Was the 44.6 meV/atom error a comparison of like with like?

E129 — E128 IS WITHDRAWN. The DFT comparison walked into the relaxation trap.

scripts/validate/rhea_expansion.py parses each RHEA frame's atomic positions into fr["positions"] at line 69 and never reads them again. Line 124 rebuilds an ideal bcc cell with bulk("W","bcc",a=a0,cubic=True) and calls only set_chemical_symbols. So the expansion was evaluated on perfect lattice sites and differenced against a DFT energy belonging to a displaced structure.

Measured directly on the frames the script accepted: mean displacement from the ideal bcc site is 0.080 A, median 0.077, and 80 per cent of atoms are displaced by more than 0.05 A. Not one frame is undisplaced.

So 44.6 meV/atom is not rung 0's error against DFT. It is the expansion's error PLUS the internal relaxation energy of the RHEA structures, and this project's own figure for relaxation is 16 to 112 meV/atom (E59, physics/lattice.py:246) - the same order as the number reported. The two are not separable from what was measured.

This is the relaxation leg of the three-convention trap, the exact failure forager/physics/energies.py was written to prevent and that E65 was retracted for. The entry that committed it is the one that instructed the project to replace its cheapest rung.

Withdrawn in full:

• the 44.6 / 70.0 meV/atom figures and the whole stratified table;
• prediction 1's "confirmed" - it was scored against a confounded measurement;
• prediction 3's instruction that 44.6 "should replace the cross-validation figure wherever rung 0's accuracy is quoted";
• the conclusion that rung 0's advertised 9.09 understates its true error by that amount.

What is NOT withdrawn, because it does not depend on the confounded arithmetic:

• rung 0's 9.09 is a fit residual against MACE and has never been checked against DFT. That remains true and remains the open question.
• data/rhea covers nine of our elements in VASP-PBE and was unused. Still true.
• RHEA's DFT is not spin-polarised (do_spinpol = False), so training on it inherits the blindness to Cr's 311 K transition. Independent of E128 and unaffected.
• The project's own 2026-09-14 note warning against fitting mixing enthalpies to a foundation model. Unaffected, and still unactioned.

Two further defects in the same script, both mine, both found by audit rather than by me:

1. rhea_expansion.py:99 - abs(fr["box"] / rep - fr["box"] / rep) < 1e-9 is identically true. The commensurability guard its own comment describes does not exist; frames are accepted on atom count alone. Latent here, because only n=16 and n=54 appeared.
2. The 2687 frames are almost all 16-atom cells at 6.46 A against a 6.0 A pair cutoff, which icet warned about and which E128 recorded as a caveat and then quoted past anyway.

How the measurement must be done instead. Either evaluate the expansion on structures that are genuinely unrelaxed, or subtract a measured relaxation energy per structure rather than assuming one. RHEA's bcc_alloys group holds 2150 structures at 54 atoms in a 9.7 A box

• clean of the cutoff problem - but they are randomly displaced too, so the convention issue is the binding one, not the cell size. No number replaces 44.6 until that is settled.

Consequence for the plan. Tier 0.1 and the entire Tier 1 justification rested on this figure. The pyeCE-on-RHEA rebuild may still be the right move - the argument from the 2026-09-14 note stands on its own - but the quantitative case for it has evaporated and must be rebuilt before the work is done, not after.