Heads-up! to https://arxiv.org/abs/2302.12209
"How to detect the spacetime curvature without rulers and #Clocks"
(A. V. Nenashev, S. D. Baranovskii)
-- which investigates the question (p. 2)
"Is it possible to figure out that a spacetime [region] is curved [instead conformally flat] by testing #CausalRelations only ?"
-- and provides proof of a positive answer through a criterion in terms of causal relations among any set of eight #events (#StitchConfiguration).
Closely related is the question
"Is it possible to figure out whether two (or more) participants are sitting still wrt. each other in a flat region (or whatever is equivalent in a conformally flat region) by testing causal relations only ?",
(referring to the notion of #InertialFrame in the sense of W. Rindler as "set of point particles sitting still wrt. each other"; cmp. http://www.scholarpedia.org/article/Special_relativity:_kinematics),
-- which is presumably solved by #tetrahedral-octahedral #PingCoincidenceLattices, closely related to #OctetTruss #PingCoincidenceLattices; see e.g. https://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycomb and https://www.google.com/search?q=%22octet+truss%22&tbm=isch&prmd=ivnbz
-- and where, notably, eight events in one particular variant of the #StitchConfiguration do indeed occur as integral part of those mentioned #PingCoincidenceLattices (namely, not surprisingly, depicted as #Octahedra in the familiar drawings of the corresponding "plain 3D" lattices).
