Does the reversible ordering test give sensible temperatures on all nine published systems?

E210 — the reversible protocol on every scorecard system (2026-09-20 23:39; queued behind E207)

Operator: "we're not just going to look at molybdenum and tantalum all our lives." Every rung-1 test so far was Mo–Ta or MoNbTaVW because that is where the published numbers were. E210 runs E207's two-leg protocol (6³, 25 + 25 temperatures 1400 ⇄ 100 K, 1000–2000 sweeps per temperature, cooling then heating in one process) on all nine distinct scorecard systems (the table's fourteen rows collapse to nine compositions) — Cr–Ta–Ti–V–W, Ta–Ti–V–W, Cr–Ta–Ti–W, Cr–Ta–V–W, Cr–Ti–V–W, Cr–Ta–Ti–V, MoNbTaVW, Mo–Nb–Ta, MoNbTaW and Mo–Ta among them — one at a time (~3 h each, ~1.5 days). For each, the heating-leg Cv peak and the SRO onset (|α| > 0.05) are reported with the CV-derived error bar and scored only against like rows. Predictions: (1) every system is reversible (floor mismatch < 3 meV, legs coincide) — if any is not, that system's number is withheld, not reported; (2) v5's Cv-peak T_c is 0.3–0.6× the like-for-like ideal-lattice value wherever one exists (MoNbTaW: 264 vs 600), i.e. the under-ordering is systematic, not a MoNbTaW quirk; (3) v5's SRO onset lands within 200 K of the H_mix-inflection rows (SOB20's "H_mix+SRO", FC17), because that is the observable those rows actually are — which would say the old scorecard was "wrong" by comparing the wrong pair of numbers, not because the model's onset is wrong; (4) the V-bearing systems (B32-like per Woodgate & Staunton) show a lower v5/literature ratio than the valence-difference B2 systems, because the model's deep-end under-fit is worst where the ordering is driven by size rather than valence. runs/e210_chain.sh; results in runs/e210_scorecard/<system>/hysteresis.json.

E210's pre-registration, annotated before it runs (2026-09-21 17:1x). Its prediction (3) — "v5's SRO onset lands within 200 K of the H_mix-inflection rows" — was written with the SRO threshold in pyeCE's units (half of Warren–Cowley) and with "onset" meaning a threshold crossing on a smooth curve, which referee 2 showed is not an observable. It is withdrawn as a scored prediction; E210's SRO curves will be reported in Warren–Cowley units and compared as curves, not onsets. Its predictions (1) and (2) — the Cv-peak temperatures — stand, but will be read from dE/dT as well as the variance channel, with the grid step (2600−100)/34 = 73.5 K as the stated resolution. And four of its nine systems (the Cr-bearing SOB20 rows) are not scoreable against the scorecard at all until SOB20's spin treatment is known; they will be run and recorded, not scored.

A bug caught by its own test, the same hour it was written (2026-09-21 17:2x). specific_heat_two_ways had a stray /KB in the variance channel, and hysteresis() reconstructed the variance with a matching *KB, so the E214 read-out (ratio 1.94, both peaks 526 K) was right while the function alone was 11,604× off. A synthetic test that builds an (E, V) pair for which the identity Var(E)/k_BT² ≡ dU/dT holds exactly returned a ratio of 11,604 instead of 1 and would not pass. Fixed; the E214 numbers are unchanged, as a cancelled pair of errors should leave them. Recorded because it is the third time today that a check built on a known answer caught what a check built on agreement between two unknowns could not.

E210 and every downstream number wait for the factor. E210 (nine systems) is released by this result and runs, because a constant sampler factor leaves its relative ordering intact and the scan is needed either way; its absolute temperatures are provisional until the factor is pinned.