Item 45: Is either liability bridge necessary?

The safety theorem consumes bounded cumulative enforcement liability over the assessment worlds. Two sufficient routes to it are available and neither dominates: the deficit bound L_t(w) <= sum_j beta_j g_j d_j(w), which needs no hypothesis about credal support; and the support bridge E_t(w) >= -(1 - theta) U_t / theta, which needs a uniform positive support capacity and an upper bound U_t on the position's value elsewhere — taken as the cube maximum gain.

The item is whether either is necessary, and whether a third route dominates both. A negative answer for both would mean the round's sufficient conditions are strictly stronger than the criterion needs, which is worth knowing before either is written into a paper as the hypothesis.

Deliverable shape: witness-checked for a trajectory violating both bridges whose market is nonetheless inexploitable; or a proof that one implies liability control in a stated class. Acceptance check: the round's existing safety fixtures run against the proposed condition. Context: .../2026-08-16-traderized-enforcement/FUNDING_AND_SAFETY.md §4a.