The Four-Qubit Hyperbolic Quadric Has Contextuality Degree 315

The contextuality degree of a set of Pauli contexts is the least number of contexts that every noncontextual plus or minus1 assignment violates. For the four-qubit hyperbolic quadric Q+(7,2), with 135 points and 1575 lines as contexts, Muller et al. conjectured from heuristic searches that the degree is 315 and that the violated contexts of every optimal assignment form a dual polar space DW(5,2). We prove both conjectures. The lower bound has a short proof by hand: every doily (GQ(2,2)) of the quadric contains ten Peres-Mermin grids covering each of its lines four times, so every assignment violates at least three of its fifteen lines, and averaging over the doilies gives 1575/5=315. The equality case is local: an assignment is optimal exactly when it violates one ruling of one grid in every doily. Using this as a SAT encoding, we show that there are exactly 240 optimal violated sets, one orbit of O+(8,2), each isomorphic to DW(5,2). The same argument gives the first lower bounds L/5 for all quadrics with L lines in N 4 qubits. The degree theorem is kernel-checked in Lean 4, and the completeness of the enumeration is certified by a DRAT proof checked by the verified checker cake lpr.