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The cause of this threshold in three-dimensional samples is not explained.","posed_since":"","precise":"In brittle amorphous materials (silicate glass, PMMA, polyacrylamide gels), single cracks become unstable to microbranching at velocities of roughly $0.4 c_R$ ($c_R$ the Rayleigh wave speed), below the branching velocity predicted by linear elastic fracture mechanics. Determine the 3D mechanism and critical velocity from a theory including near-tip nonlinear elasticity and dissipation, and predict the branch length and spacing.","problem_ref":"91c06e4b6eeec748fd5c9c57c5ebe3ccb656ad2a8d46730cf3ef06eee58c905e","references":"","settled_by":"A theory and 3D simulations predicting the microbranching velocity and branch statistics that agree with measurements in at least two materials.","status_note":"In thin gel sheets an oscillatory crack instability near the Rayleigh speed was explained by weakly nonlinear elasticity in the 2010s; the 3D microbranching threshold lacks a first-principles explanation (2026).","title":"What triggers microbranching of fast cracks in brittle amorphous 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