[ The reconstructed object is the dual of the spatial hypergraph ... i.e. its nodes are the hyperedges of the spatial hypergraph, and each hyperedge is associated with a single space atom ]
Knitting of hyperedges by events
Not the same because of the flow of elements through hyperedges
Speed in space is less than c
There exist rules that make one be able to go further in the reconstructed spatial ball vs. the causal ball. [Happens when expressions with shared elements are not both matched]
Speed in space is greater than c
Rule could disconnect its input which would limit how far the spatial ball could extend, but the causal ball would extend. I.e. you can causally reach more places in space than you can geometrically reach if space is broken by event horizons.... This is analogous to having a temporary wormhole, that then disappears, but leaves the results of its communication....
Claim: want both the past and future causal balls to be bigger than the geodesic ball.
Future Causal Ball ?
I.e. something that will reach a particular expression in the future....
There is a constant (say c) for which the future causal ball for an expression t steps in the future is always smaller than the c t step geodesic ball......
A rule that matches any collection of hyperedges out to a certain geodesic distance will simply reconstruct a geodesic ball....
[Assuming the rule is connected]
(Geodesic ball: generated by “anything goes” rule of a given diameter)
[ I.e. “geodesic speed” is the absolute upper limit ] [[ not obviously correct: the rule makes extra space ... ]]
Pre-existing network of wormholes
Wormhole network one can pre-construct
[Manipulate update order so that the space around where you are is updated faster than space further away]
If there is a higher density of nodes than usual created in a fixed number of steps ... that is effectively negative relative energy
[For Newton’s equations: given a trajectory, deduce a force that will give that]
What happens to time for people moving inside the bubble?
<Analogous to expansion of universe, where effectively space is being created by expansion>
Formation of cosmological event horizon is simply a disconnection in the causal graph
[[ Hitchhiking on the expansion of the universe ]]