Experiments · E232

Are the database's energies for strongly ordered cells right, checked against our own DFT?

Partly. As used, all four sit within 13 meV/atom of DFT; the model, not the data, missed them. One corrected label (Cr–Ti) is 21.9 off.

In the log: are RHEA's deep ordered labels right? (pre-registered 2026-09-22 20:1x)

mixedDate 2026-09-22 20:1x, as written in the logrung 4 · DFT3 predictions · 1 result paragraphEXPERIMENTS.md lines 15826–15842, lines 15929–15935
exp E232 diagram
What E232 did and how it came out, drawn from this record and the files it names (book/assets/diagrams/exp/E232.svg).

Pre-registration

  1. (1)
    |QE − corrected| ≤ 10 on all four.
    failson Cr–Ti only (21 …
  2. (2)
    On Ta–Ti and Cr–Ti — where the median Ti reference moves the label by 21 and 28 — QE sits nearer the corrected label than the one v5 saw.
    holdsfor Ta–Ti, fails for …
  3. (3)
    Falsifier: any cell > 20 off means the data carries part of the ordered-state error (for Cr–Ta that would reopen E222's reading). scripts/dft/e232_rhea_ordered_audit.py (fake-pw.x smoke test in tests/test_dft_scripts_smoke.py); chain runs/e232_chain.sh after E230, ≈ 1 h of pw.x.
    no verdict written against it
The pre-registration, as written

E232 — are RHEA's deep ordered labels right? (pre-registered 2026-09-22 20:1x)

Only one RHEA ordered label has ever met this project's QE (B2 Mo–Ta, −183.9 vs −184.5). v5 misses its own deepest ordered 16-atom rows by +56.8 (Cr–Ta, B2), +18.9 (Ta–W), +15.3 (Ta–Ti), −11.3 (Cr–Ti) meV/atom, and a ridge regression of its training residuals on excess neighbour pairs gives Mo–Ta +11.7 (NN) / −11.3 (2NN) and Cr–Ta +25 — v5 under-fits order on its own data. If the labels are right, every ordered-state miss is the model's and the refit programme is a model programme. Cells: those four RHEA decorations on ideal sites at Vegard a, QE v3 (60/720 Ry, k 7³, non-spin as RHEA), formation against refs_v3_fit. Labels frozen before any DFT (runs/e232_labels.json, E231's code path): as v5 saw them / E228-corrected — Cr–Ta −37.6 / −42.4, Ta–W −89.1 / −86.5, Ta–Ti +25.5 / +4.8, Cr–Ti +77.0 / +49.5 (B2 Mo–Ta −183.9 / −183.5 against QE −184.5). Predictions. (1) |QE − corrected| ≤ 10 on all four. (2) On Ta–Ti and Cr–Ti — where the median Ti reference moves the label by 21 and 28 — QE sits nearer the corrected label than the one v5 saw. (3) Falsifier: any cell > 20 off means the data carries part of the ordered-state error (for Cr–Ta that would reopen E222's reading). scripts/dft/e232_rhea_ordered_audit.py (fake-pw.x smoke test in tests/test_dft_scripts_smoke.py); chain runs/e232_chain.sh after E230, ≈ 1 h of pw.x.

Results

EXPERIMENTS.md · line 15929

E232 RESULT. QE vs RHEA's deepest ordered cells, (label v5 saw / corrected): Cr–Ta −35.2 vs −37.6 / −42.4; Ta–W −85.8 vs −89.1 / −86.5; Ta–Ti +12.7 vs +25.5 / +4.8; Cr–Ti +71.4 vs +77.0 / +49.5. (1) fails on Cr–Ti only (21.9 off the corrected label); (2) holds for Ta–Ti, fails for Cr–Ti; (3) fires on Cr–Ti. RHEA's ordered labels are within 13 meV/atom of QE on all four — v5 missed the same rows by up to 57, so the ordered-state error was the model's (E229 agrees). The median Ti reference is not settled: it helps Ta–Ti and hurts Cr–Ti; three strained Ti frames do not pin it.

The full record

This entry is written in 2 separate places in the log, shown here in log order.

EXPERIMENTS.md · lines 15826–15842

E232 — are RHEA's deep ordered labels right? (pre-registered 2026-09-22 20:1x)

Only one RHEA ordered label has ever met this project's QE (B2 Mo–Ta, −183.9 vs −184.5). v5 misses its own deepest ordered 16-atom rows by +56.8 (Cr–Ta, B2), +18.9 (Ta–W), +15.3 (Ta–Ti), −11.3 (Cr–Ti) meV/atom, and a ridge regression of its training residuals on excess neighbour pairs gives Mo–Ta +11.7 (NN) / −11.3 (2NN) and Cr–Ta +25 — v5 under-fits order on its own data. If the labels are right, every ordered-state miss is the model's and the refit programme is a model programme. Cells: those four RHEA decorations on ideal sites at Vegard a, QE v3 (60/720 Ry, k 7³, non-spin as RHEA), formation against refs_v3_fit. Labels frozen before any DFT (runs/e232_labels.json, E231's code path): as v5 saw them / E228-corrected — Cr–Ta −37.6 / −42.4, Ta–W −89.1 / −86.5, Ta–Ti +25.5 / +4.8, Cr–Ti +77.0 / +49.5 (B2 Mo–Ta −183.9 / −183.5 against QE −184.5). Predictions. (1) |QE − corrected| ≤ 10 on all four. (2) On Ta–Ti and Cr–Ti — where the median Ti reference moves the label by 21 and 28 — QE sits nearer the corrected label than the one v5 saw. (3) Falsifier: any cell > 20 off means the data carries part of the ordered-state error (for Cr–Ta that would reopen E222's reading). scripts/dft/e232_rhea_ordered_audit.py (fake-pw.x smoke test in tests/test_dft_scripts_smoke.py); chain runs/e232_chain.sh after E230, ≈ 1 h of pw.x.

EXPERIMENTS.md · lines 15929–15935

E232 RESULT. QE vs RHEA's deepest ordered cells, (label v5 saw / corrected): Cr–Ta −35.2 vs −37.6 / −42.4; Ta–W −85.8 vs −89.1 / −86.5; Ta–Ti +12.7 vs +25.5 / +4.8; Cr–Ti +71.4 vs +77.0 / +49.5. (1) fails on Cr–Ti only (21.9 off the corrected label); (2) holds for Ta–Ti, fails for Cr–Ti; (3) fires on Cr–Ti. RHEA's ordered labels are within 13 meV/atom of QE on all four — v5 missed the same rows by up to 57, so the ordered-state error was the model's (E229 agrees). The median Ti reference is not settled: it helps Ta–Ti and hurts Cr–Ti; three strained Ti frames do not pin it.

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