Manuscript IX-C@1 · IX-C.tex · remark · 03ce8e6b
Remark: Existence and admission are separate
The six placements and the nonconstant outputs › The two-edge expressions · lines 783–797
IX-C@1#rem:treeboundary
For (eq:g1223), a compact scalar-only polynomial kernel, if established, would pass the metric admission test because all its metric derivatives are zero. The existence of that kernel must nevertheless be proved.
For (eq:g1213) and (eq:g1323), establishing a compact distributional kernel is not sufficient: their metric derivatives must satisfy (eq:admission). The supplied calibration theorem does not provide these graph-specific results.
No claim is made here that these products fail to exist. Their existence and admission remain unproved in this manuscript.