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What I see from a left field perspective.
This has the looks of a Lissajous pattern where the inventory capacity oscillations have a long-term frequency that is 3X that of the price fluctuations, and the cycles are slightly out-of-phase. So if the price continues to drop, the curve will quasi-retrace its steps back. The amount of spread it exhibits is due the phase-shift hysteresis.
What does a 3X signify? Probably nothing but this is purely an electrical engineering view of plotting two variables that may or may not have anything to with each other.
Look at the one in the third row, second from left:

Nice try ;) but the rational-ratio Lissajous is a closed figure that retraces.
To complete the retrace, oil would have to get back down to around $15. Even without all that "liquidity" being injected by our freaked-out Fed...no.
I said that it retraces, but not exactly. Explain why as the price comes back down it is starting to retrace. I agree that it may never go back completely, but very similar to chaotic nonlinear systems a potential duty cycle limit may exist.
In any case, the pattern does give an indication of how you could get a closed-form and analytical expression for the empirical behavior that is seen.
Something like:
x=A*sin(t)+B
y=K*sin(3t+C)
the variable t is similar to time but it could creep along, speed up, or reverse itself as it creates the pattern.
Hey, I don't necessarily believe in this, just that it fits a pattern. At least as well as that stupid Logistic does for Hubbert curves :) :) :) You can probably guess by now that I was just waiting for that punchline.