Why do Fibonacci series appear in manufacturing and investing?

Fibonacci trees  equalizes inventory variance at each stage of production under the assumption transportation costs between inventories are small.

Look at the Fibonacci generator above.  Think of it as the reverse, or dual of a manufacturing network. Start at the root which represents a completed product made from eight quants of input. The eight units are represents at the leaves, and are taken from the width of the tree.  What is the minimum number of sequences needed to manufacture that product?  We need to decompose the eight units of input in a final product using the minimal stages of decomposition while keeping inventory variance minimal.  We march up the tree from the root counting the tree width as we go.

 The path from each each unit of input to the final product is the minimal number of steps.  So 8 units are combined into a sub assembly of 5, combined into a sub assembly of 3, until we get a sub assembly of 1 constructed from the 8 units of input.  The width at the top says one unit of output needs eight units of input.

Why not take all eight components to final assembly?  Because congestion rises as the eight units still require eight assemble steps.  Input inventory has to be purchased in groups of eight.  Queuing is not minimal, because any  delay jitter in  the assembly causes input inventory to jump in units of eight.  The assumption is that there is no transaction cost  in moving inventory from one stage to another, so F  spreads the inventory variance maximally among the steps using integer whole counts of input.

Let's apply this solution to the bankers yield curve at equilibrium:

Ask ourselves, what is the minimum number of steps to collect N deposits at the short end and combine them into one humongous loan to Congress while equalizing variance at each step.  The Vi are going to be a Fibonacci series, certainly, because transportation costs for cash are very low.

By the way, I should mention how I derived the numerator in the equation above, log(vi).  I went back to my Huffman encoder and scrolled down to their sample chart. And there discovered that the information content in bits should be the signal power and was log(wi) in the example. Proof by Wiki, is that valid?