relativity - How are propositions concerning spacetime curvature constructed explicitly in terms of coincidences?

Is Einstein's insight [1] that

All our well-substantiated space-time propositions amount to the determination of space-time coincidences [such as] encounters between two or more [...] material points.

and [2] his (so recognized)

[...] view, according to which the physically real consists exclusively in that which can be constructed on the basis of spacetime coincidences, spacetime points, for example, being regarded as intersections of world lines

applicable to propositions concerning spacetime curvature ?

How, for instance, is the proposition

"spacetime containing the worldline of material point A is curved"

constructed and expressed explicitly on the basis of spacetime coincidences (in which the "material point" identified as A or suitable other "material points" took part) ?

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Edit in response to the answers and comments presently provided (Sept. 12th, 2013):

• Trying to put my question more formally,

given that there is the set $S$ of any and all distinct "spacetimes" imaginable,
and that there is the function (or proposition)
$\kappa : S \rightarrow \{ true, false, undetermined \}$
which for any spacetime under consideration represents whether it is "curved", or "not curved", or not an eigenstate of "possessing any curvature" at all,

and further given a set of sufficiently many distinct names $W := \{ A, B, M, M', ... \}$,
and that there is the function
$coinc : S \rightarrow \text{ powerset}[ \text{ powerset}[ \, W \, ] \, ]$

which for any spacetime under consideration represents the set of (distinguishable) coincidences of (different, and distinctly named) "worldlines",

I'd like to know the explicit expression of the function (or proposition) $f : \text{ powerset}[ \text{ powerset}[ \, W \, ] \, ] \rightarrow \{ true, false, undetermined \}$,
for which
$\forall s \in S: f( coinc( s ) ) = \kappa( s )$.

Looking at the above quotes it may be expected that $f$ has been worked out and written down long ago already; therefore, please write it down in an answer here, or point me to the corresponding reference. However, here are

• Considerations which answers would be acceptable otherwise:

either a proof that such a requested function $f$ doesn't exist at all; presumably by exhibiting two distinct spacetimes $s_a$ and $s_b$ for which $coinc( s_a ) = coinc( s_b )$ but $\kappa( s_a ) \ne \kappa( s_b )$. (But recall the hole argument discussion relating to the difficulty of distinguishing spacetimes at all.)

Finally, if such a requested function $f$ can neither be explicitly stated, nor refuted, then

define the notion "geodesic" (which has already been used/presumed in answers below) or at least the notion "null geodesic" explicitly in terms of $coinc( s )$.