  A method allowing studies of the hadronic matter at the early evolution stage
in A+A collisions is developed. It is based on an interferometry analysis of
approximately conserved values such as the averaged phase-space density (APSD)
and the specific entropy of thermal pions. The plateau found in the APSD
behavior vs collision energy at SPS is associated, apparently, with the
deconfinement phase transition at low SPS energies; a saturation of this
quantity at the RHIC energies indicates the limiting Hagedorn temperature for
hadronic matter. It is shown that if the cubic power of effective temperature
of pion transverse spectra grows with energy similarly to the rapidity density
(that is roughly consistent with experimental data), then the interferometry
volume is inverse proportional to the pion APSD that is about a constant
because of limiting Hagedorn temperature. This sheds light on the HBT puzzle.
