3-edges extend the 2-edge Zarankiewicz framework to prove SOS rank equals edge count in generalized-C4-free biquadratic forms, improving z_3L(5,3) to 10, z_3L(6,4) to at least 16, and z_3L(5,5) to at least 16.
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Three-Edges and the SOS Rank of Biquadratic Forms: Extending the Augmented Zarankiewicz Framework
3-edges extend the 2-edge Zarankiewicz framework to prove SOS rank equals edge count in generalized-C4-free biquadratic forms, improving z_3L(5,3) to 10, z_3L(6,4) to at least 16, and z_3L(5,5) to at least 16.