What has advanced

The full retained sum has a shorter exact precomposition form: $B_4+B_7$ retain only first scalar-test derivatives after the proved cancellation, $B_5+B_6+B_8$ appear in one complete coordinate-response divergence, and $B_9$ has an explicit complete root formula.

The geometric obstruction to the simplest symbol shortcut is also precise. The sum of the selected line phases is not an ordinary clean common phase. Two missing linear constraints appear quadratically, and the observable attachment changes the ambient codimension.

These results identify work a common characteristic calculus must perform. They are not that calculus.