Remark: A sufficient window, not a universal converse

The arrival bound is deliberately conservative. Compatible orbifold characters, angular cancellations, or a particular source can eliminate a prospective additional signal. Therefore one cannot assert that every source differs from its flat response immediately outside the window.

If an additional contribution is a nonzero distribution, some compact tests detect it. An uncancelled massless image delta, or a nonzero diffracted contribution, thus prevents a global operator identity with the completion. This is different from a pointwise statement for every source.