Would rewarding exploration make the generator propose alloys with more elements?

E90 — The reward was pessimistic, so the search stopped exploring

E72 built the conservative bound drive + sigma to stop the generator being paid for finding where the expansion is wrong, and noted in the same entry that penalising uncertainty is "backwards for a rung that acquires data: a search meant to improve the model should go where the model is least sure, which is exactly what drive + sigma now punishes." That note was written and then not acted on.

The cost is now measured. On the focused twelve-element expansion, 84 distinct compositions from 4800 proposals:

The generator searched a twelve-element space and returned mostly binaries, never proposed two of the elements, and missed a composition 28 meV/atom better than anything it found, which is a plain binary an L1 distance of 0.35 from its own best. This is not a high-entropy alloy search.

And E89 made it self-reinforcing. Sampling the training set where the generator already goes lowers sigma there, which raises the reward there, which sends it there more. The fix for a leverage problem was correct in itself and compounds this one.

The two questions are different and were conflated. Where might something good be hiding is answered by an optimistic bound, drive - sigma; what can be afforded for expensive verification is answered by a pessimistic one, drive + sigma. The ladder exists to resolve the gap between them. Using the pessimistic bound as the reward asks the generator to propose only what is already known to be safe.

Predicted, running all three acquisitions on identical seeds:

1. Optimistic explores wider: more than 9 elements appear, and the share of compositions with four or more elements rises above the present 8 per cent.
2. Optimistic finds better raw driving forces, including something at or below -130, since Mo0.62 Ta0.38 at -144 raw is reachable and was not reached.
3. Optimistic's finds are less reliable on average - higher mean sigma - which is the price and the reason the ladder, not the reward, must do the filtering.
4. Ranked by the conservative bound afterwards, the optimistic run's best is at least as good as the pessimistic run's. If it is not, exploring cost more than it paid.

Outcome. The acquisition function is not the cause, and the real cause is the objective.

Predictions 2 and 4 are falsified and 1 only half holds. Optimistic saw one more element and then found fewer compositions, no four-element ones at all, and a worse answer on every measure that counts. Rewarding exploration did not produce exploration. Prediction 3 holds - its mean sigma is 38 against 30 - so it did go to less certain places; they were simply not better places.

All three collapse to about two and a half elements, which points past the search. Scoring known alloys directly, on the same screen:

The trend is monotonic: every element added makes the score worse. The generator is not failing to explore. It is finding, correctly, that this objective is maximised by simple well-matched binaries, and it reports them.

Two of those are real alloys that have been made and characterised, HfNbTaTiZr and MoNbTaVW, and this screen calls them unstable. That is not obviously an error. The screen asks whether the solid solution lies below the cheapest mixture of competitors at 90 K, where the configurational entropy of a five-element equiatomic alloy is worth about 16 meV/atom against enthalpy penalties of hundreds. At low temperature a high-entropy alloy genuinely is metastable; it is stabilised hot and retained on cooling because the atoms cannot move. The kinetic argument that makes this an engineering answer already exists in the ladder - it is what rescues MoNbTaW in E74 - but it lives at the top of the ladder, and the screen the generator learns from has no kinetics in it at all.

So the objective, not the search, decides that the answer is a binary. Asking this generator for high-entropy alloys while paying it for 90 K stability is asking for two different things. Which of these is wanted is the operator's decision and is recorded here rather than chosen: constrain the search to four or more elements; or move the screen's question to the service temperature where entropy is worth having; or carry the reachability term down from the ladder into the screen, so metastability counts.

Outcome. The acquisition function is not the cause, and the real cause is the objective.