Materials required for a construction manuscript

A subsequent manuscript seeking an actual coefficient theorem must supply, at minimum:

1. the complete prepared action and its variational conventions, including the formula for ${\ell }_3$;

2. explicit definitions of $J_3$ and $D_{\sigma }$, and a proof relating their sum to that action if such a relation is claimed;

3. the normalized free operator, its field bundles, source domains, and Green kernels;

4. definitions of $F_f$, $O_1$, $O_2$, $V_1$, $V_2$, and the proposed retarded maps;

5. the full gauge-companion and Einstein-shell contributions appearing in the prepared derivation;

6. the compact observable kernel induced by $J_D$, together with its free-shell comparison to the frozen XI-G kernel;

7. completed specification packets and proofs for obligations 4–6;

8. the extension, normalization, and admission results needed to turn the schematic bookkeeping into a coefficient theorem.

Neither the provenance note nor the general analytic interface is a substitute for these materials.