Einstein--Hilbert Dynamics in the TEBAC 9D/9D+ Defect Formalism

This preprint formulates a conservative effective-field interpretation of Einstein--Hilbert dynamics within the TEBAC 9D/9D+ framework. The observable four-dimensional spacetime is treated as a defect-supported sector inside a higher-dimensional organized geometric background rather than as the full fundamental arena. The paper records a bulk-plus-defect action ansatz, defines the induced defect metric, and derives the formal effective Einstein equation obtained from a reduced four-dimensional defect action when such a reduction is admitted. A central structural point of the paper is the clean separation between:(1) the local effective defect source tensor,(2) projected bulk corrections,(3) embedding/extrinsic corrections,and(4) the topological/invertible consistency sector. The note is explicitly formal, architectural, and programmatic. It does not claim canonical spectral extraction of all effective observables, full moduli stabilization, scheme-independent renormalized formulas, or complete quantitative matching to low-energy measurements. Instead, it fixes the Einstein--Hilbert defect architecture that later TEBAC modules are intended to instantiate and close. This version includes a status box, an import/export ledger, formal non-circularity policies, and prototype guidance for concrete realizations based on the canonical compact sector $K_5 = S^1 \times T^4$, the lifted realization with $F_4 = S^4$, the internal spectral sector, the moduli sector, and AT3 admissibility.