Item 43: A compiler that is both exact and safe, or a proof there is none

Two compilers, and they are not ordered. The violation-proportional position never loses in a world its region contains, and cannot force exact membership against bounded opposing volume. The interior-anchored position forces exact membership when the region has an interior, and loses in a plausible world at a price inside a world-inclusive region, because it holds positions where there is no violation at all.

The item is whether the two properties can be had together: a continuous expressible strategy whose position has a floor outside the region and vanishes on it. Those pull against each other — a continuous position that vanishes on a closed region is small just outside it — so a clean impossibility is the expected outcome and would be worth as much as a construction. Note the two-sided shape: interior-anchored exactness is proved only for regions with a strict interior, so the construction question is posed there. Regions with empty interior are not excluded: cube-face settlement pinning is enforced exactly by a constant position, so a general impossibility claim must not lean on empty interior. Only the earned geometry is available here.

Deliverable shape: test-supported for a construction, with the safety and exactness fixtures both green on it; witness-checked or lean-proved for an impossibility. Acceptance check: the round's existing exactness and safety sweeps, run against the new compiler, both pass. Context: .../2026-08-16-traderized-enforcement/ENFORCEMENT.md §5, Theorems 7 through 9; src/exactness.py.