Is the energy model badly wrong outside the compositions it was trained on?

E65 — WITHDRAWN: the expansion is accurate; the comparison that condemned it was not

This entry claimed the cluster expansion degrades badly outside its fitting box - four to six times its stated error at the compositions the generator reaches, and up to 563 meV/atom with the wrong sign at binaries - and that the leverage guard failed to detect it.

All of that was an artefact of how the comparison was set up, and it is withdrawn.

Two errors compounded:

1. The expansion predicts the energy of a structure on a fixed ideal lattice at 3.2935 A. It was compared against relaxed_bcc_energy, which relaxes the cell to its own equilibrium. The difference between those is the relaxation energy - a real quantity, measured in E59 at 16 to 112 meV/atom - not a model error.
2. The expansion's output had been moved onto equilibrium references by correct_references (E55), and was compared against MACE values computed against shared-lattice references. Those differ by up to 505 meV/atom for vanadium alone.

Repeated with the same lattice, the same references and no relaxation on either side, so that the only difference is the model:

Mean absolute error 3 meV/atom, against a stated cross-validation error of 5.67. The expansion is doing better than it claims, at exactly the binary compositions this entry accused it of failing at.

The number that started it - Hf-Zr at +443 meV/atom, read as "two elements that mix freely predicted to separate" - is not a chemical statement at all. It is the elastic cost of holding hafnium and zirconium, which want lattice constants of 3.565 and 3.600 A, at 3.2935. That is the same strain E53 found charged to every mixing energy in the project, and it is still present in any quantity quoted against shared-lattice references.

What was actually wrong was the reading, and the lesson is narrow and repeatable: a number from this expansion is only comparable to another number computed on the same lattice, with the same references, and with the same treatment of relaxation. Three conventions, and getting any one of them wrong produces a difference of hundreds of meV that looks exactly like a discovery.

The pair-interaction matrix in data/pair_interactions.npz is therefore valid as what it is - ideal-lattice mixing energies against equilibrium references - but it is dominated by elastic strain rather than chemistry, so it is still not the ordering descriptor it was built to be. A useful version would evaluate each pair at its own equilibrium lattice.

Nothing else in the record depends on this entry. The off-lattice driving forces, the rankings, the fly's results and the candidates were all computed consistently and are untouched.

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