The Baker Theorem of BART Positioning

The BART train doors have a simple and elegant pattern to where they will appear in the station. My colleagues seem befuddled by this behavior, when in fact its essence is simplicity itself.

But before we can describe that theorm, we need to describe the universe of the BART system:

Axiom 1: For each station σ, there exist β black spots, where β is a positive integral value.
Axiom1a: β=20 for all currently known instances of σ.

Axiom 2: For every train τ, there exist γ cars, where γ is a positive integral value.

Axiom 3: For every car χ, there are δ doors, where δ is a positive integral value.
Axiom 3a: δ=2 for all currently known instances of χ.

Axiom 4: In order for all passengers π to disembark from an instance of χ in an instance of σ, there must be a door paired with a black spot, therefore β ≥ δγ.

Lemma 1: In order to satisfy Axiom 4, γ ≤ 10.

Axiom 5: BART trains endeavor to stop in such a way that given β1, the number of black spots ρ beyond the leading edge of the train, and β2, the number of β beyond the trailing edge of the train, β1 = β2.

Armed with this knowledge and the simplest powers of deduction, one can arrive at fascinating observations. To wit:

The Baker Theorem of BART Positioning

To determine the black spot ρ*, the leadingmost or trailingmost black spot ρ for which ρ will be paired with a door χ, one need only calculate the following formula:

ρ* = (β / δ) - γ

And given Axioms 1a and 3a, we can simplify the formula to:

ρ* = 10 - γ

This theorem holds in all cases except when the driver is a fucking jackass.