candidate_required_fields: rank dimension count

policy_visibility: public

prompt: Compute exactly ∫_Gr(2,4) c_4(Sym^3 S*) by torus localization. Return the rank, dimension, and integer count.

split: train


policy_visibility: public

prompt: For the supplied five quadratic jets, compute the exact 20×20 multiplication map, its kernel, and the quadratic obstruction from the supplied second-order term.

split: train


policy_visibility: public

prompt: A line moves in a 4-dimensional family in P^3. For surfaces of degree 7, compute the line-incidence codimension.

split: train


policy_visibility: public

prompt: Use Koszul resolutions to compute the linear-strand source/target dimensions and the maximal-rank nonlinear Betti prediction.

split: train


policy_visibility: public

prompt: Normalize the raw free anticanonical degrees 2 and 3, compute the Apéry set and conductor, and test the stated bound 2.

split: train


policy_visibility: public

prompt: Verify the standard rank-two skew lattice, the span index of the two cycles, and the Picard-Lefschetz transvection in the first cycle.

split: train


policy_visibility: public

prompt: Verify the chain condition and integral homology of the one-cell CW chain complex for S^1.

split: train


policy_visibility: public

prompt: Verify that the supplied operator strictly raises a two-step filtration and compute the ideal nilpotence exponent.

split: train


policy_visibility: public

prompt: Compute the torsion cokernel and regular-character count for independent contact orders 2 and 3.

split: train


policy_visibility: public

prompt: Compute the Hodge-line exponents p^h-1 and their product for p=3 and h=1,2,3.

split: train


policy_visibility: public

prompt: For p=5 and ramification index e=3, determine tameness and the p-completed relative logarithmic differential module.

split: train