Interested in mathematical statements in bulk; cf continuum limit for spacetime etc.
In interesting theories, there’s an endless frontier of things to prove.
“Time” is the progress of mathematics; working out “what follows from what” [establish that something definitely doesn’t follow if you have to go backwards on the multiway graph]
Models are a way to organize all possible “syntactic” mathematical statements. E.g. for strings, part of what the model could pull out is just be how long the string is.
Given a model consistent with the partial order, you can say things about math just from the model, without having to trace the detailed multiway connections.
[Constructing a model that doesn’t involve too much computation to build: should not require going down timelike direction too far]
What is the structure of the multiway system? What is the analog of flat space?
Significance of proof cones?
Going between two points in metamathematical space; how many “proof geodesics” are there? If there are multiple ones, it implies curvature, which implies that the model-equivalence surfaces are not flat. [Model-like hypersurface? <Not quite; more model observation frame>]
Homotopies in physics case?
Relation of multiway graph to causal graph in this case?