Does the chosen alloy really stay disordered when checked with DFT?

E242 — the survivor at DFT: does Mo₅₁Ti₃₈W₃Ta₃ order? (pre-registered 2026-09-23 22:0x)

E222's design on E241's survivor. The e6 model (seed 0; the ensemble re-evaluates) is annealed from five starts to its 54-atom ground state at the survivor's composition (ground_state.py), and a seed-fixed random decoration of the same composition is written (random_cell.py); both at ideal bcc sites and the Vegard constant, QE at the rung-4 standard (60/720 Ry, k 4³, MV 0.02), on the A100 through the spin-aware ladder. ΔE_order = E(random) − E(ground), per atom. Predictions. (1) e6's own ΔE_order on these two cells is < 5 meV/atom (its rung 1 finds no transition down to 60 K; by E222's Bragg–Williams scaling ~20–30 K per meV). (2) Decisive: DFT ΔE_order ≤ 5 meV/atom → e6's ordering energetics confirmed at this composition and the find stands as the ladder's first full pass; 5–15 → not established (a transition could sit at ~100–400 K), reported as such; > 15 → e6 is wrong here and the find FAILS. The e6 ground state is the lowest state the MODEL finds, so a small DFT ΔE_order is a lower bound that cannot rule out a different DFT-preferred order — stated, not hidden. (3) The random cell's DFT formation energy is within 15 meV/atom of e6's (with E239's open Ti-reference caveat: the old-label frame may carry ~x_Ti·30 meV). (4) Known answer for e6's rung 1 (runs in parallel on the Mac): equiatomic Mo–Ta through the production path (ECEVerifier, e6 ensemble mean, exact evaluator) must show a transition inside the sweep between 500 and 2600 K (published CE+MC 2020 ± 545 K; v5 985 K on the same sampler); "no transition" there would void E240.

E242 addendum (2026-09-24 00:08, before any DFT result) — the cells' actual composition. Both 54-atom cells round the survivor's nine-element x to whole atoms: Mo₂₈Ti₂₁Ta₂W₂Zr₁ (runs/e242_random/Mo51Ti38W3Ta3_random/random_cell.json), i.e. Mo 51.9, Ti 38.9, Ta 3.7, W 3.7, Zr 1.9 at.%. Cr, Hf, Nb and V (0.63 at.% each in x, 0.34 atoms each) are absent. The name Mo₅₁Ti₃₈W₃Ta₃ is x's four largest shares; ΔE_order is measured on the rounded cell, and the verdict applies to that composition. Predictions unchanged.

E242 (4) RESULT (22:4x) — e6's rung 1 passes the Mo–Ta known answer. Equiatomic Mo–Ta through the production path (ECEVerifier, three-member e6 mean, exact evaluator): T = 1149 ± 114 K by the energy-slope channel, α₁(Mo–Ta) = −1.00 on cooling (perfect B2) — inside the pre-registered 500–2600 K (published CE+MC 2020 ± 545 K; v5 985 K). E240 is not void. Caveat it exposes: the fluctuation channel peaks at 80 K here — a spurious low-temperature peak from energy still drifting where the sampler freezes, while the true transition sits at 1149 K. Both channels therefore have cold-end artefacts. The 2026-09-23 fix uses the fluctuation channel only when the slope channel found no peak, and the five finds it failed had mid-range fluctuation peaks (331–575 K), not cold-end ones; failing an ambiguous find is the safe direction, but those five are "not established", not proven to order. runs/e242_mota_known_answer.json.

E242 — the two DFT cells are not the same composition; fixed before scoring (2026-09-24 01:57). Both cells reached JOB DONE on the A100 (runs/e242_dft.log: ordered −235006.117 eV, random −235777.395 eV). Their totals differ by 771 eV because the cells differ by one atom. The ordered cell is Mo₂₇Ti₂₁Ta₂W₂Zr₂: the anneal keeps whatever counts pyeCE's sampler produced (ground_state.json). The random cell is Mo₂₈Ti₂₁Ta₂W₂Zr₁: random_cell.py rounds x by largest remainder. This is the same defect the site check found in E222 (Cr₁₄Ta₁₃Ti₁₄W₁₃ vs Cr₁₄Ta₁₄Ti₁₃W₁₃). The model-side "ΔE_order(v5) +21.7 meV/atom" printed by ground_state.py is no ordering energy either. It sets the 54-atom ground state against the model's random mean at the continuous x, which also carries 0.63 at.% each of Cr, Hf, Nb and V. Nothing is scored on these pairs. Fix, under the pre-registration's own wording ("a seed-fixed random decoration of the same composition"):

• random_cell.py gains --counts, which takes the ordered cell's exact counts.
• A new random cell is drawn at Mo₂₇Ti₂₁Ta₂W₂Zr₂ with seed 0, at the same Vegard constant (3.2448 Å), and computed at the same rung-4 standard.
• e6's own ΔE_order for (1) is taken on the two 54-atom cells of that composition, with the random side as the mean over decorations of the same 54 atoms.
• The Mo₂₈ random cell already computed is kept for prediction (3), which needs only a random cell and its own e6 value. Predictions unchanged.

