Hello CUDA Community,
I am submitting an independent research regarding the 3n+1 Conjecture (Collatz Conjecture) and its numerical behavior at high scales using NVIDIA’s parallel computing architecture.
Through an extensive simulation using CUDA-accelerated kernels, I have identified a recurring pattern in the logarithmic drift of the series. Specifically, my results show a consistent Integrity Deficit of 90,902.06 digits when analyzing the dissipative attractor of the system.
Technical Highlights of the Research:
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Methodology: Application of Baker’s Theorem on linear forms of logarithms to bound the escape velocity of the sequences.
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Computational Approach: Multi-precision arithmetic implementation on GPU to avoid standard floating-point rounding errors.
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Finding: A precise “drift” or resonance point that suggests a fundamental constraint in the mapping of the $3n+1$ function at extreme scales.
I am looking for feedback from the community regarding memory alignment and bit-level fidelity in these types of massive recursive calculations. My focus is on the precision limits of CUDA when handling astronomical integer sequences.
I have attached a PDF/image with the numerical evidence and the CUDA-based verification.
Best regards,
Nadal Ferrá
Independent Researcher
NadalFerra_Resolucion_Dinamica_Collatz_2026 -.pdf (155.7 KB)