Quick update:

When I said:

"(more specifically the linear equations of curves with N control points aka "binding points" / "points of stability" / "fixed points" / "immovable points", etc.)" -- there's a terminology mix-up here -- the control points (A, B, C, D) are (obviously) variable / flexible in nature, but the values from Pascal's Triangle are (obviously!) bound/stable/fixed to their respective row!

So that's what I meant to say...

So my apologies for having messed-up the terminology there!

(You know what I meant! :-) )

Anyway, some very interesting responses and connections! Thanks to everyone who responded!