The \(\varphi\) method of semi operators, the first half of my research

[JmsNxn]

Those are suggestive images. Idk if If I'm saying something idiot... but they looks like the white circle is an artifact that can be removed to show the smooth and nice surface underneath...

Too bad I Wanted to be strong on programming...

So far, they do appear to be artifacts, and that's the story I'm sticking to! I have every reason to believe that's the case, because any Schroder iteration will have artifacts exactly about there. So, all's not loss. The problem is I'm not sure how to seamlessly program in a transition from repelling to neutral. This has two problems, near the neutral fixed points everything starts to geek out, and at the neutral case I don't even have code to run, I just return(0) (which only accounts for a measure zero area, so never expect to see it). I somehow have to account for the geeking out near the neutral case. I have a close up of this happening:



   



This is over a \(0.4\) window in the \(x\) axis of \(3 [0.5] x\) centered at \(x = \exp(1)\).



This isn't necessarily a bad thing. But it's not really a good thing. I think though, if this dip is happening it gives us a much more stringent manner of describing the actual semi-operators... they won't have this blip. I think the make or break will be to actually correct this dip. And honestly, it does seem possible, it is still continuous, it's just sharp is all... Which could be due to code (which is highly probable) or due to this is exactly what it looks like. But when I run my code for the \(x = e - 0.1\), it's already failing in the preliminary stages (constructing the Schroder function), before it even gets to the bennet protocol. So it's very likely this is just a programming error. If not, all is still not lost. This is still just the modified bennet.



EDIT:

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Also Mphlee, I have mathematical evidence this is a computing error.

   

If you look at the Lambert branch, there are points where it is always a curve, but it no longer looks like a function. This is what we are seeing near \(e\), and it's precisely a Lambert branching problem. I have to continue this curve which isn't a function, while maintaining holomorphy.

I solved half the riddle mathematically, and I see much better why this shit code error is happening. Don't lose faith yet...