Reference agreement and topology

Away from nonzero relative cones the crossed lines are smooth; on the cones their wavefront covectors are conormal. Pulled-back crossed covectors have form

A nonzero one can have zero $y$-component only on $\Sigma$. Internal rows have zero $y$-covector. Thus the ordinary product is defined on $U\setminus \Sigma$. On compact subdomains, small relative translations preserve nonopposition. Pullback continuity, compact-parameter bounds, and fixed-factor multiplication apply under these verified hypotheses BDH (Proposition 5.1, Theorems 5.9 and 6.1).

The supported reference exists on $U\setminus N_{\mathrm{mark}}$, and $T_{\mathrm{supp}}$ agrees with it there. No maximal canonical-domain equality is asserted. Extension theory has additional scaling and microlocal hypotheses Dang; it is not used to infer the raw limit.

The displayed compact-stage remainder bounds imply strong distributional convergence for the corresponding subtracted sector families: bounded test sets have common compact support and bounded finite seminorms. No wavefront-normal convergence theorem is asserted.