D_spatial

The module extends the one-dimensional continuum-limit second-order result to a full spatial lattice. On the product lattice $\mathbb{Z}\times\mathbb{Z}\times\mathbb{Z}$, the multi-dimensional lattice Laplacian is the sum of independent one-dimensional second-difference operators along each axis; the continuum limit is then $\nabla^2$ with $O(a^2)$ error.

In the Recognition framework the spatial dimension is not free: the forcing chain (T0–T8) forces $D=3$ at step T8. This definition simply names that forced value for use in gravity lattice constructions. Related constants elsewhere in the monolith (active-edge count $A$, various normalizers $Z$) are unrelated name collisions; here $D$ is purely the spatial rank of the lattice.

No proof. The declaration is a def that assigns the natural-number literal 3. Downstream lemmas treat it as the fixed rank of the product lattice and of the three-term Laplacian decomposition.

Pins the ambient dimension for every subsequent object in Gravity.LatticeConvergence: the type of lattice fields on $\mathbb{Z}^3$, the identity that the $D=3$ Laplacian has exactly three axial terms, the scaled Laplacian convergence theorem, and the $O(a^2)$ continuum error. That continuum Laplacian is the kinetic operator whose continuum limit supplies the linearized Ricci piece $R_{\mu\nu}\sim\nabla^2 h_{\mu\nu}$ in harmonic gauge, linking the discrete ledger to classical gravity.

Framework landmark: T8 of the unified forcing chain, which forces three spatial dimensions. The definition does not re-prove T8; it imports the forced value so the lattice analysis can stay dimensionally rigid.