Can the ladder flag alloys holding elements with their own transition in the working range?

E122 — Closing the magnetic hole, or rather admitting it

Every rung of this ladder is spin-blind. The cluster expansion is fitted to MACE-MPA-0, which carries no spin degree of freedom, and the Quantum ESPRESSO runs are not spin-polarised. Three of the twelve elements undergo a transition inside the 90-1000 K service window in their pure form:

Cr    311 K    antiferromagnetic Neel transition (incommensurate spin-density wave)
Ni    627 K    ferromagnetic Curie point
Co    695 K    hcp -> fcc allotropic transition

None of the other nine has a transition in the window: Ti, Zr and Hf transform hcp->bcc at 1155, 1136 and 2013 K, all above it; Nb and Ta go superconducting at 9.2 and 4.5 K, below it; Mo, W, V and Cu have none.

What is being added is a flag, not a prediction. A fraction-weighted estimate of an alloy's magnetic transition would be inventing physics: Cr's Neel temperature in particular falls steeply with alloying, and the ordering is an incommensurate spin-density wave whose existence depends on Fermi-surface nesting that dilution destroys. The honest statement the ladder can make is: this composition contains an element whose own transition lies in the window, and no rung here can evaluate what happens to it. That is a declaration of ignorance, and it is worth more than a number that pretends otherwise.

Predicted, against E117's 55 feasible compositions:

1. Between 8 and 12 of the 55 are flagged. E118 found 11 of 55 contain Cr, Ni, Cu or Co above 5 per cent; copper has no transition in the window, so the flagged count should be at most 11 and at least 8.
2. Cr0.75 Ni0.25 is flagged, and it is the top of E118's Pareto front on oxidation. The composition that currently looks best on every axis the ladder can compute is one whose most likely failure mode the ladder cannot compute. If it is not flagged, the gate is broken.
3. Mo0.50 Ta0.50, the driving-force optimum, is NOT flagged, and neither is any composition drawn only from the refractory eight.

Falsified if the flag catches compositions containing none of Cr, Ni or Co, which would mean the element table is wrong, or if it catches everything, which would mean the fraction threshold is doing no work.

E122 result: all three predictions confirmed, and the flag exposes a structural problem sharper than the hole it was built to record.

forager/physics/transitions.py flags a composition when a present element (above 5 per cent) has a pure-element transition inside the window. Verifier.screen now returns transitions_unmodelled and has_unmodelled_transition. 228 passing, one new test.

Against E117's 55 feasible compositions: 10 flagged, inside the predicted 8 to 12. Cr0.75 Ni0.25 is flagged, as predicted, and it is the top of E118's Pareto front. No composition drawn only from the refractory eight is flagged, also as predicted.

The structural finding is in the two lists side by side.

flagged (10)                         oxidation penalty    clear (45)              oxidation
Cr0.75 Ni0.25                              0.06           Mo0.50 Ta0.50              2.05
Co0.33 Cr0.33 Ni0.33                       0.18           Mo0.75 Nb0.25              2.33
Co0.25 Cr0.25 Cu0.25 Ni0.25                0.26           W0.75 Ta0.25               1.90
Cr0.25 Mo0.25 V0.25 W0.25                  0.94           Mo0.50 V0.50               2.75
Cr0.33 V0.33 W0.33                         0.83           Ta0.75 W0.25               1.70

The best oxidation score among the 45 compositions the ladder can model is 1.70. The best among the 10 it cannot is 0.06 - twenty-eight times better. The separation is clean: the only way to resist oxygen at 1000 K in this element set is chromium, nickel or cobalt, and those are exactly the three elements whose transitions this ladder cannot evaluate.

So the ladder's competence and the application's requirement are anti-correlated. This is not a bug in the gate; the gate is what made it visible. Two consequences:

• Everything the ladder currently endorses is oxidation-poor. Mo0.50 Ta0.50, the driving-force optimum, carries a penalty of 2.05 against Cr0.75 Ni0.25's 0.06.
• Every candidate that would satisfy the oxygen requirement needs physics this project does not have - a spin-polarised model, or CALPHAD with magnetic terms assessed against experiment. Neither is in the ladder and neither is a small addition.

The flag does not resolve that. It stops the ladder reporting a complete-looking verdict on compositions where it has none, which was the whole point: Cr0.75 Ni0.25 is no longer silently endorsed. Whether to extend the ladder into spin-polarised territory, or to accept that this element set cannot meet the oxygen requirement and change the element set, is the operator's decision and is now stated as one.