Combinatorics allocation and optimal flow

Matilde, my new hero got me thinking about that Fischer metric, it measures the change in data significance  between in coordinates on the hypothetical Riemann surface.

Number of combinations seems to be the root of significance. Mix things one at a time, two at a time or three at a time.  The two period model, one side contracts the number of combinations, the other expands.  So we have an allocation problem, what is the maximum entropy assignment of basis set algebras that make  a more smooth Riemann surface. That means a stickiness, an elasticity ratio,  A number of combinatorics left over, the Solow growth residual!

Customers make combinations taken two at a time. Inventory has to match, with one combination to spare. We get combinations of input and output. We still get a queue. Some customers do a one period, some do a three period. But inventory refuses to do three period combinations, not available except for low price. One perioders are no problem, a better profit.  But the two periods form the bulk of its operations.

Set and number of elements are controlled by the overlap function, which is quantized.  We restrict ourselves to quantum entanglement.

Lagrange himself

We have to prove we make a σ-algebras:

The main use of σ-algebras is in the definition of measures; specifically, the collection of those subsets for which a given measure is defined is necessarily a σ-algebra. This concept is important in mathematical analysis as the foundation for Lebesgue integration, and in probability theory, where it is interpreted as the collection of events which can be assigned probabilities. Also, in probability, σ-algebras are pivotal in the definition of conditional expectation.
In statistics, (sub) σ-algebras are needed for a formal mathematical definition of sufficient statistic,^[1] particularly when the statistic is a function or a random process and the notion of conditional density is not applicable.


So the overlapping bubbles need this:

Let X be some set, and let 2^X represent its power set. Then a subset Σ ⊂ 2^X is called a σ-algebra if it satisfies the following three properties:^[2]

1. X is in Σ.
2. Σ is closed under complementation: If A is in Σ, then so is its complement, X\A.
3. Σ is closed under countable unions: If A₁, A₂, A₃, ... are in Σ, then so is A = A₁ ∪ A₂ ∪ A₃ ∪ … .

From these properties, it follows that the σ-algebra is also closed under countable intersections (by applying De Morgan's laws).

I think the bubble get this for us. We do not need them spherical, we need each bubble conserved.