Did fixing the pure elements' reference energies make the energy model match quantum calculations?

E186 — the nine references, fixed (13:07). Hf and Ti from RHEA's own bcc end-member cells (bcc_binary_alloys, 12 and 3, MACE-corrected in pass 1: Hf −12.5669, Ti −7.7438 eV/atom; their fitted intercepts had sat +195 and +79 meV above). Zr has no bcc cell in RHEA, so its bcc energy is RHEA's own hcp minimum (−8.5205, idx 12991, V 23.4 ų) plus the within-QE difference E_bcc − E_hcp = +88.5 meV (60/720 Ry, MV 0.02; vc-relaxed hcp at V 23.33; literature PBE +70–80) — an ACWF-class transfer, ~1–3 meV, not a cross-code total. Zr's intercept had sat +282 meV above. Pass 2 with all nine fixed (rhea_labels_formation_strain0.10_pureref9.jsonl): the 554 hcp-rich (>0.5) cells move from −68.3 to +76.4 meV/atom — where two QE cells put them (+90, +100) — while the Mo–Ta random cell stays at −73.7 and the refractory region is untouched. The eCE was never the problem in that region; the reference convention was. v5 refit launched (runs/ece_v5_pureref9); prediction as in E183's record: E172/E183 within 30 meV of +100/+90, refractory ratios 0.8–1.3, holdout slope ≥ 0.8.

E186 result (14:27) — v5 on the nine-reference labels: the cheap rung now agrees with DFT across the whole space it was tested in. Test loss 3.0e-4; holdout (refractory compositions, unchanged split): pred = 0.746 × true − 12.0, r 0.904, MAE 12.2 (v4: 0.839, 0.850, 15.0). Against every DFT cell on disk:

cell                     v4       v5       DFT     DFT/v5   |DFT−v5|
E172  Hf/Zr-rich        +12.2   +104.8    +97.2    0.93      7.6
E183  Hf/Zr-rich        −35.1    +79.6    +89.7    1.13     10.2
E176  Mo14Nb14Ta13W13   −55.5    −51.9    −49.1    0.95      2.7
E177  Mo27Ta18Ti5Hf2V2  −78.8    −75.1    −71.1    0.95      4.0
E179  same, seed 1      −90.7    −66.9    −72.5    1.08      5.6
E180  Mo27Ta27          −96.4    −80.3    −89.8    1.12      9.6

Prediction: edge cells within 30 of +100/+90 — confirmed (7.6, 10.2); refractory ratios in 0.8–1.3 — confirmed (0.93–1.13); holdout slope ≥ 0.8 — falsified (0.746). The slope fell while r rose and MAE fell: on the refractory-only holdout the fit now carries a −12 meV intercept and a shallower slope, i.e. a small systematic compression within the refractory block, while the absolute agreement with DFT there is 3–10 meV. The holdout slope is a weaker instrument than six independent DFT cells and is recorded, not headlined. v5 (runs/ece_v5_pureref9) is the eCE rung from here; v4 is retired. The week's arc, in one line: 2–4× "compression" → regression references (v3b) → fitted hcp-former references (v4) → nine corrected pure references (v5): each step was a convention, not the model, and the model was right once its zero was.

cell                     v4       v5       DFT     DFT/v5   |DFT−v5|
E172  Hf/Zr-rich        +12.2   +104.8    +97.2    0.93      7.6
E183  Hf/Zr-rich        −35.1    +79.6    +89.7    1.13     10.2
E176  Mo14Nb14Ta13W13   −55.5    −51.9    −49.1    0.95      2.7
E177  Mo27Ta18Ti5Hf2V2  −78.8    −75.1    −71.1    0.95      4.0
E179  same, seed 1      −90.7    −66.9    −72.5    1.08      5.6
E180  Mo27Ta27          −96.4    −80.3    −89.8    1.12      9.6