The component order and matched equivalence

The permitted equivalences and domain invariance must be fixed before an extraction is applied. Restricting them after encountering a symmetry obstruction changes the claim.

Scheduled ancestry $R_{\mathrm{sch}}$, unconditional influence $R_{\inf }$, and a later independently supplied geometric relation $R_{\sup }$ remain distinct. In a complete definite-order network, $R_{\inf }\subseteq R_{\mathrm{sch}}$; containment in $R_{\sup }$ requires a separate embedding certificate CheungVIIJ,CheungEn06A,CheungXXIIA. The frozen extraction here represents the component order of ${R_{\inf }}_D$, not all three relations at once.