@paulbalduf

> #causalSetTheory [...] assumes ST is fundamentally discrete, not like a lattice, but more like a random #graph edges representing causal relations

Btw.: can labelling events be understood e.g. such that (causally connected and ordered) events with the same label are specifically chronologically connected; being visited by the same identifiable participant?

> [...] surprisingly hard [...] order emerges dynamically, can change during the simulation. [...] random [...] random [...] Poisson sprinklings [...] The difficulty: edges must represent consistent order relations in the poset. Say I want to generate a random poset by adding one edge at a time at random. [...] quite costly to do even a single update.

The #causalSetTheory problem that occupies me is quite the opposite of "random" (and thus perhaps rather simple to solve), namely:

Would the causal sets community please provide an _explicit example_ of a graph which is

(1) consistent with ("can be exctly embedded in", "necessarily occurs in") any suitably extended region of 3+1-dim (conformally) _flat_ spacetime, and ideally also

(2) inconsistent with ("can not be exactly embedded in") any suitably extended region of 3+1-dim uniform (conformally) _non-flat_ spacetime, and ideally also

(3) with at least some of its chronological ordered subgraphs being subsets of the timelike worldlines of constituents of an inertial frame (in Rindler's sense, and thus indeed very much like a lattice -- e.g. an octet-truss #PingCoincidenceLattice)

?

(If that's really not as easily done as I envision, and indeed providing instances of "well-stitchedness" ( https://arxiv.org/abs/2302.12209 ) then I'd like to learn about remaining difficulties.)