Conclusion for the proposed manuscript bridges

For V to VII-B, the completed deliverable is a sharp conditional compatibility theorem. In a genuinely common flat setting, the compact wave-shell relation supplies the propagator-smoothness input, while conservation is the decisive full-space condition. The actual conservation and bundle/domain identification for VII-B's $L^{\ast }a$ remain unproved by the supplied record. No repair of the original off-shell bilinear insertion is asserted.

For XV-F to XVI-D, the completed deliverable is a precise non-discharge result: a smooth witness response does not supply a full distributional identification, reconstruction descent, characteristic composition, or output admission. XVI-H's compact three-slot construction does not change that inference without the missing bridge certificate.

Consequently this paper releases neither the actual XV joint graph nor an admitted quantum retarded coefficient. It claims no interacting Ward identity, sharp-width limit, or ultraviolet completion.