Hierarchical organization of tau topography across the Alzheimer's disease continuum integrates amyloid, connectome, and intrinsic molecular vulnerability.

Tau pathology defines the Alzheimer's disease (AD) continuum and is spatially heterogeneous, yet the roles of amyloid-β (Aβ), connectome architecture, and intrinsic molecular vulnerability remain unclear. Here we integrated Aβ- and tau-PET, diffusion MRI, resting-state fMRI, and transcriptomic maps across the AD continuum. We found that tau pathology followed a hierarchical spatial gradient that progressively stratified by Aβ and clinical stages. Across the AD continuum, Aβ covariance and structural and functional connectivity were associated with tau covariance, and their derived propagation signatures further recapitulated regional tau burden, explaining substantial spatial variance. A residual tau pattern not captured by the modeled propagation signatures was further identified and was associated with reproducible transcriptional gradients involving intracellular signaling, synaptic programs, mitochondrial bioenergetics, and post-transcriptional regulation, with stage-specific shifts in biology. Importantly, tau geometry related to epicenter segregation and perivascular diffusion and mediated their associations with clinical expression. These findings position tau topography as an integrative marker coupling Aβ, connectivity, and intrinsic molecular vulnerability, and indicate that tau geometry is related to the link between network organization and cognitive decline.