Denisaran wrote:

Let (a,b) be an ordered cell source cell for xyt chain A.

Then (b,a) is an ordered cell from which there may be an xyt chain B different from A.

Whatever the length of A, and whatever the length of B, each and every right hand link of A is strongly linked to each and every right hand link of B.

Completely absurd.

It's a few days back, but in the interval I hope it has dawned that the absurd party wasn't the one being targeted...

Re'born : this is the real Aran speaking

...wrote

If you have an xyt-chain (a b) - ... - (w x) (where (w x) might be modulo some t-candidates)

and if you have another xyt-chain (b a) - ... - (y z) (where, again, (y z) might be modulo some t-candidates),

then we can read the first chain as saying if a is not true, then x is true and the second as saying if b is not true then z is true. Since a or b is true, we conclude x or z is true, i.e., x is strongly linked to z.

Aran, is this what you are saying?

I am saying that but more than that.

All of the right-hand links in the ordered cells in the respective xyt chains (starting from cell C respectively ordered (a,b) and (b,a)) are strong-linked : not merely the final cell.

Think of it in terms of transport : each of the right-hand links in the starting cell ie b for (a,b) and a for (b,a) is in effect transported by the xyt chain (remembering that the "backward-looking" t candidates by virtue of their seeing preceding "truths" in the chain do not hinder chain progression).

Then each T (as in Truth) in the first chain is strong-linked to each T in the second.

This generates multiple strong-links.

What I was saying (and Denis seems unable to see this point) is that within his own system, if he wants it to be efficient, or less inefficient, he could easily (ie for little extra work) examine these links for possible eliminations.

Note that eliminations found in this way might not necessarily be found by any xyt chain examined singly. One cannot in fact say at what point they would emerge in that system.

As to the example I gave, it is entirely well-founded.

Here it is again :

Suppose that P and Q are nrc-linked cells in the respective chains.

Say the ordered cells are P (257) and Q (1345) (ie t candidates 5 and 34)

=>7P 5Q strongly linked

=>given the nrc-link : P <5>.

Thus whether or not there was a z elimination, there is a t elimination in this example.

(Apparently I'm misusing "nrc-linked" which in any case just means "sees")

So P and Q see each other and are in the respective chains.

Therefore their right-hand links (or "True" candidates) are strongly-linked.

Hence either 7 is true in P or 5 in Q or both, and whatever, 5 must be eliminated from P.

In this example, it so happens that a "t" candidate is eliminated.

I did not say and am not saying that there will necessarily be t eliminations, nor indeed any eliminations.

If I used the "t" elimination in my example it was to illustrate the curiosity of setting out to target "z" eliminations (plural because of both chains) and ending up...

paradoxically... with a "t" one.

Of course, a second type of possible elimination arises where the respective right-hand links are strongly linked on the same candidate, say w. In this case any w seen by both is eliminated (which does not impose the condition that the strong-link candidates see each other).