lattice_tensor_components

Module G-004 asks whether a graviton exists in Recognition Science. The RS answer is that gravity is emergent ledger curvature, not a force carried by a spin-2 quantum; asking for a mediating particle is a category error.

Counting continuum-like GW polarizations on the lattice starts from the raw component count of a symmetric spatial 2-tensor. That count is the triangular number $D(D+1)/2$. Upstream, spatial dimension is fixed at $D=3$ by the forcing chain (T8), so the raw count is six. A separate lattice trace removes one component; gauge (transverse) constraints remove $D$ more.

The sibling metric-from-defect development treats the J-cost defect density as the source of curvature, so the tensor whose components are counted here is the lattice avatar of the metric perturbation, not a fundamental gauge field.

Definitional one-liner: the value is the arithmetic expression $D(D+1)/2$, i.e. the number of independent entries in a symmetric $D\times D$ matrix. No lemmas or tactics; integer division is exact because $D(D+1)$ is always even.

Direct input to lattice_gw_modes, which subtracts the lattice trace constraint and the $D$ gauge constraints to obtain the independent GW mode count. For the forced $D=3$ that yields $6-1-3=2$, matching continuum GR and supporting the module claim that lattice GW polarizations equal two without introducing a separate graviton quantum.

This sits inside the three concrete G-004 claims: no gauge-boson origin for $\kappa$, GW polarizations equal two, and the BMV entanglement-rate prediction. It is pure kinematics of the lattice tensor; the dynamical claim that gravity is emergent (not particle-mediated) is carried by the surrounding theorems on $\kappa$ from $\phi$ alone.