With more sampling per temperature, does the reweighted rung pass every known answer, and do the HEA leaders survive it?

E245c — more sampling: 300 + 1000 sweeps per temperature (pre-registered 2026-09-24 10:54)

The operator's decision (option 2): fix the root cause, the cooling leg's lag, rather than the reading. Protocol: E245b's grid, reading (R1 and R2, faithful to the reference) and two seeds. Per temperature the sweeps rise from 100 + 200 to 300 + 1000, where Fable measured the Ising hysteresis collapsing (T_c 1410: cooling/heating 1246/1370 K → 1346/1350; 1050: 1038/1006 → 1000/1014; ratio 0.956–0.959, inside r = 0.95 ± 0.03). Cost is 47 × 1300 sweeps ≈ 6.5 h per seed at 0.385 s/sweep, ≈ 13 core-hours per composition.

Bars are set from what each exact answer must be, not from any reading at this protocol:

The seeds are FRESH (6 and 7). Any Ising with ≥ 2 significant peaks voids E245c.

Scope and order.

• The top 8 of E244's 16 HEA leaders by rung-0 p (walk_finds.select), two seeds each.
• Their legs are sampled now, alongside the known answers. Sampling embodies no decision.
• They are read, through rung 1 and then rung 2's MACE hull, only after every known answer holds.
• About 104 core-hours in all: up to 6 single-core jobs, niced, with DFT on the A100 and no local pw.x. Roughly a day.

E244's predictions (2)–(4) are scored on these 8: ≥ 5 of 8 fail or come out not established; ≤ 2 pass rung 1; any pass goes to DFT (matched cells), and DFT then confirms or fails it.

E245c scope amendment (2026-09-24 10:55, before any sampling). The top 8 of E244's leaders by rung-0 p were near-duplicates of one family (Mo₃₅ plus Ta/W around 55 % plus two elements exactly on the 5 % floor). They are HEAs by the definition's letter, but sit on its boundary: the reward still pulls toward the Mo–Ta–W corner. The 8 are now taken greedily by p with every pair ≥ 0.30 apart in L1 (25 distinct families among the 40 pooled leaders), in runs/e245c/candidates.json. Predictions unchanged.

Result, known answers part 1 (2026-09-24 12:39; read at 11:47, seeds 6+7, 300 + 1000 sweeps). All six exact-answer controls hold their pre-registered bars:

K5 is the one that failed in E245 and E245b (two significant peaks on seeds 4+5); with 1000 measured sweeps it reads one. The four finite T_c land 1–3 % above the exact values (1425/1410, 1076/1050, 512/500, 93/90), inside the ±3 % calibration uncertainty on r. K3 (Mo–Ta on e6) is still sampling; the candidates are not read until it holds.

E245c candidate reader, fixed before any candidate is read (2026-09-24 14:15). e245c_run.py cand-read refuses to run until every known answer's reading holds its bar (checked from the saved readings, K3 included). It builds E244's verifier exactly as the E244 walk did (e6 ensemble, reweighted rung 1, MACE hull). Rung 1 reads the saved legs through the production ECEVerifier.reweighted_rung1 (new legs_d argument, tested to give the sampled path's answer without re-sampling), and rung 2 is walk_finds.walk to the lattice rung. Scoring, as written now:

• E244 (2) holds if ≥ 5 of 8 have p_rung1 < 0.5 (a fail, or not established, which reads p 0);
• E244 (3) holds if ≤ 2 have p_rung1 ≥ 0.5;
• a candidate goes to DFT (matched cells, E242's bars) if the ladder's combined p over rungs 0–2 is ≥ 0.5.

Smoke test: candidate 0's composition with K2a's Ising legs standing in, read end to end in 355 s (rung 1 511.6 K, identical to the production read of those legs; rung 2 bcc 0.999). Scheduling only: runs/e245c_read_chain.sh adds two single-core workers for the fourth round of candidate legs once the known answers hold (same seeds, same protocol), and reads each candidate as both its legs land.

