Does the corrected sampler reproduce published ordering temperatures across nine alloys?

E210b — the nine-system scorecard by the second sampler, pre-registered (2026-09-21 19:1x)

Operator's decision after the Colab question: the pyeCE E210 run is stopped after its first system (Cr20Ta20Ti20V20W20 finishes as a cross-check; the chain that would launch the other eight is killed) and the scorecard is run by the second sampler instead — locally, one core, runs/e210b_chain.sh. Colab was declined on the numbers: a sequential Metropolis chain gains nothing from a GPU, Colab's CPU is ≥ 8× slower than this machine for exactly this loop, the CLI handle cannot hold a multi-hour job, and it would ship the trained model off the machine.

The instrument. scripts/ordering/v5_metropolis.py, generalised today: any composition in the PRIM's nine elements (--alloy Cr20Ta20Ti20V20W20, largest-remainder counts on 432 sites), Warren–Cowley α for every unlike pair on four shells (alpha{k}_pairs; alpha{k} is the strongest ordering pair, the convention the pyeCE reader uses), a partial_<leg>.json after every temperature, done only after both legs. Tested against forager.physics.order.warren_cowley on a B2-like (Mo,W | Nb,Ta) cell to 1e-9 for every pair (tests/test_v5_metropolis_multicomponent.py). It samples at the temperature it reports and needs no decoding — the two defects of the pyeCE path are absent by construction. Protocol: 2600 → 100 → 2600 K physical, 35 rungs per leg (73.5 K), 150 + 350 sweeps (E216's), ~2 h per system on one core.

Predictions, carried over from E210 (2026-09-20) and restated on the physical axis. (1) every system is reversible: floor mismatch < 3 meV, the two legs' dE/dT peaks within one grid step — a system that is not has its number withheld. (2) v5's dE/dT T_c is 0.5–1.0× the like-for-like ideal-lattice rows (KOS19 MoNbTaW 600, KW23 MoNbTaW 1110 and Mo–Ta 2020): the measured points so far are 0.88× (MoNbTaW, censored ≥ 528), ~0.5× (Mo–Ta), 0.93× (MoNbTaVW against an H_mix row). E210's original "0.3–0.6×" was on the nominal axis. (3) no SRO-onset observable is claimed (ledger, 2026-09-21); SRO is reported as decoded curves and compared where SOB20/FC17 publish H_mix inflections only as context. (4) the V-bearing (B32-like) systems show a lower v5/literature ratio than the valence-difference B2 systems. (5) cross-check: on Cr20Ta20Ti20V20W20 the pyeCE run's E(T_nominal) equals this sampler's E(2·T_nominal) within 1 meV/atom over the overlap 200–2600 K physical, as E214 did for Mo–Ta (0.41 meV). Scoring: published_odt.comparable() per row; results in runs/e210b_scorecard/<system>/mc.json.

E210b, first system (2026-09-21 19:5x): Cr20Ta20Ti20V20W20. 6³, 35 + 35 rungs (73.5 K), 150 + 350 sweeps, 3.1 h on one core. dE/dT peak 747 ± 74 K cooling / 830 ± 184 K heating, both inside the sweep — the 2600 K ceiling does not censor it despite α(Cr–Ta) = −0.15 already at the ceiling; variance-channel peaks 693 / 475 (the heating one weak at 350 sweeps). Floor order: Ta–Ti is the strongest pair (α₁ −0.47 / −0.49), then V–W (−0.31), Cr–W (−0.27), Cr–Ta (−0.25); E from +46.1 meV/atom at 2600 K to −40.1 at 100 K; junction mismatch −0.06 meV. Scored: (1) reversible on energy (< 3 meV) — the two dE/dT peaks are 83 K apart against a 73.5 K grid step, ten kelvin past the pre-registered "within one step", and inside the heating peak's own 184 K width; reported as unresolved, not as hysteresis. (2) no cv_peak/chi_peak row exists for this system; against SOB20's F_mix crossing 900 K and H_mix inflection 1000 K (context only, not like-for-like) v5 sits at 0.75–0.92×. (5) cross-check against the pyeCE run's cooling leg (scripts/ordering/e210b_crosscheck.py): E_pyeCE(T_nominal) − E_sampler(2 T) has mean |diff| 1.05 meV/atom over 17 overlapping states (bar 1.0) — 0.3–0.9 meV away from the transition and 2.9–3.8 meV on the two rungs straddling it (935 and 788 K physical), where 350 sweeps of two different samplers disagree on how far the order has run. The factor of two holds on a quinary as it did on Mo–Ta; the bar is missed by 0.05 meV because of the transition rungs alone. The α columns of that table compare different pairs (the pyeCE reader picks V–W as its strongest decoded pair, the sampler Ta–Ti) and are not a like-for-like check. Eight systems remain, ~3 h each.

E210b, second system (2026-09-22 00:2x): Ta25Ti25V25W25. dE/dT peak 463 ± 74 K cooling / 546 ± 74 K heating (variance 471 / 525), both inside the sweep; junction mismatch −0.07 meV; floor order Ta–W (α₁ −0.47), V–W (−0.40), Ta–Ti (−0.33), with Ta–V (+0.39) and Ti–V (+0.28) avoiding; E from −2 meV/atom at 2600 K to −66 at 100 K. Against SOB20's F_mix crossing at 500 K (context, not like-for-like) the two legs bracket it: 0.93× / 1.09×. Second system in a row where heating sits ~80 K above cooling — one rung plus ten kelvin — with the energy reversible to < 0.1 meV: at 150 + 350 sweeps the cooling leg undercools and the heating leg overshoots by about half a rung each, so the pair brackets the transition and their midpoint (505 K here, 789 K for Cr20Ta20Ti20V20W20) is the estimate, the half-gap (±40 K) its bar. The pre-registered "within one grid step" is missed by the same ten kelvin twice; the protocol is reversible on energy and the gap is a sweep-count effect, not hysteresis. Third system (Cr25Ta25Ti25W25) running.

