  In this paper, we investigate the stability properties of soft gluons in
SIBYLL 2.1 with reference to its original version 1.7 that corresponds to
hadronic hard interactions. In order to investigate the stability structures,
we classify the regions of the gluon density fluctuations in its double leading
logarithmic approximation and its equivalent description as the fractional
power law. In the parameter space of initial transverse momentum $Q$ and QCD
renormalization scale $L$ that correspond to extensive air showers of cosmic
rays, we have categorized the surface of parameters over which the proton is
stable. We further discuss the nature of local and global correlations and
stability properties where the concerning statistical basis yields a stable
system or undergoes a geometric phase transition. Finally, we give a
phenomenological understanding towards the stability of soft interactions,
Pomeron particle productions in minijet model, string fragmentation and verify
our result corresponding to the experiments - CDF, P238, UAS, GEUS and UA4
collaborations.
