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Using the new criteria of partial photoneutron reaction cross sections reliability – special transitional multiplicity sorting functions Fi = SIG(g,in)/SIG(g,xn), ratios of correspondent partial reaction cross sections to the total neutron yield reaction cross section SIG(g,xn) = SIG(g,n) + 2SIG(g,2n) + 3SIG(g,3n) + … free from the problems of experimental obtaining of neutron multiplicity sorting – experimental data [2] obtained using quasimonoenergetic annihilation photons for 188,189Os isotopes were analyzed. From clear physical point of view absolute values of Fi must be definitely < 1.00 for i = 1, < 0.50 for i = 2, < 0.33 for i = 3, etc.: larger absolute values mean that neutron multiplicity sorting was carried out incorrectly. Primarily that is resulted in appearance of non-physical negative values in SIG(g,n). That was shown that for all 4 nuclei mentioned data for (g,n), (g,2n) and (g,3n) reactions are not physically reliable – there are many energy ranges in which non-physical negative SIG(g,n) values clear correlate with non-physical extra large F2 values. New data were obtained for 188,189Os isotopes in the frame of new experimentally-theoretical method for reliable partial photoneutron reaction cross section evaluation SIGeval(g,in) based on using as initial for evaluation the only (g,xn) reaction cross section SIGexp(g,xn) and describing of partial reaction competition in accordance with equations Ftheori of modern model of photonuclear reactions by the way SIGeval(g,in) = Ftheori • SIGexp(g,xn). New reliable and authentic evaluated SIG(g,n), SIG(g,2n) and SIG(g,3n) cross section data for 188,189Os were obtained. Large (till ~ 30 %) deviations of those from the experimental ones are discussed first of all from the point of view of important physical consequences.