The equation

Here is the equation, let us simplify for banking, using my partly inaccurate hand waving.

The thing in the middle is the implied hologram dimension, the dimension that has been collapsed into the bit error function. What is not shown for banking is our Hamiltonian, it is empirical, it is implied in the pre-balancing of the loan and deposit queues, independent of error minimization.

In the general form, those independent queues are being recovered, in the banking form they are actually known slightly ex post.  I say slightly by noting the Plancks constant has become market uncertainty due to serialization, he commutator process executed by pit boss. So a mechanical pit boss, not quite obeying the infinite divisibility of Euler, can combinatorically find that imaginary axis.

The finite sum on the right is the resulting sequence of typical transactions after matching. It s the 'white' sequence of the fixed transaction channel minus the bit error sequence. The delta density on the left is the amount of 'momentum' that needs to be accommodated by energy, in the form of liquidity.

Think of it as trying to shift the distribution of transactions from one mean to another and keeping variation within bounds. The process needs to obey the Hamiltonian, implied in the empirical process.  If this were Walmart, then the part on the left is like the path the checkout manager takes up and down the line, the stuff in the middle the amount of queue imbalance he accumulates, and the stuff on the right the implied mass movement of people when he changes 'items per basket'.

Pre-conditioned queues

Back to the idea of taking a typical sample of some parabolic sequence and slightly encoding it to minimize transaction cost of information flow. The idea was, we don;t know the forces, the Hamitonian, but we can pre-measure, ex post, and get a good guess.

But we presume an asynchronous sequence and this equation actually finds an an X axis, they can call it time because it finds a complete sequence on the right. The X axis is as accurate as market uncertainty because of serialization bouncing up against market uncertainty.

That part on the left is what the pit boss is telling folks about shifting supply and demand for the current index step. The equation implies the pit boss never gets to that exact optimum liquidity as that is an iirrational outcome not bound by some finite approximation.

When using the imaginary X axis as time, the spectral sparsity means insurance, you are likely to jump about the mean as large as your market uncertainty.  For example, your annual time is mostly partly invalid until the seasonal adjustments become clear. Then there is clearing of the seasonal election cycle. Then the final clearing of an incomplete generational cycle.

But, banking is computationally efficient in finding the farthest that delta index can stretch.  Physicist have a much tougher problem.

The pit boss and the commutator

The pit boss, when issuing interest swaps, implies: If everyone were slightly ex post, then these rearrangements would keep market error within bounds. The commutator function is a willingness of risk equalized traders to trust the algorithm via power of attorney and a contract. The pit boss, has power to reverse order or sequence withing some bound.  That makes enough of commutator function, and a reverse, to complete the hologram and velocity equation works. The pit boss is making something called a quotient ring.

The quotient ring is adiabatic

If prices were a density then delta prices must remain within a bounds of prices via homomorphic transform (node by node adaptation of the generators). That implies the firms and households keep a reserve because the pit boss will be slightly shifting order of events, ex post. (Oh! beans were expensive last quarter.)  The pit boss expects folks to hold reserve inventory space and slightly surplus goods as the cost of currency risk. In this model, everyone suffers from ATM fees.

In aggregate, over the monetary zone, the idea is that all agents optimize the ratio of spare inventory space to goods in inventory, m a logistics problem of having the quantized  'basket' optimally full. That is the condition where supply tends towrd demand, and visa versa.

Real trees

The hologram conditions are met when an summation of biomass on the branches and roots can  match vertical nutrient flow through the trunk. The accuracy is high, but external forces highly variable. Indoor bonsai gardening solves this equation better. The quantizations are the vertical flow vascular tissues up the trunk. There should be tiny horizontal vascular flow, the commutator function, bit error.

So the equation is about the tiny horizontal micro hairs in tree trunks, the currency risk function, the cost of having a Walmart line manager, the utility of round off space in fractional approximation, the cost of changing the map in Huffman encoding. It is bout the thing in the middle with the imaginary 'i'.