Less paid. Still rejected. An Evidence Press briefing.

Suppose a restructured debt contract pays less than a reference contract at every date. It may seem obvious that the lighter contract must pass any reasonable burden-sharing test. This mathematical candidate shows why one particular duration veto can disagree.

Duration is a weighted average payment time. Removing a late payment can lower the total amount owed while also bringing that average time forward. In an exact example, both endpoint states pass the duration test, but every interior state fails. A small perturbation makes both endpoint tests pass strictly, so equality at the boundary is not the explanation.

The paper derives an exact identity showing when removing a payment raises or lowers duration. It then separates three checks: present value, service during a programme window, and duration. On each declared trigger region, the first two are affine and the third becomes a quadratic inequality. This permits exact certificates rather than a numerical grid.

The strongest extension uses two state variables and an oblique trigger. One early payment must be chosen before the later state is known. Off trigger, programme service allows at most twenty-five. On trigger, duration lowers the sharp cap to one hundred and ten sevenths. As the late uplift changes, the binding constraint switches exactly at seventy-five sevenths.

These numbers belong to constructed cash flows and a stipulated rule. Institutional comparability may permit substitutions and consider features that this separate three-veto screen omits. The paper does not authenticate a contract, recommend a restructuring, rank welfare, assess sustainability, or issue a country verdict.

The public package includes the self-contained paper, exact inputs, certificates, an implementation-diverse checker, negative controls and accessible formats. This remains an anonymous, AI-assisted, unrefereed candidate. This briefing uses an AI-generated voice and is not additional scientific evidence.