Numerical Analysis of Collatz Conjecture: Identified 90,902-Digit Integrity Deficit using CUDA HPC

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:

  • Methodology: Application of Baker’s Theorem on linear forms of logarithms to bound the escape velocity of the sequences.

  • Computational Approach: Multi-precision arithmetic implementation on GPU to avoid standard floating-point rounding errors.

  • 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)

GitHub - duirk/Numerical-Analysis-of-Collatz-Conjecture-Identified-90-902-Digit-Integrity-Deficit-using-CUDA-HPC · GitHub I leave the codes in case you want to discover and analyze it in more detail :)