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It has no nonzero time-shift generator to demonstrate." } } ], "timeReversalExclusion": { "assumptions": "Autonomous Gray–Scott equations with spatially uniform coefficients, ordinary spatial isometries, and unchanged concentration channels.", "statement": "An exact constraint q(gx,-t+c)=q(x,t) forces a classical solution to be stationary.", "proof": "Spatial equivariance gives F(g*q)=g*F(q). Differentiating the time-reflection constraint gives -g*q_t(-t+c)=q_t(t), whereas the equation and the constraint give g*q_t(-t+c)=q_t(t). Therefore q_t=0.", "appliesToListedGroups": false } }