  We study the recently reported qmetric (or zero-point-length) expressions of
the Ricci (bi)scalar $R_{(q)}$ (namely, expressions of the Ricci scalar in a
spacetime with a limit length $L_0$ built in), focusing specifically on the
case of null separated events. A feature of these expressions is that, when
considered in the coincidence limit $p \to P$, they generically exhibit a
dependence on the geodesic along which the varying point $p$ approached $P$,
sort of memory of how $p$ went to $P$. This fact demands a deeper understanding
of the meaning of the quantity $R_{(q)}$, for this latter tells about curvature
of spacetime as a whole at $P$ and would not be supposed to depend on whichever
vector we might happen to consider at $P$. Here, we try to search for a
framework in which these two apparently conflicting aspects might be
consistently reconciled. We find a tentative sense in which this could be
achieved by endowing spacetime of a specific operational meaning. This comes,
however, at the price (or with the benefit) of having a spacetime no longer
arbitrary but, in a specific sense, constrained. The constraint turns out to be
in the form of a relation between spacetime geometry in the large scale (as
compared to $L_0$) and the matter content, namely as sort of field equations.
This comes thanks to something which happens to coincide with the expression of
balance of (matter and spacetime) exchanged heats, i.e. the thermodynamic
variational principle from which the field equations have been reported to be
derivable. This establishes a link between (this specific, operational
understanding of) the meaning of the limit expression of $R_{(q)}$ on one side
and the (large-scale) field equations on the other, this way reconnecting (once
more) the latter to a quantum feature.
