Item 40: Is bounded cumulative enforcement liability necessary?

Reframed at the September 2026 checkpoint, not answered. The affordability line now builds a substantial theory on top of this hypothesis — persistence, timeliness, and the endpoint composition all consume it — which raises the item's value and sharpens what its failure would cost. Until it is settled, every "unaffordable" verdict in the line means the known route to safety no longer applies, not no safe policy exists, and the checkpoint's status ledger says so. Context: projects/normativity/legitimacy/checkpoint-2026-09-01/OPEN_PROBLEMS.md §6.

The preservation theorem's hypothesis is that the enforcement position's cumulative value over the assessed worlds is bounded below:

for every n and every ω ∈ Ω_n^live, Σ_{t≤n} E_t(ω) ≥ −B .

That is sufficient. Its converse is not proved, and one direction of the converse is known to fail — weak enforcement has zero liability while excluding live worlds outright, so unbounded liability is not implied by aggressive enforcement.

The item is the necessity direction, or its refutation. If a trajectory can violate the bound with no efficiently computable trader able to harvest it, that counterexample is the more valuable outcome, because it would mean the hypothesis is strictly stronger than the criterion needs and the round's formulation is not the canonical one.

Note what the item is not. It is not about the declared-quantity certificate Σ_t (ε_t + C_t)·D_t/δ_t, which is a conservative sufficient upper bound — it maximizes over the live worlds independently at each date, where the criterion follows a single world across dates. A certificate that diverges establishes only that the current proof does not certify safety. The round carries a fixture where the realized liability at one followed world diverges too, which is the stronger statement and the one this item's converse would have to engage.

Deliverable shape: witness-checked for a refutation; derived or better for necessity. Acceptance check: the trajectory is exhibited in exact rationals with a stated efficiently-computable trader class. Context: .../2026-08-16-traderized-enforcement/FUNDING_AND_SAFETY.md, NORMATIVE_SAFETY.md §5; src/outflow.py.