Denis, I didn't invent Eureka notation. It's a logical convention people use, and sometimes people use it in different ways, just as people speak different languages and dialects and so on. You are welcome to consider it or the way people use it flawed. I don't really care about that. (I do like your more consistent version of it as a mathematician, though I find it less clear than the cell-focused approach as a manual solver.)
Please read my definitions before talking about them.
I have read your definitions, and I am trying to understand why you have chosen to define and notate as you have. If your goal is for no one to ever want to understand your work, then you are doing a good job of that I suppose. For what it's worth, I find your work quite interesting - if I didn't, I wouldn't bother with having this conversation in the first place.
When I say the continuity is really between Z and the CSP-Variables, what I mean is that in order to have a complete whip, certain conditions must hold for each CSP-Variable - namely that each candidate of a CSP-Variable in the whip must be left-linking, t-, z-, or right-linking. If there is a candidate that is
not one of those (what you call "pending"), then you have a partial whip (at least, if it's a candidate for Vn; presumably if the pending candidate were earlier in the pattern it would just be a shorter partial whip and stop at that point?). You have continuity
as you have defined it in either case, and for the purpose of programming CSP-Rules that distinction may very well matter! But for the purpose of proving an elimination in a sudoku, continuity of a chain of left-linking and right-linking is irrelevant if there are extra candidates around which aren't t- or z- candidates. What matters is the whole structure of Z, the CSP-Variables, and candidates within those variables.
1) Can't you see a single continuous line?
2) How do you do draw it without the llcs?
3) How do you draw it if the llcs are replaced by groups?
4) Can you explain how having a blob of 3 candidates instead of 1 make the graphic clearer?
5) How do you make the difference between a whip and a braid without the llcs?
1. I never said I couldn't see a single continuous line.
2. The graphical representation of a thing (or lack thereof) in no way impacts its logical validity. (But for what it's worth, I would probably draw it similarly to your dot at the end showing there is no pending candidate for 4 in c4, except this would then link to the pending candidate; for the first link, 7r4c1 with a thin arrow to a dot in c2 with a thick arrow to 7r3c2. This would be far clearer to me as a manual solver than having one of the 7s in c2 highlighted red and another ignored. But maybe that's just me.)
3. How would you draw it for g-whip? It's exactly the same challenge. (I'd probably use a similar notation as before, with the grouped candidates connected to the dot.)
4. For understanding why it works logically, having all the candidates necessary to verify that it works logically seems clearer to me. My contention is that if verification is
not the goal of the notation or graphical representation, then the llc is equally redundant. Again, YMMV.
5. I'm not sure it's a distinction that necessarily needs to be made, any more than it is necessary
logically to have names for a bunch of different patterns (e.g. XY-Wing, Skyscraper) that are all types of AIC. Naming conventions are a help to the manual solver more than anything. For you, the distinctions between whips, g-whips, braids, etc. are distinctions worth making, and you have done so with the first four characters of the line when you notate it "whip". (And for someone "totally submerged by the old view of chains", maybe a whip without z-candidates vs. a whip with z-candidates would be a distinction worth making, I dunno.) What I don't understand, still, is the
why - why you have defined continuity in the way you have (even noting that with braids you are relaxing continuity!), why you have made a distinction between whips and braids at all, why you have made a distinction between llcs and t-candidates, etc.
