Support, topology, and comparison boundaries

This is the scalar topology retained from X-D-ST, not its width-removal theorem STRecords. It does not topologize a complete cubic as a degree-one scalar class.

The Green operators of Stage 1 are continuous test-to-smooth maps on compact observation reserves. Their matrix entries are finite compositions with constant differential operators. Compactly smeared Green and nilpotence identities therefore depend continuously on the fixed test data BGP. This is not an operator-norm estimate in a physical representation.

For the obstruction, the right-hand side of (eq:positive) is continuous in the smooth data on fixed compact supports. More explicitly, if $|{\sigma }_{\epsilon }^{\prime \prime }|\ge a>0$ on $\mathrm{supp}\zeta$, then

This gives a local stability certificate when the stated positive lower bounds are supplied. It is not a theorem uniform in shrinking widths or arbitrary moving profiles.