Empirical Analysis of Record Collatz Peaks for Prime Initial Values - version 2

An Empirical Upper Logarithmic Boundary in Collatz Peak Growth (Kazakov Envelope) The purpose of this study is to investigate the geometric structure of record peak growth in Collatz trajectories for prime initial values up to 10^6. While the Collatz conjecture concerns convergence to 1, this work focuses instead on transient amplification behavior and record maxima. The central question is whether peak growth exhibits structural regularity when observed under logarithmic scaling. All prime numbers p ≤ 10^6 were enumerated using a sieve method. For each prime p, the full Collatz trajectory was computed deterministically until reaching 1. The maximum value encountered in the trajectory was recorded as Peak(p). Record peaks were defined as values exceeding all previous Peak values in increasing order of p. All visualizations were performed in (log p, log Peak(p)) space.