The Bottom Up Solution
was the start of it all!

The Bottom Up Solution arose from scientific investigation
of fats and oils using mass spectrometry.
I manually solved all possible solutions to Critical Ratios
used to derive structural information about triacylglycerols, triglycerides.

When I saw the shape of the Bottom Up Solution,
it was obvious that it was half of an octahedron.

Then the question arose...
What is the full octahedron?
The answer is: The Simulacrum System.

The First Report was 2005: 
The Bottom Up Solution to the
Triacylglycerol Lipidome.
Byrdwell, in  Lipids

Figure 3 in the BUS

Figure 3, shown at the top of the page, represents the solution for a Type II TAG.
An ABA/AAB triagylglycerol (TAG) is a fat with two chains the same and one different. The [AA]/[AB] ratio gives structural information-- a Critical Ratio.

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Figure 4 in the BUS

Figure 4 was the three-level-deep nested solution. It used three Critical Ratios.
It showed how to nest solutions.
The Bottom Up Solution led to 
The Unit Simulacrum and 
The Simulacrum System

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The Bottom Up Solution

The Bottom Up solution showed that structural information could be derived from Critical Ratios.
Those Critical Ratios were made from accumulated knowledge of TAGs.
The Interpretation Matrix holds the knowledge of the Ratios, relationships.

Critical Ratios define the meaning in the fragments

The history of publications provided the knowledge for the ratios used in TAG analysis, called Critical Ratios.

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The Simulacrum

The BUS was half an octahedron.
The full octahedron shows all solutions,
including those not selected in the BUS.
The Simulacrum System shows all solutions, Seen and Unseen, constructed and not constructed,
selected and not selected.
The sum of all possiblilties based on two values or a value and a ratio.

Ratios of Ratios

The BUS required solutions for three-level deep nested Critical Ratios. It was Ratios of Ratios of Ratios.
Type I: MH/[DAG]
Type II: MH/Σ[DAG]; [AA]/[AB]
Type III;MH/Σ[DAG]; [AC]/([AB]+[BC]);[AB]/[BC] 

The UBUS 2 was also in 2015.

Byrdwell, W. C., "The Updated Bottom Up Solution Applied to Atmospheric Pressure Photoionization and Electrospray Ionization Mass Spectrometry", Journal of the American Oil Chemists' Society, 92(11):1533-1547 (2015), DOI: 10.1007/s11746-015-2735-z.

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Table 1 in the UBUS 2

Table 1 shows the use of the [MH]+/Σ[DAG]+ for APPI-MS was the same as the BUS and the UBUS, being half an octahedron.  
The three-level-deep nested solutions had Fibonacci Ratios as Critical Limits. 

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Table 3 in the UBUS 2

Table 3 used the ratio [MNH4]+/Σ[DAG]+ for ESI-MS, and led to consideration of the Path Not Taken, the Σ[DAG]+/[MNH4]+ ratio.
The UBUS was half an octahedron, the UBUS2 led to the other half octahedron. When the two halves were combined it gave The Simulacrum System.

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