Correction-class and contact analysis

The inherited correction class $\mathcal{A}$ is not defined (D0.16–D0.17). The following statements are therefore all that can be made.

1. For the actual graph, neither $d_0$ nor the quotient $\mathrm{Hom}(H,Y)/\{a{|}_H:a\in \mathcal{A}\}$ is evaluable (Propositions prop:D0 and prop:nolift).

2. For the jet module, the relative obstruction vanishes in the unrestricted puncture-supported class (Proposition prop:unrestricted), and cancellation within the narrower class of extension changes is equivalent to the existence of an extension $T^{\prime }$ with $H_{T^{\prime }}=H$ (Corollary cor:extension). Whether such an extension exists for a given $T^{\circ }$ is not decided in general here; it is decided affirmatively in Proposition prop:example.

3. No separated witness exists in the jet module for any extension lift. This is a property of that module, not a statement that the actual graph lacks separated defects.

4. A proposed cancellation for the actual graph must satisfy the support, normalization, tensor, continuity, and microlocal conditions of the frozen class, none of which is available to check.

No obstruction is asserted. No cancellation is asserted for the actual graph.