Proposition: The three roles are not members

XIII-C, lines 358–392, specifies $D_{\Gamma }$, $w_{\Gamma }$, $S_{\Gamma /I}$ by role and displays no formula for any of them XIIICpart; the fourth and fifth passes of the patch and the present reading agree. In particular: the operator $D_{\Gamma }$ is named “specified” without a display; the weight space ${\mathcal{W}}_{\Gamma }$ of admissible $w_{\Gamma }$ is not stated to be polynomial, finite-dimensional, or a vector space; $S_{\Gamma /I}$ is an inherited coefficient whose graph is not displayed. Since the switches ${\sigma }_{\epsilon }$, $g$ are themselves open (Proposition prop:Q3), $w_{\Gamma }$ cannot be instantiated from Patch 3 either. Q4 fails at $D_{\Gamma }$.

Proof. The record.