forceMove, challenge & default outcome

Hi George,
yes, that makes this point clear, thank you.

Is there a notion to differ between the two following situations:

a) {j} → (j+1)_A ; with A being the mover
b) {j} → (j+1)_A → (j+2)_B → {j+3}_C = (j+3)_A,B,C = {k}

In a) A is the mover and made his move, so this state can be enforced.
In b) a complete turn has happened, every mover signed

or is this just an artificial choice (assigning a special role in the state where the 1st participant has the next move)? However, for the pre- and post-fund setup (up to n and 2n), this state indeed has a special role…

The background on this question is what has been discussed here.

The case a) above is what I would refer to an atomic game transition in the sense that A makes his move, everybody (inlcuding the adjudicator) could use the game logic to check if it is valid.

Now suppose we have a long of-chain sequence with 3 atomic game transitions between each {}:

{a}* → … → {i} → {j}, with {a}* being a quite old state on chain.
Now A as mover makes his move as in a), B does not respond.

A want’s to challenge J+1; therefore however it is required to be brought on-chain.

What would A now do?
Would A need to provide the full sequence → … → {i} → {j}-> (j+1)_A?
Or would it be sufficient to provide a subset of it?

Alex
P.S.:
Another try to explain what puzzles me:
suppose we have a complex game logic. Suppose we have sate 6 on-chain.
To check a valid transition in the game we need each atomic game transition.
If we have a longer off-chain game sequence, e.g. up to turnNumber 101.
It is not generally possible that the transition form 6 to 101 (without atomic transitions provided) can be checked to really fulfill the game logic.
This in turn means that every participant (it’s wallet) needs to store all transition up to 101…