For the rest of your paragraph, it is based on the view of a chain as a chain of inferences, which a whip is not.
Verification of llc=>rlc at each stage requires some "work" from the reader, namely checking that each candidate not named in the CSP-Variable but still present in the PM is a z or t one.
The rest of my paragraph is simply restating what you yourself have said here. If there is any candidate which is present in the PM but not named or z- or t-, then it is not a complete whip (though it may be a partial whip) - verification will fail.
Further, your "llc=>rlc" here is an inference. It's the equivalent of "If not llc, then rlc", which is true if the other conditions are met (namely that any other candidate for that CSP-Variable is a z- or t- candidate). For that matter, "direct binary contradictions" are inferences, equivalent to "If X, then not Y". You can say the whip is the continuous chain of links absent the inferences, but that's a distinction without a difference to me. At best, the inferences are just hidden in either the general whip elimination theorem or the particular form of the theorem given by the statement of the whip.
Verification of continuity should be trivial for the reader, given the presence of all the candidates necessary to check it. Contrary to what you say, continuity is an essential condition for the manual solver.
Verification of continuity is trivial given the presence of the llcs, yes. Without the llcs, verification is precisely the same amount of "work" as verification that the other candidates are z- or t- candidates. The llcs are linked to the previous (in the case of whips) or a previous (in the case of braids) rlc or Z; z- candidates and t-candidates are linked to a previous rlc or Z. If the latter is "obvious", so is the former. If you gave me a whip without notating the llcs, I would have no more trouble following it than I currently do - you have given me all the information needed in stating that it is a whip and in specifying the CSP-Variables and rlcs, I just have to do the work to verify the links between each candidate present and Z or a previous rlc. (And the same is true of braids; in the case of whips, I simply have the additional information that at least one candidate for each CSP-Variable is linked to the previous rlc.)
(To clarify something I said earlier so there's no confusion: "In the cases where there is both a left-linking candidate and a t-candidate, losing the t-candidate leaves the whip unchanged (since we still have the llc), while losing the llc leaves us with slightly different whip using the t-candidate". This should say "t-candidate which is also linked to the previous rlc; if the t-candidate links to a different rlc, losing the llc would instead become a shorter whip or a braid, depending on what the rest of the whip looked like. Personally, I would consider drawing a distinction between these types of t-candidate - maybe l-candidate for this sort of candidate which is interchangable with the llc - in addition to or instead of the distinction between z-candidates and t-candidates, if such distinctions are necessary at all.)
Beware of approximative language.
Quoting from BUM, emphasis mine:
"A chain is defined as a continuous sequence of candidates, where continuity means that each candidate is linked to the previous one."
"Finally, braids and g-braids allow another type of extension, where the continuity condition is relaxed: in Figure 1.3, imagine that, instead of being linked to the pending candidate R1 for the previous CSP-Variable V1, “left linking candidates” C2,1 and C2,2 for V2 were linked to Z; or that, instead of being linked to the pending candidate R2 for the previous CSP-Variable V2, “left linking candidates” C3,1 and C3,2 for V3 were linked to Z or to a more distant pending candidate, e.g. R1."
It seems to me that braids are relaxing continuity itself, according to the definition you have provided here. Maybe the distinction between "continuity" and "continuity condition" you are making is more rigorously defined elsewhere, but it sure seems blurred here.
