Does first-principles physics rank the alloys the same way the fast potential does?

EXPERIMENTS.md · lines 4229–4274

E78 — First principles agrees with the potential about the ranking, to 1 and 4 meV/atom

The E75 prediction, tested on the repaired comparison of E77. Seven structures at 16 atoms: four elemental references and three alloys, every one on the same cell, the same lattice constant, the same cutoffs, the same 3x3x3 grid and the same pseudopotentials, none relaxed. Mixing energies, each model against its own elemental references:

Prediction was agreement within 30 meV/atom, falsification above 50. Mean 28, worst 30. It holds.

And the useful part is that the disagreement is an offset, not scatter. MACE over-binds every one of these alloys by 26 to 30 meV/atom against PBE-PAW, which is the ordinary behaviour of a foundation potential on formation energies and is nearly constant here. It therefore cancels in the only quantity the search uses - the gap between one alloy and another:

One and four meV/atom, against a k-point error of about four. The agreement is as close as this measurement can resolve, both models order the three alloys identically, and the ranking the generator learned is confirmed from first principles on the three compositions tested.

What this does not say. Three structures, one arrangement each, unrelaxed, at 16 atoms. It does not check the off-lattice hull, where the competitors are Laves phases nobody has computed here in DFT, and it does not check the ordering temperature, which is a Monte Carlo result the potential is used thousands of times inside. It checks the one number the generator is rewarded on, and that number survives.

A second rounding trap, found inside the repair. The mixing energy must be weighted by the cell's ACTUAL composition, not the requested one: a 16-atom cell cannot hold Mo0.6216, it holds ten Mo and six Ta. That third of a per cent multiplies the difference between two pseudopotential zero-points - Mo at -4951 eV/atom, Ta at -9893 - and arrives as 25 eV/atom. With requested fractions the table read +16,677 and +37,649 meV/atom, and the equiatomic reference, the only composition a 16-atom cell represents exactly, was the one row that looked believable. A table in which the control is fine and everything else is absurd is the signature of this class of bug, not of a physics result.