E210b, fourth system, and the scorecard so far (2026-09-22 02:5x). Cr₂₅Ta₂₅V₂₅W₂₅: highest-T peak 1272 K (1210/1335) against SOB20's ODTT 1300 — ratio 0.98. The four finished systems, scored like-for-like against the corrected table:

Three of four within 21 %, one of them to 2 %. This is the rung that was "0.5× published and under active-learning repair" on 2026-09-18; the repair was a sampler that ran at twice its stated temperature and a table that compared a heat-capacity peak with a free-energy crossing. Note what the fourth column does not say: v5 puts its strongest ordering on Cr–Ta in both Cr-bearing systems, where SOB20 report Cr–V. On Cr–Ta–V–W the temperature still agrees to 2 % with the wrong pair driving it, which is a warning about reading agreement as validation — and precisely why E222 tests the pair and not the temperature.

E210b, fifth system: Cr₂₅Ti₂₅V₂₅W₂₅ — largest peak 796 / 947 K (cooling/heating), highest-T 796 / 1151 (the heating leg carries a small hot bump), floor α₁ −0.34 (Cr–Ti), E −54 meV/atom, reversible. Not scoreable yet: the table holds only its F_mix value (700 K); the H_mix ODTT is being retrieved from SOB20's Table 2. Note the strongest pair here is Cr–Ti, not Cr–Ta or Cr–V.

E210b, systems 6–8. Cr₂₅Ta₂₅Ti₂₅V₂₅: highest-T 646 K (563/730) vs SOB20 700 → 0.92, pairs Cr–Ta −0.64 and Cr–V −0.55 (SOB20: Cr–V). Mo₂₀Nb₂₀Ta₂₀V₂₀W₂₀: 841 K (916/765; largest 733) vs FC17's 750 H_mix inflection → 1.12 (0.98 by the largest peak), pairs Mo–Ta −1.49, Mo–Nb −1.00. Mo₃₃Nb₃₃Ta₃₃: 1100 K, no resolved published value (WAK23), pairs Mo–Ta −0.87. All three reversible (junction ≤ 0.02 meV). Scorecard so far: 1.08, 1.21, 0.98, 1.22, 0.92, 1.12 — six of six comparable systems within 22 %, plus the Cr–Ta–Ti–W 2.92 that E222 explains. The ninth (MoNbTaW, the only cv_peak/chi_peak row) is running.

Seed variance, two of three seeds. v5 refitted with seed 1: held-out MAE 7.4 against seed 0's 7.2 (RMSE 10.7 vs 9.2, bias +2.6 vs +0.5). Preliminary spread ≈ 0.2 meV in MAE, so v7's 9.3 and v7b's 9.9 sit well outside it and their degradation is real, not fit noise — the pre-registered branch "a VASP-RHEA vs QE frame offset must be fitted per group before rows are merged" is the one that applies, pending seed 2 (paused by the guardian at load 13.6). E221 (the kinetics anchor) is on its second cell. The fcc reference redo landed: Fe fcc (non-spin) now fits inside its low bracket at a₀ = 3.4617 Å, E_min −4479.7572 eV/atom (the first pass had read the default 0.96–1.02 bracket, whose minimum sat below 0.96; the _lo_e80 scan at 0.93–0.99 brackets it). All five fcc references (Al, Co, Cu, Fe, Ni) are bracketed; E226 can read them.

E210b, ninth system: MoNbTaW (Mo₂₅Nb₂₅Ta₂₅W₂₅) — v5 orders it at under half the published temperature. runs/e210b_scorecard/Mo25Nb25Ta25W25/mc.json: dE/dT peaks 247 K cooling / 321 K heating (one grid step, 73.5 K, apart); heat-capacity (variance) peaks 174 / 321 K; floors agree to 0.0004 meV/atom, so it is reversible by (1). Strongest pair Mo–Ta, α₁ at the cooling peak −1.38 (B2 on (Mo,W | Nb,Ta)). This is the scorecard's one heat-capacity-peak row and the only like-for-like comparison with the KOS19 / KW23 CE+MC work on this chemistry: 0.41× KOS19's ideal-lattice 600 K by the same observable (variance-peak mean 247 K), 0.47× by the ladder's highest-T convention (284 K), and 0.22–0.26× KW23's 1110 K susceptibility peak. Prediction (2) (0.5–1.0×) fails for MoNbTaW. The scorecard therefore reads: six of seven comparable systems within 22 % (1.08, 1.21, 0.98, 1.22, 0.92, 1.12), MoNbTaW at 0.41, and Cr–Ta–Ti–W at 2.92 (E222). The two rows that fall short are the two from CE + Monte Carlo work on Mo–Nb–Ta–W (KOS19/KW23 here; Mo–Ta at 0.49× v5 and 0.57× e6 in E242 (4)). v5 under-orders the Mo-group B2 systems while matching the SOB20 rows. The survivor is 52 % Mo. This is why E242's DFT, not rung 1, decides it. (KOS19's relaxed-lattice 250–350 K, a different ground state, is not the comparable row and is not scored.)