Successor-closed distributional afterstate values rank siblings as well as fair D4

The strongest dependable player in this repository is a search that looks four of the player's own moves ahead and averages over the luck in between — fair D4. It is slow. The obvious shortcut is to train a network that looks at a board once and says how promising it is, then use it to pick a column directly. Every previous attempt here broke in the same way, described on the sibling trap page: the model learned the outcome of the move that was actually played, and then had to choose among six other columns it had never been shown.

This theory says the break is fixable by changing the data rather than the network. Make the scorer action-free — it reads only the board after a move resolves, plus the visible next disc and the rise clock, so there is no "which move was this" input to shortcut on. Then make the training data successor-closed: at every position, label every legal column, under the same imagined runs of luck, so no candidate is ever out-of-sample. If that works, the model can replace the four-move search as the thing that picks the column, with the search kept only as a fallback.

Where it stands. This theory has code, four registered experiments, and four recorded results — it is not a paper idea. The record's own assessment is not-supported-as-tested: once the labels were made stable enough to judge anything, the learned scorer trailed the four-move search on every preregistered ranking comparison. The mechanism was not shown to be broken; the specific configuration was shown not to beat the reference.

How you could help. The results name two suspects, not one. The scorer was stopped undertrained (11 of a planned 20 epochs), and its labels came from a deliberately weak one-move continuation player. Evidence that would move this theory is a rerun of the same frozen ranking gate with a fully trained model, or with labels generated by a stronger continuation policy — either result, better or worse, is informative. Evidence that the gap survives both would close the direct-replacement reading for good.