Asymptotically safe in the index space

If we have an arc function that takes our generators from 'segmented real line' to sequential integers then we are in index space.

If we are asymptotically safe, then each agent views the economic index space, going forward, as a sequence of available indices in which the agent interleaves its own transactions.  This is the fractional approximation part. the pit boss forces the approximation to stay within bounds. This model appears in most economics as a convexity requirement, I think. They all assume the agent can find the shortest path. 

In these models, then the limitation is the significance of your transaction rate, how accurate is the allocation of index spectrum?  That sets the limit on model complexity, and rank is a short hand measure of complexity. The same applies to physics I think, which is why the experimented with the concept, it can give you a bound on standard particle complexity..