PAPER / ARXIV:2609.10614
Reinaldo Inácio
RESUMO
Generative models now propose millions of "stable" crystal structures, and their own referees have shown that stability is not discovery; no public benchmark asks whether a candidate has the physics to do a job. For superconductors the job is twofold: to pair, with a definite gap symmetry, and to become wire. We present a physics judge that answers both from a structure alone (DFT+U, a gated Wannier model, the full rank-4 RPA susceptibility on a $24^3$ mesh, the linearized gap equation, an irreducible-representation classifier, a manufacturability funnel) and measure what it says about what generators propose. With answer keys pre-registered before computing, the judge was calibrated on six known superconductors (Nb, Nb$_3$Sn, MgB$_2$, BaFe$_2$As$_2$, La$_{2-x}$Sr$_x$CuO$_4$, YBa$_2$Cu$_3$O$_7$), recovering the expected class in all six after two dated corrections. On the ruthenium analogue of the iron pnictide, with two runs and their criterion pre-registered the day before, it returns a null verdict at the same physical interaction where iron gives s$\pm$ ($\lambda_1 \le 0.0007$ versus 0.096; critical U 4.17 versus 0.97 eV); the pre-registered equal-alpha run fails the letter of the criterion, and we declare the resolution in favour of absolute U as post-hoc. The funnel reproduces the industrial map with thresholds fixed before running. Three generation audits follow: a descriptor sweep over 150 Materials Project metals re-finds the canon; 1,248 MatterGen structures yield 0 candidates that are new, stable and carry a pairing motif; mechanism filters over 47,893 compounds, validated by a blind hold-out, re-derive the community's analogies: geometry plus d-count is necessary but not sufficient. Generation re-finds what is known; judgment is the bottleneck. We propose a public benchmark over the eleven lists of AI-proposed superconductor candidates, none of which classifies gap symmetry.
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