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High-order harmonic generation stands as a unique nonlinear optical up-conversion process, mediated by a laser-driven electron recollision mechanism, which has been shown to conserve energy, linear momentum, and spin and orbital angular momentum. Here, we present theoretical simulations that demonstrate that this process also conserves a mixture of the latter, the torus-knot angular momentum J γ , by producing high-order harmonics with driving pulses that are invariant under coordinateddoi:10.1103/physrevlett.122.203201 fatcat:57afi4se4vhrboakronrmgc3ey