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Topological constraint theory (TCT) classifies disordered networks as flexible, stressed-rigid, or isostatic based on the balance between the number of topological constraints and degrees of freedom. In contrast with the predictions from a mean-field enumeration of the constraints, the isostatic state—wherein the network is rigid but free of stress—has been suggested to be achieved within a range of compositions, the intermediate phase, rather than at a fixed threshold. However, our understanding of the nature and potential structural signatures of the intermediate phase remains elusive. Here, based on molecular dynamics simulations of calcium–silicate–hydrate systems with varying compositions, we seek for some mechanical and structural signatures of the intermediate phase. We show that this system exhibits a composition-driven rigidity transition. We find that the fracture toughness, fracture energy, mechanical reversibility, and creep compliance exhibit an anomalous behavior within a compositional window at the vicinity of the isostatic threshold. These features are argued to constitute a mechanical signature of an intermediate phase. Notably, we identify a clear structural signature of the intermediate phase in the medium-range order of this system, which is indicative of an optimal space-filling tendency. Based on these simulations, we demonstrate that the intermediate phase observed in this system arises from a bifurcation between the rigidity and stress transitions. These features might be revealed to be generic to isostatic disordered networks.