Manuscript XVI-A@1 · XVI-A.tex · section · 8177be5d

Proof obligations 4–6

Proof obligations 4–6 · lines 799–872

The obligations below preserve the original numbering. The indexing is that of (eq:index4)–(eq:index6).

Specify the kernel realization of $R_{1} (V_{1}; O_{1})$ associated with the prepared source $J_{D}$ , and complete the packet of Section sec:packet for that realization.

Prove the identified wavefront estimates and support conditions needed for every operation in that slot, with $ε$ fixed. State the final output distribution and its required cone bound.

Present gap. The kernel realization, its input and output manifolds, its maps, and its slot-specific discharge criterion have not been supplied.

Status: Unresolved.

Stop. No first retarded slot is constructed by this note.

Specify the kernel realization of $R_{1} (V_{2}; F_{f})$ associated with $J_{D}$ , and complete the packet of Section sec:packet.

Retain the gauge companion in the complete kernel derivation. Prove the identified wavefront estimates and support conditions for the full expression, with $ε$ fixed. Do not replace the complete expression by one obtained by setting the gauge companion to zero.

Present gap. Neither the complete prepared kernel nor the estimate controlling its gauge-companion contribution has been supplied.

Status: Unresolved.

Stop. No second retarded slot is constructed by this note.

Specify the kernel realization of $\frac{1}{2} R_{2} (V_{1}, V_{1}; F_{f})$ associated with $J_{D}$ , and complete the packet of Section sec:packet.

Retain the Einstein-shell term in the complete derivation. Prove the identified estimates for repeated contractions, pullbacks, pairings, integrations, and any required diagonal extensions, with $ε$ fixed. Do not substitute a gauge-fixed free-shell condition for an unproved Einstein-shell hypothesis.

Present gap. The quadratic kernel, its repeated-operation recipe, its extension data, and its slot-specific discharge criterion have not been supplied.

Status: Unresolved.

Stop. No quadratic retarded slot is constructed by this note.

Absence of any listed estimate leaves the corresponding obligation unresolved. It is not a proof of nonexistence. Conversely, a later proof of one estimate discharges only the task identified by that proof.