So let's get back to chained bots. They take bets on input and place them on output. The rules are simple, on input there must be at least one bet pending. The bot then can place a bet upstream, but only one. Thus on input, we will have one or two bets in the queue and on output zero or one. These rules enforce spectal allocation and minimum redundancy.
What kind of bets does the bot place upstream? Bets to cover gains and losses from its own operations. The bot can lose when the radical in the root function goes negative, mainly because the input went from long bot coins to suddenly short. The bot generally wins then that radical goes to 4, as that is a unit gain. Do not quote me just yet though.
The radical indicates how much second derivative the bot needs, and that is he valuable stuff. So, on a win or lose, the bot will save or borrow upstream, and cannot process inout bets until his bet upstream is cleared, And of course, the number of input bets is always posted, and that modifies the amount if secodn derivative available to cover each bet in the input queue.
So, in the end, what is happening is that the bot network is shipping around the Shannon clock, mainly making sure there is enough bet spectrum up and down the chain to keep queues stable. I am pretty sure that for the adapting network, the input rate is Phi^2, and the output rate Phi; though do not quote me just yet. For unadapted, fixed SNR the rates are 2 for input and 1/2 for output, I think. Though these may be the sum of series rates as the aggregate rate is broken up. That is, in the fixed SNR case the output rates go as (1/3)^n, and the input go as (2/3)^n; where n is the network order at that level. his should be the lowest energy level result.
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