Pretty well for the above, compared to the below.
Okay, I'll try to pose this in a way that gets us the info needed for meaningful build decisions while minimizing workload for you. My present understanding is this:
*Eldritch at baseline does not grant any effective Arcanum levels no matter how much we scale it
*Eldritch with a few Techniques does not grant any effective Arcanum levels but does raise our mana pool significantly
*Eldritch with numerous Techniques focused on spellcasting
does grant effective Arcanum levels but to an unspecified degree. This may or may not scale with further Eldritch levels.
What would really help with build design and variety is a comparison of just these scenarios:
*Case 1: In the specific case where we have Eldritch 7, Arcanum 7 and 4 techniques devoted to the goal of "improve our effective Arcanum level via Eldritch," what is our effective Arcanum level? I know Techniques vary greatly but let's just assume Sol has the best four Techniques for that specific goal, all at level 3.
*Case 2: As above, but we have Eldritch 8, Arcanum 6.
*Case 3: Eldritch 8, Arcanum 6, and 0 Spellcasting Techniques
Of course Eldritch does plenty besides buffing Arcanum, but this is the specific detail we're really trying to pin down. We will most likely be choosing from the above three builds so a specific comparison with precise numbers would be maximally helpful!
My intuition given your prior responses is that, in Case 1, we will probably get something like +2.1 effective Arcanum Levels and +750% Mana Pool from Eldritch 7 and its four Techniques, for a total Arcanum Level of 9. Case 2 would grant maybe +2.4 Arcanum Levels and +1000% Mana Pool instead, for a total Arcanum Level of 8.4. Case 3 would basically grant +0 effective Arcanum Levels.
If this intuition is more or less correct, you can just confirm that instead of answering in detail.
Others have advanced a more optimistic view that Eldritch by itself grants about +.25 Arcanum per level, with Techniques maybe amplifying that to +.5 Arcanum per level, so we can expect a total Arcanum Level of ~11 if we take four spellcasting Techniques.
If instead their intuition is more or less correct, you can just confirm that instead of answering in detail.