For thefirst time primary hot isotope distributions are experimentally reconstructed in intermediate heavyion collisions and used with antisymmetrized molecular dynamics (AMD) calculations to determine density, temperature, and symmetry energy coefficient in a self-consistent manner. A kinematical focusing method is employed to reconstruct the primary hot fragment-yield distributions for multifragmentation events observed in the reaction system 64 Zn + 112 Sn at 40 MeV/nucleon. The reconstructed yield distributions are in good agreement with the primary isotope distributions of AMD simulations. The experimentally extracted values of the symmetry energy coefficient relative to the temperature, a sym /T , are compared with those of the AMD simulations with different density dependence of the symmetry energy term. The calculated a sym /T values change according to the different interactions. By comparison of the experimental values of a sym /T with those of calculations, the density of the source at fragment formation was determined to be ρ/ρ 0 = (0.63 ± 0.03). Using this density, the symmetry energy coefficient and the temperature are determined in a self-consistent manner as a sym = (24.7 ± 1.9) MeV and T = (4.9 ± 0.2) MeV. PACS number(s): 25.70.PqConstraining the density dependence of the symmetry energy is one of the key objectives of contemporary nuclear physics. It plays a key role for various phenomena in nuclear astrophysics, nuclear structure, and nuclear reactions [1,2]. Heavy-ion collisions provide a unique opportunity to study the nuclear symmetry energy and its density dependence at and around normal nuclear matter density. However, reliable extraction is difficult because of the complexity of the reaction dynamics.In violent heavy-ion collisions in the intermediate energy regime (20 E inc a few hundred MeV/nucleon), intermediate mass fragments (IMFs) are copiously produced through a multifragmentation process. Nuclear multifragmentation was predicted a long time ago [3] and has been studied extensively following the advent of 4π detectors. Studies of nuclear multifragmentation provide important information on the properties of the hot nuclear matter equation of state. The recent status of the experimental and theoretical work is reviewed in Refs. [4][5][6].In general, the nuclear multifragmentation process, can be divided into three stages, i.e., dynamical compression and * wada@comp.tamu.edu heating, expansion and freeze-out of primary fragments, and finally the separation and cooling of the primary fragments by evaporation.Different models have been developed to model the multifragmentation process. These include dynamical transport models such as fermionic molecular dynamics (FMD) [7], antisymmetrized molecular dynamics (AMD) [8][9][10] constrained molecular dynamics (CoMD) [11], improved quantum molecular dynamics model (ImQMD) [12], quantum molecular dynamics model (QMD) [13], Vlasov-Uehling-Uhlenbeck theory (VUU) [14], the stochastic mean field (SMF) [15], Boltzmann-Uehling-Uhlenbeck (BUU) [16] a...