Item 61: A normative source with summable enforcement liability

The end-to-end slice establishes that the unconditional traderization theorem's admissibility hypothesis holds exactly for injunctions that change nothing about the prices, so every operative injunction with content depends on the charged branch. The condition that branch needs is

sum_t (eps_t + M_t) * D_t / delta_t  <  infinity

where D_t = max over omega live at t of sum_j d_{t,j}(omega) is outflow.LiveDeficitCertificate.by_enumeration's sharp aggregate, computed for the **exact day-t compiled force request over the exact live-world assessment state**. No source in this repository is shown to satisfy it, which makes this the single condition the architecture's safety claim rests on.

Four things the slice established that constrain what an answer may look like, and that a round taking this item should not have to rediscover:

1. **D_t is not monotone across days.** A frozen injunction over Expect(X) compiles to a different row system each day, and the precision-k reading of a value is ceil(x*k)/k, which is not monotone in k. The slice exhibits D_1 = 0 and D_2 = 1/6 on one injunction with a strictly growing stage. An argument that settlement drives the sum down must therefore say something about the mesh, not only about the worlds.
2. The charge is presentation-dependent. D_t sums across rows, so stating one demand twice doubles it while enforcing the same prices. The condition is about a schedule of presentations.
3. The tolerance route is bounded. While delta_t <= 1 — and a looser promise is vacuous on prices in [0,1] — the charge dominates (eps_t + M_t) * D_t, so summability requires sum_t (eps_t + M_t) * D_t < infinity.
4. Two of the three factors therefore have to carry it, and the slice exhibits both routes working synthetically: the deficit going to zero under settlement, and the ordinary aggregate's bound decaying.

Deliverable shape: test-supported at minimum — a normative source with an explicit settlement trajectory and presentation schedule, and either a proof that the sum converges or a witness that it does not for a source the architecture would call legitimate. Acceptance check: a runner drives the slice's trajectories harness over the declared trajectory, computes D_t per date through LiveDeficitCertificate.by_enumeration, and reports the partial sums against a stated bound. Context: projects/normativity/legitimacy/rounds/2026-08-25-end-to-end-vertical-slice/FINDINGS.md §6 and its src/trajectories.py, which carries four synthetic trajectories, two convergent and two not; projects/normativity/rounds/2026-08-16-traderized-enforcement/FUNDING_AND_SAFETY.md §9. Consumed by: any round claiming the normative layer preserves the logical-induction guarantee, which is every downstream round.