Does refitting the energy model on the larger new training set give a better model?

E238 — the rung-0/1 model that ships (pre-registered 2026-09-23 15:1x)

Labels (runs/rhea_labels_final_gated_sites.jsonl, 5,836 rows): E231's refined cubic pass-1 (true lattice minimum) + E234b's non-cubic pass-1 (ideal-shape reference, A100; 2,020 rows) → pass 2 with the refined MEDIAN pure references and the 0.10 Å strain cut (5,878) → the site gate's 42 far-displaced rows dropped → every row carries its own ideal sites (merged emission fix: no row is written in file order, none is skipped). Arms, 3 seeds each (MPS), v5's other settings: A embedding 6, pairs 10 Å — the candidate; B embedding 6, pairs 6 Å — range on the new labels; C as A, trusted rows only (5,713); D embedding 5, pairs 10 Å — re-tests E237's e5 miss on the new labels. Scored on the eleven unbiased QE cells, the four Mo–Ta cells, B2 Mo–Ta, the same held-48 file as E237, seed sd, and E223's three DFT random cells. Predictions. (1) A meets E237's targets (MAE ≤ 14, Mo–Ta mean < +15, held-48 ≤ 9) AND holds E223's random cells at mean |error| ≤ 8 (v5 6.3). (2) A beats B on the eleven cells by ≥ 2 (E233 moved 4.7 at embedding 3) without losing more than 1 on held-48. (3) C is within 1.5 of A on every metric (123 rows). (4) D misses the random-cell bar again (> 10): the miss is the embedding's, not the labels'. Decision: ship A if (1) holds, unless another arm beats it on BOTH the eleven cells and the random cells by more than the seed sd; if A fails (1), ship the arm that passes both; if none does, rung 0/1 stay on E237's e6 ensemble (old labels), stated as such. runs/e238_chain.sh, two fits at a time.

E238 addendum (15:1x, before any fit finished) — rung 1's Hamiltonian. Measured, exact evaluator, one thread, 432 sites: 10 Å pairs (embedding 3) 449 moves/s, embedding 6 at 6 Å 1,709. Rung 1 on a three-member 10 Å ensemble is ~1.8 M moves at ~150/s ≈ 3–4 h per composition; the 6 Å ensemble ≈ 50 min. Rule: rung 0 uses the arm the decision above ships; rung 1 uses arm B (6 Å) instead of A if B is within one seed sd of A on the ordering-sensitive rows — the four Mo–Ta cells' mean, B2 Mo–Ta and the two E191 MoNbTaVW ordered cells — otherwise rung 1 uses A and the re-walk is sized for it. Either way rung1_model names what was sampled.

Formal checks (Lean 4 + Mathlib, formal/, 15:xx–16:xx). The identities the ladder's numbers rest on are now machine-checked, each tied to a pytest of the production function (formal/README.md): the 2T temperature convention (pyeCE's acceptance at T ⇔ the true chain at s·T; transition_ece and hysteresis return s × nominal), detailed balance and stationarity of sweep's one-attempt kernel (checked numerically on the exact 4-site transition matrix to 1e-15), the SRO decode (exact for α < 0; no decoder exists for α ≥ 0 — pyeCE's real encoder used), Warren–Cowley symmetry and the bound α ≥ max(1 − 1/x_a, 1 − 1/x_b) with equality iff perfect order, the labeller's volume miss (within the searched ±4 % bracket a miss only raises a label; an edge minimum is flagged vertex_interior = false, marked untrusted, and — by default — still trained on), and the exact evaluator's feature fold. Adversarial review of the STATEMENTS (fidelity, vacuity via compiled witnesses, 4/4 code mutations caught) found two overclaims, both fixed. No proof found the code disagreeing with the mathematics. All 5,836 E238 labels have an interior minimum.

E238 early read and a POST-HOC diagnostic (16:1x). Seed 0 of arms A and B, scored before the other seeds: both new-label fits carry a negative signed bias on the eleven QE cells (A −11.3, B −8.3; E237's e6 seed 0 on the old labels +3.4) and over-bind E223's random cells (mean |error| A 16.9, B 16.8, old e6 seed 0 9.3). One seed each — the decision still waits for three. Cause located in the labels: on the 4,134 rows shared with v5 the new labels equal E231's exactly and sit 9.3 meV/atom below v5's, almost all composition-linear — the median pure references against v5's minimum (per unit fraction: Ti −33.5, Cr −28.1, Hf −22.0, others within 6). The pure evidence is thin: Ti has 3 pure frames, Hf's 12 corrected frames spread 34 meV; the least-corrected frame sits at the median for Hf and Ti, at the minimum for Cr. Diagnostic, declared post hoc and NOT a decision arm: a 2×2 at embedding 6 / 6 Å, one seed per new cell — {v5's rows, all rows} × {minimum, median references}; the other two cells exist (E237's e6 seed 0; arm B seed 0). It says whether the over-binding is the reference choice or the 1,702 added ordered rows. runs/e238diag_chain.sh.

E238 diagnostic RESULT (17:2x) — the over-binding is the median references, not the new rows. Embedding 6, 6 Å, seed 0 each; E223's three DFT random cells, mean |error| (meV/atom):

Eleven QE cells: 7.1 / 8.2 / 6.2 / 9.4 (same order: old-min, old-med, new-min, new-med); held-48 10.6 / 10.0 / 7.8 / 13.4. With minimum references the new rows cost nothing on the random cells and give the best held-48 of the four; with median references both row sets over-bind. The ordering-sensitive rows move within seed noise (four Mo–Ta cells' mean +4.3 / +1.8 / −4.5 / −6.0 (−4.5 corrected 2026-09-24 00:09 from −3.5: runs/e238diag_report.txt per-cell −22 +4 −0 −0); per-cell seed sd ~8), consistent with a composition-linear shift cancelling at fixed composition. Single seeds, and these are test cells: this LOCATES the problem, it does not choose the reference — E239's anchor cells do that, independently. Consequence now: every E238 arm carries median references, so E238's pre-registered fallback applies until E239 lands — rung 0/1 on E237's e6 ensemble (old labels), which is also the best measured model on the search's random cells (6.1).

E238 RESULT (20:2x) — no new-label arm ships; the fallback stands. Three-seed ensembles (runs/e238_report.txt), meV/atom:

(1) FAILS — A meets E237's three targets but over-binds the random cells by 19.6 (bar 8). (2) FALSIFIED — 10 Å pairs did not beat 6 Å on the eleven cells (11.0 vs 6.5) on these labels; they did on held-48 (8.6 vs 13.8). (3) FALSIFIED as worded (C differs from A by 2.6–3.7 on three metrics; ensemble-mean noise is ~4 per cell, so this is not evidence that trust matters). (4) CONFIRMED — e5 misses the random-cell bar again (13.6). Decision (pre-registered fallback): no arm passes both faces, so rung 0/1 stay on E237's e6 ensemble on the old labels — already the model E240 walks with. Cause, from the diagnostic: every arm carries the median Ti/Cr/Hf references; E239 measures the right ones, after which the new labels (which cost nothing on the random cells with minimum references and gave the best held-48) are refitted and re-tested.