Semi-stable second-order polynomials on the varifold of rays of the $A_3$ space

Minimal riggings making it possible to impose relatively semi-stable quadratic forms with constant coefficients on the varifold of trivariate affine ray space. It has been proved that there are two such riggings, and each of them generates its own structure in cotangent bundle of the specified varifold. It is proved that in any of these cases relative semi-stable quadratic differential form on the ruled space is proportional to the form that imposes a semi-Riemannian metric on the varifold of added vectors. Stationery state groups are identified for the discovered additional structures, and one-dimensional sub-groups are specified for these groups. This work is apparently related to the works [4, 5, 6] of the second author.