# how the divergence field emerges from the antisymmetric tensor

For an antisymmetric rank-(2,0) tensor built from a scalar amplitude t ( $$T^{12}=t, T^{21}=-t$$ ), the divergence is the 90°-rotated gradient, $$∇\_a T^{ab} = (−∂\_y t, ∂\_x t)$$. The demo shows that the antisymmetric tensor encodes a circulation-like field whose divergence is orthogonal to ∇t and has the same local magnitude structure, illustrating the geometric relation between antisymmetry and rotation.

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