What counts as a replacement

For the documentary question, a replacement would have to be an explicitly identified alternative to:

1. the bilinear source symbol of $J_3$, or

2. the selected inverse $-\mathcal{P}{E_0}^{\mathrm{R}}$,

together with a calculation showing removal of the named XI-G witness mechanism while stating the retained normalization, domains, and observation data.

The preparation $J_D={\sigma }_{\epsilon }{J}_3+{\mathcal{D}}_{\sigma }$ is not described here as a replacement of the frozen bulk symbol or inverse. It is the existing density-prepared source to be analyzed.

The defensible documentary conclusion is:

No verified replacement satisfying this description is identified in the supplied record.

This statement is not a theorem that no such replacement can exist, and it is not a reason to stop analysis of the existing prepared source.