As a first approximation, it is not false, But mentally eliminating all the candidates nrc-linked to z may unduly eliminate potential left-linking candidates and you may miss some xyzt-chains.
I don't see that removing z candidates as described could hinder chain progession
Let C be such a cell : it's structure is llc z t.. rlc
For the case you describe, we have llc=z, so the structure is : z t.. rlc
If z is removed under my approach, it is reduced to t.. rlc
which in the chain reduces to rlc=>chain progression.
Before I can answer, I need to know what is reversed.
If it is only a and b, then the resulting sequence of candidates may not even be a chain.
If it is the whole chain then it may not be an xyt-chain. (If it is, it is probably a mere xy-chain.)
The source bivalue is reversed.
There will be situations (not infrequent) where there is a resulting xyt chain.
We know that any right link in either chain is strongly linked to any right link in the other chain.
Therefore when any right link in the one is nrc-linked to any right link in the other, there is elimination potential of two orders:
i) when the respective right-links are on the same digit => potential elim
ii) when any non llr-digit in either cell is also a right-link in the other cell => actual elim.
This is something easily checkable by a program.
What I am saying is that after application of your sudorules to xyt chains examined, if only to be rejected, there is at hand a source of potential eliminations ie the confrontation of the xyt and yxt chains.
The Paradox is that a potential source of elimination at hand via sudorules is ignored under sudorules because it doesn't have a name in sudorules.
Many players use T&E and purists usually look down on them.
My results show that any elimination done by T&E (the very precise form of T&E I've defined) can always be recast (and moreover in a constructive way) as a pattern-based elimination. The practical consequence is that using such form of T&E, you can't go beyond what the logic of resolution rules allows.
Given your definition of T&E
Definition: Given a resolution theory T (i.e. a set of resolution rules) and a candidate z, T&E(T, z) is the following resolution technique:
- start an auxiliary grid by copying the current PM; in this auxiliary grid, delete z as a candidate and add it as a decided value; apply to this auxiliary PM all the rules in T until quiescence;
- if a contradiction is thus obtained in this auxiliary PM, then eliminate z from the original one; if no contradiction is obtained, then merely go back to the original PM.
I read that to mean : apply sudorules in any order to z, and if there is a resulting contradiction such that <z>, then this can be represented by a braid such that <z>.
But the braid incorporates all sudorules being the highest form of sudorules, so necessarily this will apply.
I don't see that you are saying anything more than A=>A.