E242 (1) and (3) RESULTS (2026-09-24 02:01); (2), the decisive one, waits for the matched random cell.

(1) Falsified, on every seed. runs/e242_model_side.json (scripts/ordering/e242_model_side.py). Each seed is evaluated on the anneal's 54-atom ground state and on the mean of 32 seed-fixed shuffles of the same 54 atoms:

The prediction was < 5. The model's own energetics say this composition orders. By the Bragg–Williams scaling this entry used (~20–30 K per meV), that puts ordering at roughly 450–680 K, inside the window. So e6 contradicts its own rung 1, which read "no transition down to 60 K". The rung-1 record shows why the two disagree (runs/e240_walk/15_Mo51Ti38W3Ta3.json):

• its energy at the 60 K floor is −106.5 meV/atom, against rung 0's random-solution −83.7; the sampler did order, by 23 meV/atom, the size of ΔE_order above;
• neither transition channel found a peak on the 227 K grid.

A gradual ordering with no sharp peak is being read as "no transition", and so as a pass. scripts/ordering/e242_rung1_curve.py re-runs the same rung on a 60 K grid to show where the energy falls (runs/e242_rung1_curve.json). Until that lands, the survivor's rung-1 pass is not established, and E240/E241's "silent to 60 K" verdicts share the doubt.

(3) Falsified as written. runs/e242_formation.json, the same references and ensemble as E223's scoring:

The pre-registered caveat (the old-label frame may carry ~x_Ti·30 ≈ 12 meV/atom of Ti reference) could account for about half of the random cell's miss; E239 measures it. Either way e6 binds this Mo–Ti composition too deeply.

The ordered and random totals above are NOT an ordering energy: the cells differ by one atom (addendum above). (2) is scored only on the matched pair (runs/e242b_dft_chain.sh, queued behind E221's W cell).

E242 diagnostic RESULT: the survivor orders inside the window. runs/e242_rung1_curve.json uses the same e6 ensemble, cell and sweeps as E240's rung 1, but a 60 K grid (floor 80 K). The EXISTING peak reader finds a transition inside the sweep: dE/dT at 320 ± 180 K, the fluctuation channel at 492 K. The energy falls from −84.0 (740 K) to −106.9 meV/atom (80 K), and α₁(Mo–Ta) reaches −0.53. The survivor fails rung 1. The blind spot that passed it was mainly E240's 227 K grid, on which no peak resolved and "no peak" read as a pass. The survivor fails whatever E242's DFT (2) says about the ordering energy's size. E241 must re-choose from finds re-read on a fine grid.

E242 (2) RESULT (2026-09-24 03:46): the survivor FAILS. It orders, and the model knew it. The matched cells hold the same 54 atoms (Mo₂₇Ti₂₁Ta₂W₂Zr₂) at the same Vegard constant and rung-4 standard; both are non-magnetic and converged (26 and 28 SCF iterations):

• ordered −235006.117 eV;
• random −235004.736 eV (runs/e242b_dft.log).

DFT ΔE_order = +25.6 meV/atom. The bar was > 15 → the find fails.

The pre-registration's wording, "e6 is wrong here", assumed e6's own ΔE_order was small, and (1) showed it was not. e6's energetics are right:

So the failure was never the model's. Rung 1's coarse-grid reading turned an ordering it had actually sampled into a pass (E242 diagnostic: peak 320 ± 180 K on the fine grid). Final E242 scorecard:

• (1) falsified: e6's ΔE_order is 17–33, not < 5;
• (2) fails, ΔE_order 25.6 by DFT;
• (3) falsified as written: e6 − DFT is −21.3 on the random cell, about half of it possibly the Ti reference;
• (4) passed: Mo–Ta at 1149 K.

The ladder's first full walk ends with no survivor. Rung 1 as corrected (E244's fine grid) would have stopped this composition before DFT.

E242 correction (2026-09-27 00:05): the Mo–Ta reference. This entry and its pre-registration quote "published CE+MC 2020 ± 545 K". Kim & Widom (Phys. Rev. Materials 7, 063803, 2023) give 2020 K with no uncertainty: the susceptibility peak of an unrelaxed 1024-atom lattice under a four-site cluster model with a 21 meV/atom error. The ±545 K is published_error_K: this project's rule, 2020 × √2 × 21 / 110, where 110 meV/atom is the ordering energy a nearest-neighbour bcc Ising model needs to order at 2020 K, inferred here, not given in the paper. It was written correctly on 2026-09-21 ("by this project's own rule") and lost the qualifier in later copies. No other publication found reports it; other estimates cited in a 2026 paper range from 800 ± 200 to 1770 K (not yet read in the originals). The known-answer bar (500–2600 K) never used the ±545 K, so the E242 (4) verdict is unchanged.