W_endogenous_matches_wallpaper_groups

This module is Pass 2 of the wallpaper endogenous bridge. The framework still imports the classical constant $W = 17$ (Fedorov 1891) and does not re-prove wallpaper classification. Instead it defines an RS-native candidate from cube combinatorics:

$W_{\mathrm{endogenous}}(d) := E_{\mathrm{passive}}(d) + F(d)$, with closed form $d \cdot 2^{d-1} - 1 + 2d$. Here $E_{\mathrm{passive}}$ counts passive field edges and $F$ counts cube faces.

Spatial dimension is fixed at $D = 3$ by the forcing chain (T8). At that value the split is $E_{\mathrm{passive}} = 11$ and $F = 6$, so the candidate evaluates to 17 and can be compared directly to the imported wallpaper constant.

Term-mode proof by native_decide. Both sides reduce to concrete natural numbers at $D = 3$: the endogenous formula expands to $11 + 6$, and the imported wallpaper constant is the literal 17. The kernel decides the equality by computation; no algebraic lemmas are invoked.

Closes the counting-layer identity that makes the endogenous candidate match the classical $W$ at the forced dimension. Downstream, W_from_cube_eq_wallpaper_groups rewrites the cube-derived $W$ through this equality, and the generator-level slot-closure theorems treat the wallpaper slot as exactly $E_{\mathrm{passive}} + F$ at $D = 3$.

In the Recognition framework this is a bridge step toward full endogeneity of $W$: the classical import remains, but the $11 + 6 = 17$ decomposition is now machine-checked and tied to T8 ($D = 3$). It does not yet replace Fedorov's classification; it only certifies that the RS cube count lands on the same integer.