candidate_required_fields: rank dimension count

policy_visibility: public

prompt: Compute exactly ∫_Gr(4,9) c_20(Sym^3 S*) by torus localization. Return the rank, dimension, and integer count.

split: eval


policy_visibility: public

prompt: Compute the exact corank and second-order obstruction for the weighted fifth jet.

split: eval


policy_visibility: public

prompt: For a cubic threefold of index 2 with a 2-dimensional Fano surface of lines and d=9, compute the incidence codimension.

split: eval


policy_visibility: public

prompt: Compute the maximal-rank cokernel prediction for two quadratic hypersurface coordinate rings glued along a linear-plus-quadratic complete intersection.

split: eval


policy_visibility: public

prompt: For the product benchmark with raw degrees 6 and 7, compute the exact conductor and test the quadratic bound 36.

split: eval


policy_visibility: public

prompt: Verify primitivity, pairing-one connectivity data, and an exact transvection for the rank-four configuration.

split: eval


policy_visibility: public

prompt: Compute integral homology, including torsion, for the supplied three-term chain complex.

split: eval


policy_visibility: public

prompt: Compute the nilpotence exponent of the ideal generated by the two exact filtration-raising matrices.

split: eval


policy_visibility: public

prompt: Distinguish the order-four torsion group with invariant factors 2,2 from the cyclic order-four case.

split: eval


policy_visibility: public

prompt: Compute all ten odd-characteristic Hasse weights at p=3, their exact product, and state the terminal supersingular multiplicity used by the task.

split: eval


policy_visibility: public

prompt: For p=3 and e=9, compute the exact p-adic valuation, tameness, and p-primary annihilator of the Kummer dlog class.

split: eval