Frozen target and release criteria

Use

All external functions, widths, and propagators remain fixed. The carrier and line conventions are

Metric–scalar propagator blocks vanish.

The interaction is

The observable contains its scalar-sourced slot once:

The grouped retained target is

The cross-line difference stays grouped. No intermediate mixed $H$–${G_{\mathrm{act}}}^{\mathrm{A}}$ product is defined.

The endings, applied only to (eq:target), are:

1. Constructed: a common microlocal representation, a joint principal-symbol section, and a complete remainder estimate establish the required cancellation; or one characteristic prescription has all named domain, degree, normalization, ambiguity, and wavefront data proved.

2. Proved obstructed: an explicit incompatibility excludes every map in a previously declared class.

3. Unresolved: the common symbol, remainder, or prescription theorem is missing.

A vanishing leading section is sufficient only when the remainder control actually supplies the required distribution. A formal order improvement does not define an otherwise undefined product.

The elementary phase failure, the excess-route failure, and $Q\lambda$ are not universal obstruction theorems for this target.