Funny Cat, I really didn't mean to be offensive or arrogant.
Allow me to clarify my posts above. Carefully following the OP's scenario, we essentially have:
A. Two hard panned, high passed mono tracks.
B. One channel, say, R being low passed and mixed equally into the above tracks.
Now, before we flip the phase of B, let's consider a second what we have now.
Given the LP filter in B is the exact inverse of the HP in A (say, both are first pole and set to same cutoff), the right channel will now be equivalent to the original input (no changes at all). The left channel will now contain the LF of the right channel, and given a high correlation between L and R, will sound very much like the original. If the correlation is low (high difference between L and R, in this case under 60Hz), we might get some bump or strong cancellations in the left channel.
More clearly. The result will be the original signal + an unpredictable bass in the left channel. You can do the same with a dual mono EQ.
Now let's flip the phase of B, as described.
Given the same assumptions as above (HP/LP are inverses of each other), With B now polarity flipped, the result will be:
L = the same unpredictable Bass region as above.
R = a huge bump over the cutoff area (with "holes" around it).
Again, you could have achieved the same by simply launching a dual mono EQ and blindly messing around with the lowest bands. In doubt, try the same with white noise and measure the output freq response.
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As for the Christortion process, it does something very different. Give me a min to explain how it works, it will probably make clear what I meant with crude (I'll try in simple words and intentionally leave out a few details).
The process works like this, the plugin takes the input signal and generates various harmonics. It can generate 2nd harmonics, 3rd, 4th, and so on. Each harmonic can be specified in form of a coefficient describing how strong this harmonic will be. Each harmonic can also have certain polarity.
At runtime, the plugin simply does this ("*" stands for multiplication):
// second harmonic
y = x * x * secondCoefficient
// third harmonic
y = x * x * x * thirdCoefficient
// fourth harmonic
y = x * x * x * x * fourthCoefficient
(and so on...)
All partials are then simply being added to the original signal. Finito!
This is a super powerful construct called the Taylor series. It can approximate most type of functions. Most function such as log(), sin(), sqrt() have their own Taylor series.
Now the truly crude aspect is that the coefficients mentioned above are super sensitive and their effect hard to control. A bit like lottery. Try and error does not work. This would be somewhat equivalent to offering an EQ in biquad form. It's super flexible, but setting cutoff and Q properly is rocket science. That's why you typically have an additional layer in between giving these low level coefficients some "tactile sense" (say, by offering params such as "drive", "colour", "hardness", "symmetry", "shape" and so on).
I didn't mean to call your decision "crude" or "bad". Just saying that it's not what the OP did.