Would the screen's claim that chromium–nickel is stable survive a proper relaxation?

EXPERIMENTS.md · lines 6068–6101

E104 — Cr-Ni was a model error. The uncertainty term was right and I was about to remove it.

Fable predicted the Cr-Ni result would not survive a real relaxation and named the test. Run: 54-site cells, cell and ions relaxed with MACE, two occupations each, compared against the same hull the screen uses.

Cr-Ni is a false positive. It is 86 meV/atom above the hull, not 82 below, and the screen was wrong about it by 168. Mo-Nb survives at -71, inside the screen's own error bar - it is real as a solid solution, though it orders once the bcc superstructures are admitted (+31 against the full hull).

So E100 is withdrawn in full. "Cr-Ni is competitive and the search is at fault" was wrong on both halves. The composition is not competitive, and the uncertainty term - sigma, which runs 49 there against 25 in the refractory corner because the expansion has no Cr/Co/Cu/Ni relaxations to stand on - was correctly de-ranking a claim from the model's edge. It is the same instrument that caught pure vanadium at -91 in E72, doing the same job, and I spent the evening arguing it should be removed.

Two independent analyses converged on why. The second found that the anchor term is an algebraic identity that cancels for every composition, so the whole composition-dependent content of the relaxation correction is the single constant 4.94 on the size-misfit term - and that constant was fitted on 120 relaxations containing no Cr, Co, Cu or Ni at all. Two forms indistinguishable on that fit set (leave-one-out 24.3 against 24.5) diverge by 122 meV/atom at Cr0.64Ni0.36. The measurement above lands in that gap.

And I mis-compared hulls on the way, quoting relaxed energies against the hull containing bcc orderings while the screen used the one without - a question every solid solution loses at 0 K by construction. Caught before reporting, but it is the three-convention trap again and it was the third time this week.