What sampling can lose

A row that has zero probability in one preparation is not thereby tested in that run. If only one nonzero row is sampled, the observed weighted image can have smaller rank.

For a known probability vector $p$, a record-retaining weighted table is

Its rank equals two whenever the ${\beta }_{+}$ and ${\beta }_{-}$ fibers each receive positive total probability. The default preparation has this property.

Keeping the complete code distinguishes rowwise information from the single scalar average

That average generally loses information. None of these classical row operations weights the action density or changes the integration-by-parts quotient of Section sec:certificate.