Item 74: Is the finite-horizon infeasibility certificate complete for the causal problem?

A Farkas pair (y, z) with positive deficit refutes finite-horizon affordability on any settlement-consistent path, and that direction is proved. The converse is open, and it is the difference between a diagnostic and a dichotomy: a program feasible on every path separately may still admit no causal policy, because the per-path relaxation hands the controller the path in advance.

Settle it. Either exhibit a certificate class complete for the causal problem — the transport plan of the Deferred Service Transfer theorem is already a flow, so flow/cut duality on the plan is the first place to look — or exhibit a causally unaffordable instance every path of which is feasible, which shows no per-path certificate class can be complete and moves the question to certificates over policies.

Sequencing. Take item 40 first, and the existence of an affordable schedule second — with the service variable now typed as enforcement intensity, that question is well posed for the first time: does a schedule with divergent enforcement intensity for every persistent reason exist inside the per-date liability capacity boxes, against an adversarial docket arrival process? Until the necessity of bounded cumulative enforcement liability is settled or refuted, an finite-horizon infeasibility certificate for the causal problem certifies the failure of a hypothesis whose necessity is unknown, and every "unaffordable" verdict in this line means "the known route to safety no longer applies" rather than "no safe policy exists".

What the dual object probably is. The account is signed and cumulative and must stay above a floor at every world the settlement process keeps live, so what has to be separated is a policy from a family of adversary responses rather than a point from a per-path feasible set. That points at a potential or supermartingale over the assessment family — a function of the history upper-bounding the account slack still achievable, decreasing along every admissible control, starting below what is owed — rather than a flow or a cut. A cut is a sum of per-date capacities and the account is not, so flow/cut duality recovers the per-path relaxation and cannot see the cross-period financing the alternating countermodel exhibits.

Deliverable shape: witness-checked for the separating instance, or a stated theorem with an exact-rational fixture inhabiting its hypotheses for the completeness direction. Acceptance check: the round's runner is discovered by python3 tests/run.py and passes; a registered entry, if one is filed, is accepted by python3 -m checkers.run.

Context: projects/normativity/legitimacy/rounds/2026-08-31-normative-affordability/EXISTENCE_AND_DUALITY.md §4 for the certificate and the soundness proof, §1–§3 for the causal problem it is a relaxation of, that round's FOLLOWUP_REPORT.md for why the account is signed and what that does to the dual, and its src/overload.py and src/li_account.py with the matching modules under tests/ for the exact instances; projects/normativity/legitimacy/rounds/2026-08-30-liability-theory/DUALITY.md for the synchronic certificate the horizon version extends. A solution ships: the theorem or the separating instance, and in either case a statement of what a certificate can and cannot be fed back into Answerability as.