The supplied restricted hh obstruction

The predecessor reports testing the $hh$ pole derivative against the image of

in its 13-generator dimension-two $X$-presentation. For the relaxed map allowing independent $X,X^{\prime }$ in

it reports on a 15-structure $hh$ space

Fixed-normalization failures, including the listed $\xi =1,2,\frac{1}{2}$ tests, are also reported. The four-dimensional projection is reported to have rank five on six structures and to accept both the derivative and the undifferentiated $\xi =1$ pole SuppliedBot.

The full generator list, ambient basis, matrices, original minors, and left-kernel rows are absent from the supplied artifacts. The relaxed rank report is not extended to additional parameters and is not newly re-certified.

Define the named source-relative obstruction

If the reported ranks hold for those actual arrays, this class is nonzero at $\xi =1,2$, because adjoining the target raises rank. That excludes only the tested class. The four-dimensional test is nondiscriminating in the reported comparison, not invalid for every purpose.

A complete rank-seven image certificate on 15 rows needs an original $7\times 7$ minor and an $8\times 15$ complete left-kernel matrix, with a nonzero target pairing.