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We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branch choice varies across the brain. Our framework reveals hidden degeneracies in MRI parameter estimation for neuronal tissue, provides microstructural and orientational maps in the whole brain without constraints or priors, and connects modern biophysical modeling with clinical MRI.We estimate neuronal compartment fractions, diffusivities, and orientations from diffusion MRI.We derive analytically and confirm numerically degeneracies in parameter estimation.Parameter accuracy and precision is tied to topology of minimization landscape.The degeneracy in fitting landscape is formulated in terms of the branch selection.Branch choice varies across the brain, based on the high-b acquisition.