E245c read delayed (2026-09-25 12:26). K3's legs landed at 17:07 on 09-24, but the read chain never ran the reader: zsh did not split its command string, the command was "not found", and the chain logged that as a failed known answer and stopped. Nothing was read and no data was affected. K3 is being read now; the chain is rewritten (command as an array, refusal and crash told apart, control flow smoke-tested with a stub). The two extra workers are dropped: legs take about 8.7 h, not 6.5, so the original workers reach the last round before an extra one could finish it.

E245c known answers, part 2 (2026-09-25 17:42; K3 read 17:42). K3, equiatomic Mo–Ta on e6, holds: 1120 ± 42 K, one significant peak, FWHM/T 0.37, p_rung1 1.000; the sampler froze at 879 K and R1 found the frozen legs in the ground state's phase (Δα 0.02 on 2 readable pairs, gap 1.1 meV/atom). Bar: p ≥ 0.7, one peak, R1 quiet. E244 had predicted 1160–1220 K from the 227 K grid's 1149 ± 114 K; the reweighted reading sits 40 K below that range and inside its error. All seven known answers hold. The reweighted rung 1 is validated, and the eight candidates are read under it now (runs/e245c_read_chain.sh).

E245c candidate RESULT (read by 2026-09-25 23:59; written 2026-09-26 12:50). The eight diverse HEA leaders of E244, two seeds each at 300 + 1000 sweeps, read by the validated reweighted rung 1 and then rung 2's MACE hull (runs/e245c/cand<i>_reading.json):

• E244 (2) holds: 7 of 8 fail or come out not established on rung 1 (bar ≥ 5).
• E244 (3) holds: 1 of 8 passes rung 1 (bar ≤ 2).
• To DFT, by the pre-registered rule: Mo₃₅Ta₃₃W₂₂Nb₅Ti₅.

What the pass is, stated plainly. It passes because its ordering peak sits 44 K above the window's top edge (p 0.86 that the transition is not inside it), and R1 found the frozen legs in the model's ordered ground state. So by the model it is ordered at every temperature in the window, not a random solid solution; the ladder's requirement ("no transition inside 90–1000 K") has counted that as a pass since K1 (an Ising ordering at 1410 K is a pass by design). It is also an HEA only by the definition's letter: Nb and Ti sit exactly on the 5 % floor, and the rest is Mo–Ta–W, whose Mo–Ta pair orders at 1120 K on this model (K3). E242's DFT bar measures the ordering energy itself (≤ 5 meV/atom confirms,

15 fails), so it will most likely fail this find for the same reason rung 1 passed it. Which reading the project wants, "no transition inside the window" or "disordered throughout it", is a decision for the operator, and is recorded here before any DFT.

The other seven are the regime's typical answer: broad heat-capacity features between 255 and 836 K, gradual short-range order rather than a sharp transition, inside the window. Two sit lowest on rung 2's bcc probability (#4 at 0.71, #6 at 0.84).

e6's ordering energies against DFT on matched cells (2026-09-26 23:50; post hoc, prompted by an external review). The eleven unbiased QE cells (score_unbiased_qe.py) hold two same-composition sets: B2 Mo–Ta with three random Mo–Ta cells, and an ordered MoNbTaVW (Mo₃W₃Nb₃Ta₃V₄) with three random ones; all 16 atoms, ideal bcc sites at the Vegard constant, single SCF (unrelaxed). ΔE_ord = E_random − E_ordered, meV/atom:

e6 overstates the ordering energy on both, by +18 % on Mo–Ta and +66 % on MoNbTaVW: its ordered cells sit 5–7 meV/atom too low and its random cells 2–16 too high. E242's 54-atom pair went the other way by a little (+22.6 against +25.6). So the model does not under-bind the ordered state; if anything it drives ordering too hard, which would raise its T_c, not lower it. The gap to Kim & Widom's 2020 K is not explained by an under-bound B2, and KW23's own number is a different observable (χ peak at L = 8, unrelaxed tetrahedron lookup, 21 meV/atom MAE, no ordering energy or uncertainty given; the paper notes Mo–Ta is observed only as a disordered solid solution). Correction to this project's own quotation: "published 2020 ± 545 K" was wrong. KW23 gives 2020 K with no error bar; ±545 K is published_error_K's propagation using an ordering energy (110 meV/atom) this project inferred.