Proposition: What the recovered class does and does not supply

1. ${\mathcal{C}}_{\mathrm{part}}$ is a class of coefficient values (distributions), each supported in the closed set $C_{\mathrm{coll}}:=\overline{{\bigcup }_I{\Delta }_I}\cap {\mathcal{K}}_{\mathrm{gr}}$, where ${\mathcal{K}}_{\mathrm{gr}}$ is the compact graph closure named in Definition def:Cpart.

2. XV-B's correction class is a vector space $\mathcal{A}\subseteq \mathrm{Hom}({\mathcal{P}}_{\mathrm{int}},Y)$ of maps. The record does not state which presentation-level maps are permitted; in particular it does not state that $\mathcal{A}=\{a\in \mathrm{Hom}({\mathcal{P}}_{\mathrm{int}},Y):a({\mathcal{P}}_{\mathrm{int}})\subseteq {\mathcal{C}}_{\mathrm{part}}\}$, nor any continuity, tensor, or covariance restriction on $a$.

3. The collision sets are defined in XIII-C's graph variables; their lift to $W$ with coordinates $(a,b,z,y)$, and the inclusion $C_{\mathrm{coll}}\subseteq W\setminus U_{\mathrm{can}}$ needed for ${\mathcal{C}}_{\mathrm{part}}\subseteq Y=\ker r_O$, are not supplied; the three refusals of sec:fifthpass show the inclusion cannot be read off from ${\mathcal{N}}_{\mathrm{att}}$.

4. The parametrization of ${\mathcal{C}}_{\mathrm{part}}$ ($D_{\Gamma }$, the admissible $w_{\Gamma }$, $S_{\Gamma /I}$) consists of roles specified in XIII-C, not formulas. Exhaustiveness of any affine family built from ${\mathcal{C}}_{\mathrm{part}}$ cannot be checked.

Hence D0.17 is T for the definition and R for the parametrization, and D0.17 does not pass to status S.

Proof. (i) is the support clause of Definition def:Cpart. (ii)–(iv) are statements about the record: the reproduced passages XIIICcoll,XIIICpart,XIIICvertex contain the two definitions above, the vertex table, and nothing further; the fifth pass confirms that $D_{\Gamma }$, $w_{\Gamma }$, $S_{\Gamma /I}$ are roles; $U_{\mathrm{can}}$ is in status P (D0.8).