Does rewarding low energy steer the search toward alloys that fail the ordering test?

E117 — Is rung 0's reward anti-aligned with the actual requirement?

Fable's review makes a claim that, if true, invalidates the whole generator loop rather than its search: mixing enthalpy and ordering tendency are the same number. Strong unlike-pair attraction is what puts a composition below the hull AND what drives B2 ordering. The generator maximises -drive_conservative, so it is steered towards the strongest orderer - which is precisely what rung 1 then rejects for ordering inside the 90-1000 K window.

If that holds, the ladder's first rung is selecting against its own second rung's criterion, and no amount of exploration fixes it. It is cheap to test: screen() already returns both drive_conservative and T_order for the same composition.

The related bookkeeping claim is already confirmed: the off-lattice hull holds 5 Mo-Ta binaries and all five are Laves (C14/C15) or Mo2Ta - no bcc-ordered Mo-Ta at all, because E85's coordination-number filter removed the B2. That filter is defensible on its own terms, since the expansion is supposed to cover the bcc lattice and the hull the off-lattice competitors, so the two must not double-count. But it means drive_conservative answers "does this beat the Laves phases", not "is this the ground state", and the ordering question is delegated entirely to rung 1.

Enumerating the composition grid settles Fable's other question at the same time - whether the search is broken or the objective is: all 28 binaries at 25/50/75, all equiatomic ternaries, quaternaries and quinaries of the 12 elements, one rung-0 screen each.

Predicted:

1. Mo-Ta near 50:50 is at or very near the minimum of drive_conservative over the whole grid. If so the search was never broken: it found the objective's true optimum, and E114's and E116's collapse diagnosis, while correct as description, blamed the wrong component.
2. drive_conservative and T_order are strongly NEGATIVELY correlated - the more negative the driving force, the higher the ordering temperature. Spearman rho below -0.5.
3. Consequently the top-ranked compositions by reward are disproportionately those that order INSIDE the 90-1000 K window, i.e. the ones that fail the requirement. Measured as: the fraction of the best-50 by reward with orders_in_window true exceeds the fraction over the whole grid.

Falsified if rho is near zero or positive, in which case the driving force and the ordering temperature are independent, rung 0 is a legitimate cheap filter, and the problem really is the search after all.

E117 result: prediction 1 confirmed, predictions 2 and 3 FALSIFIED. The objective is not anti-aligned - it is a 12-fold enrichment. Fable's central claim does not survive measurement.

1705 grid compositions, one rung-0 screen each.

Prediction 1 confirmed. Mo0.50 Ta0.50 at -86.6 meV/atom is the global minimum of drive_conservative over the entire grid. The search was never broken. It converges on the objective's true optimum, and E114's and E116's collapse diagnosis - correct as description - blamed the wrong component.

Predictions 2 and 3 falsified, and the first pass of this analysis was wrong too. p_survives_window is 1 - p_happens, and p_happens is the probability of decomposition into off-lattice competitors, not of the order-disorder transition. Reading it as the phase requirement conflated two independent failure modes. The requirement needs both: no decomposition (p_survives_window > 0.9) and no ordering transition inside the window (orders_in_window false).

Scored properly:

passes BOTH tests, whole grid          55 of 1705   =  3.2%
passes BOTH, best 50 by reward                      = 38%
Spearman(drive_conservative, passes)      -0.250

A twelve-fold enrichment. Rewarding driving force is a good filter for the actual requirement, not a bad one. Fable's claim that "mixing enthalpy and ordering tendency are the same number, so the objective steers towards what rung 1 rejects" is falsified for this grid: the correlation runs the other way.

What is genuinely wrong is the reporting, not the search or the objective. Fifty-five compositions pass, and the generator reports the top few. The diversity that was missing is an archive over the feasible set, which is the weaker "multi-basin reporting" use of MAP-Elites, not MAP-Elites as a replacement optimiser. That is consistent with E114, where MAP-Elites-as-optimiser lost by 98.8 meV/atom.

Widening to twelve elements paid off, measurably. Eleven of the 55 passing compositions contain Cr, Ni, Cu or Co, including Cr0.75 Ni0.25 at -30.2 meV/atom with no transition in the window. The eight-element space could not represent any of them.

Unverified claims from the same review, recorded because they would outrank everything above if true. None is in any rung, and none has been checked here:

• MoO3 volatilises above ~800 K, so a Mo-rich alloy may not survive 1000 K in oxygen at all.
• Ti, Zr and Hf are ruled out for liquid-oxygen service by impact ignition (NASA-STD-6001).
• Mo and W are brittle at 90 K (ductile-brittle transition ~300-450 K and ~500-700 K), so a Mo-Ta part that never changes phase can still crack on thermal cycling.

If those hold, the requirement is not a phase-stability problem at all for this element set, and Mo-Ta - which this experiment confirms is the correct answer to the question as posed - is the wrong answer to the question that matters. Checking them is the next task, and it is cheap: they are literature constants, not simulations.