A logarithmic-Quadratic Upper-Bound conjecture for Odd Collatz Trajectories

This research note proposes a logarithmic-quadratic upper-bound conjecture for the maximum odd value occurring in forward Collatz trajectories. Extensive exact-integer computations provide supporting evidence, including exhaustive testing of all odd starting values from 3 to below one billion and additional large-integer tests. The proposed bound remains a conjecture and is not presented as a proof of the Collatz conjecture.