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Indeed.

  • “White relative exposure” changes: White- and black-point and midtone-contrast by shifting
  • “Black relative exposure” changes: Blackpoint, midtone-contrast slightly by shifting, highlight contrast(slightly)
  • “contrast” changes: midtone-contrast, blackpoint and whitepoint (slightly)
  • “hardness” changes: shadow/dark-, midtone-, highlight-contrast and blackpoint (slightly)
  • “Latitude” changes: shadow/dark-, midtone-(slightly) and highlight-contrast
  • “shadow/highlight balance” changes: shadow/dark-, midtone- and highlight-contrast, blackpoint(slightly)

This is not an exhaustive list, meaning: I did not try all combinations of parameters, nor all parameters, but only the quickly accessible ones. Also, as you mentioned, certain parameter combinations give inversions and clipped values. Some of these can be mitigated by switching to cubic splines.
To ‘learn’ the theory behind the sliders I suggest practicing a lot as well as looking at the resulting curves in @jandren 's tonecurve-explorer https://share.streamlit.io/jandren/tone-curve-explorer. Or, as others have suggested, make working presents and use them without fine tuning them too much after application.

EDIT: I should clarify: the “by shifting” expression used above means that it shifts the contrast slope that you have either up or down, effectively changing the contrast in the midtones.

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