Status ledger and debugging corrections

Sharp-width limit and ultraviolet claims & Outside scope. Not open problems assigned to this note.

The principal corrections to XVI-H-v3 are:

1. Witness compatibility is closed. Equality with $T_D$ follows from identical definitions, and the same four-term extension gives ${\mathcal{O}}_{\mathbb{C}}=T^{\mathbb{C}}$ on the common complexified domain. The existing witness theorem then supplies the remaining chain.

2. Kernel specialization is qualified, not refused. Partial contraction to $j_{\lambda }$ is proved. It is not mistaken for a full-kernel identity or a uniqueness theorem from witness data.

3. Kernel existence and admission are separated. The compact representation is established under the stated inputs; full-kernel wavefront/admission remains unresolved.

4. General tests are used in the construction. Formula (eq:t-test), not only a pairing on decomposable tests, defines the distribution. Compact support and properness are stated explicitly.

5. Bulk and switch premises are separated. The displayed switch monomials are audited. The unexpanded bulk coefficient is not silently derived.

6. Derivative indices do not reuse frequency. $\lambda$ denotes frequency, while repeated spacetime indices have separate names.

7. The switch audit is bounded. The inherited signs and hypotheses are reproduced explicitly. A full XI-G source verification is not claimed, and the representative is not presented as admission by itself.

8. Layout is made multipage-safe. Defined theorem environments, a width-aware scope box, and a longtable replace the overlong one-page ledger.