3-band active EQ: questions/discussion

I'd love to understand a little more about the mathematics behind a hidden gem of the datasheet realm. I speak of the TI LF353, and it's stellar datasheet!

It has a bunch of great stuff in it, but I found this one bit truly inspiring and it happens to be at the core of what you might call my "flagship" build I'm in the middle of finalizing...

LF353EQ.png
So I guess I'll get the ball rolling:

I think I know how certain aspects of this topology work, but not all. I understand that there are 3 bands of frequencies set up in the second half of the opamp, with each band having a pot control where at center, it's "equalized" and not providing boost or cut. Beyond that, there is loose understanding of what's going on, and I guess I'm just looking for a little clarity/extra knowledge.

My general questions are these:

-is my assumption correct that in each band, the gain/cut is determined by the ratio of pot size/inline resistor sizes for that band?
IE- high eq: when "low", R2(1.28k)<(waylowerthan)<R1(500k+1.28k) in trad. inv. feedback loop, and when "high" R2(500k+1.28k)>(wayhigherthan)>R1(1.28k)

-what resistance values in particular correspond to each capacitor to form the filter network for each band? IE: for the high band, is it C-5n and R1.8k?

-what is the importance of the ratios of 1.8k/3/6k/11k...? I notice that 1.8x1.8=3.24 and 3.24x3.24=10.49... But also that 1.8+3.6= 5.4k... which is roughly half of 11k. I'd like to think this is important, and would like to know more specifically why... or what the scale really is here if it isn't arbitrary.

-in my current design, I have omitted the first half of the opamp, and am only using the second opamp stage, running at 9v. It seems to work ok without the first half, which seems to be a simple non-inverting buffer with a high-pass filter (5u/10k) on it to get rid of the super low stuff. Does this buffer/filter help the low eq band control in any way, or is it mostly unnecessary with the other coupling cap (1u) on it's output? Like, is it only there because the 353 is a dual amp, and the datasheets objective is "showing a way to use the whole chip"?

last one...

-in the schematic provided, the second half of the opamp is in an inverted configuration... it shows the (+) input as grounded. I'm curious about this. Is it vital for the correct operation of the EQ design? In my design, I have (+) with a +4.5V reference voltage, and it seems to be behaving as expected. I assume in their application, 15v supply and 0v reference just means a bigger voltage swing for the boost/cut than my 9v supply and 4.5v reference... I guess in short, I'd like to know a little more about the nuances of biasing this as a standalone stage, as that's what I am currently doing/intend to do.

Thanks in advance to anyone willing to take the time to demystify this active eq setup an join in the discussion!
Even running it as I have it (slightly altered cap/res/pot values, single opamp stage, and 4.5vreffed) it is a really kickass part of my build's guts, and I'm excited to tweak it even more but with some real knowledge behind what I'm actually tweaking...

CHEERS!🍻
 
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