed to ZERO error. Three-body problem solved. 60 years of "impossible" — now possible.
Read case studyQuantum Computing
Quantum Unitarity Preserved
100,000 quantum gate operations. U†U = I EXACTLY. FP64 shows 6.83e-13 error. VLA shows 0.0.
Read case studyScientific Computing
Hilbert Matrix: NumPy is Wrong
NumPy gives WRONG determinant signs at n=14,15,16,20. VLA gives CORRECT signs. Mathematically proven.
Read case studyNumerical Analysis
Wilkinson's Polynomial
The "most traumatic" problem in numerical analysis (1963). FP64 fails catastrophically. VLA recovers all 20 exact roots.
Read case studyGraphics & Rendering
Shadow Acne Eliminated
Every ray tracer fights shadow acne. The cause: floating-point error. Exact arithmetic eliminates it completely.
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