In the file attached to this post, there is a theorem due to the author about the asymptotic behavior of the descriptive complexity in the causal graph and its connection with the logarithm of time. Here are the links of the main references for this paper, besides the standard material of the Wolfram Physics Project:
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S. Wolfram paper’s Origins of randomness in physical systems,
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William K. George paper’s Could time be logarithmic?.
JMRCaballero.pdf (252 KB)