Matching Hayek's triangles

A little more on methods for automatic S/L banking:




That is what the S/L system is about, except we use a value added generator as the closest approximation of a Hayek triangle. A generator is the encoding tree for the string of deposits and loans, taken separately, but in a queue stabilized regime we can treat this a a finite element system and perform difference in triangle areas.

Consider the simple case, the deposit tree is a balanced equilateral tree an so is the current queue of loan balances. Then, the trees are balanced when the area of one is within a bounded error of the other, except our precision is equal to the size of a rank, when viewed as balanced trees instead of triangles.

In the smooth case, using solid triangles, the area of deposits minus loans is:

D^2 - L^2 which has to be less than required variance.  The common factor has been removed.  This is the hyperbolic system. It is made up of two Shannon systems back to back.

The key to understanding the interest swap is that is is a redistribution of deposits alone, all parties keep at least one interest payment in their  deposit account to support the redistribution.

Step 1:

The deposit tree has grown by rank (one unit of error), while the loan tree remains the same.

Step 2:

The pit boss incrementally shifts deposits, taking from the borrowers and spreading the swaps out to nearest neighbors in the deposit tree.  What happens?  Innovations drop in the deposit queue, as if the 'items per basket' does not have the variation it had before, the deposit tree drops rank and loans match deposits to one bounded error.

Alternate step 1:

The deposit tree has shrunken by rank (one unit of error), while the loan tree remains the same.

Step 2:
 The pit boss also distributes from the deposit accounts from the borrowers to non-borrower neighbors. But the effect is to introduce innovations in the deposit tree, it grows one unit in rank.

The pit boss is distributes innovations, liquidity.  It is altering the customer queues by altering items per basket. If the deposits need a greater variation of items per basket then the pit boss expands the number of checkout counters.  If the pit boss needs to shrink the deposit innovations, then the variation in 'items per basket' decrease and the number of checkout counters decrease.

It is actually the second derivative of L/S that is being altered.  That is liquidity, supply matching demand within the bound error.

There are tricks with market making that make the two trees 'homogeneous (they can be compared by shape within a bounded error).  The extra work of inserting small loans and deposit owned by the pit boss is the market making function needed to make the trees homogeneous. These should always tend to canceled out to keep the accumulated market making risk below the bound.   Liquidity is a finite, conserved quantity. If the trees can be matched to a unit of rank the pis boss accumulated market acount should be small and bound.

Loans do not change, the traders have the responsibility to monitor the tree and estimate a future interest cost and react accordingly.  Depositors have that same responsibility, and all traders have equal round robin access to the trees There are issues with how much deposit needs to be in account least the borrower gets a 'fails to deliver'.

It is all about value added networks, directed graphs that are optimally quantized at the nodes so bunching does not occur..

There is a lot of work I have not done, as I do not get paid.  But the theory is correct, a mathematician who understand this should report to Thiel capital immediately. I be watching movies while someone else gets rich.

Short cuts

We have two Shannon systems, deposits are encoded to match the noise of loans and loans are encoded to match the noise of deposits.  Reducing the innovations in the deposit stream can be done by simple changing items per basket to set the rank of deposits properly, then just scale the dollar value of deposits directly.  And using this method one can see that multi color trading pit can be constructed by ganging the two color systems.

What is a dual Shannon system? An optimally coded  bidirectional channel moving liquidity, in this case.

But that short cut needs further proof and elaboration. I may or may not continue pursuing this, I suggest ou entrepreneur get a good mathematician and work out the theory completely.

Is this quantum mechanics?

Sure is.  We are composing a superposition of a finite set of 'sequence states'  The sequences are defined by feeding a uniform random variable into our generators to specify a finite set of sequences that match the boundary conditions.  Do we tunnel, like quantum systems? Yes, we will get the occasional 'fails to deliver' and these have to be handled outside the S/L system.