Experiments · E177
No. DFT gave −71.1 meV/atom against −17.9 and −10.9 from the two models; most of the gap was later traced to the labels' references.
In the log: the third rung-4 cell, at a search find
book/assets/diagrams/exp/E177.svg).E175's refit is deferred: two QE points cannot separate an offset from a scale, and the
slope is already measured. What the flywheel needs is cells at the search's own finds,
where the compression is paid out. The search's rung 0 is the icet CE on ce_12element
(not the eCE), so this cell tests both. The finds are not recorded by composition in the
run logs, so one was taken from the same screen: 300 random compositions over the eight
pseudopotential elements, best qualifying hit (p ≥ 0.832) at L1 ≥ 0.15 from every RHEA
training composition and from MoNbTaW: Mo 0.488 Ta 0.328 Ti 0.098 Hf 0.044 V 0.042 —
the Mo–Ta basin the fly and the CEM keep returning to. icet rung 0: e_bcc −10.9 meV/atom,
drive_cold −67.2, drive_hot −162, σ 36.6, T_order 709 K, p 0.910. Cell: Mo₂₇Ta₁₈Ti₅Hf₂V₂
(multinomial rounding), seed-0 decoration, Vegard a = 3.2419 Å, E176's settings, single
SCF. eCE E_lattice = −17.9 meV/atom; references from refs_v2/.
Predictions.
E177 result — prediction 1 falsified downward: the cheap rungs under-read the search's
own basin by 4×. JOB DONE in 36 iterations (prediction 3 confirmed; the SCF tail crept
from 1e-6 to 1e-7 over ten iterations — Mo–Ta's dense Fermi surface, not sloshing).
E/atom −6463.52661 eV at Vegard; references Hf/Mo/Ta/Ti/V from refs_v2/, all bracketed:
E_form(DFT) = −71.1 meV/atom eCE −17.9 (ratio 4.0) icet −10.9 (off by 60)
Prediction 1: falsified — below −50, by the branch written in advance: "the cheap rungs under-read this basin by more than the scale".
Prediction 2: confirmed — the icet CE, the rung that paid for this find, is off by 60 meV/atom, three times the bar. Three cells now:
cell eCE icet DFT DFT/eCE where E172 Hf/Zr-rich +51.2 — +97.2 1.9 thin edge E176 MoNbTaW −21.9 — −49.1 2.2 data centre E177 Mo–Ta basin find −17.9 −10.9 −71.1 4.0 the search's basin
Not an offset, not a constant scale: a composition-dependent under-reading, worst where the search goes. The sign is the consoling part — the finds are more favourable than they were paid for, not less. The uncomfortable part is the ordering temperature: rung 1's T_order for this composition (709 K, inside the window, so a fail) is proportional to the ordering energy the same models supply; under-read by 4×, the true ordering temperature is well above the window, which is a pass by the ladder's own rule ("ordered throughout, a different material"). The cheap rungs are not just miscalibrating the reward; they are placing the transition on the wrong side of 1000 K for the search's best basin.
Branch. (a) The flywheel refit must be local, not a scale — the eCE's species embedding can carry per-composition corrections, but only if the QE cells sit in its training set with the per-source term, and three points are still too few. (b) Before that, the most load-bearing claim tonight rests on one decoration: E179 replicates E177 with the seed-1 decoration of Mo₂₇Ta₁₈Ti₅Hf₂V₂ at the same Vegard a (19 of 54 sites coincide with seed 0; eCE scores it −11.9 vs seed 0's −17.9 — a 6 meV decoration spread on the model's side, recorded before DFT). Prediction: E_form within the decoration noise floor, |ΔE| ≤ 12.4 meV/atom of −71.1; if the two decorations differ by more than 25, ordering within the cell (a lucky Mo–Ta arrangement) is doing the work and the composition-level number needs several decorations. (c) The icet CE's 60 meV miss at its own find is the number that should replace "8.1 meV vs DFT" in every summary of the bottom rung: that figure was a fit residual on RHEA's distribution; this is the error where the search lives.
This entry is written in 2 separate places in the log, shown here in log order.
E175's refit is deferred: two QE points cannot separate an offset from a scale, and the
slope is already measured. What the flywheel needs is cells at the search's own finds,
where the compression is paid out. The search's rung 0 is the icet CE on ce_12element
(not the eCE), so this cell tests both. The finds are not recorded by composition in the
run logs, so one was taken from the same screen: 300 random compositions over the eight
pseudopotential elements, best qualifying hit (p ≥ 0.832) at L1 ≥ 0.15 from every RHEA
training composition and from MoNbTaW: Mo 0.488 Ta 0.328 Ti 0.098 Hf 0.044 V 0.042 —
the Mo–Ta basin the fly and the CEM keep returning to. icet rung 0: e_bcc −10.9 meV/atom,
drive_cold −67.2, drive_hot −162, σ 36.6, T_order 709 K, p 0.910. Cell: Mo₂₇Ta₁₈Ti₅Hf₂V₂
(multinomial rounding), seed-0 decoration, Vegard a = 3.2419 Å, E176's settings, single
SCF. eCE E_lattice = −17.9 meV/atom; references from refs_v2/.
Predictions.
E177 result — prediction 1 falsified downward: the cheap rungs under-read the search's
own basin by 4×. JOB DONE in 36 iterations (prediction 3 confirmed; the SCF tail crept
from 1e-6 to 1e-7 over ten iterations — Mo–Ta's dense Fermi surface, not sloshing).
E/atom −6463.52661 eV at Vegard; references Hf/Mo/Ta/Ti/V from refs_v2/, all bracketed:
E_form(DFT) = −71.1 meV/atom eCE −17.9 (ratio 4.0) icet −10.9 (off by 60)
Prediction 1: falsified — below −50, by the branch written in advance: "the cheap rungs under-read this basin by more than the scale".
Prediction 2: confirmed — the icet CE, the rung that paid for this find, is off by 60 meV/atom, three times the bar. Three cells now:
cell eCE icet DFT DFT/eCE where E172 Hf/Zr-rich +51.2 — +97.2 1.9 thin edge E176 MoNbTaW −21.9 — −49.1 2.2 data centre E177 Mo–Ta basin find −17.9 −10.9 −71.1 4.0 the search's basin
Not an offset, not a constant scale: a composition-dependent under-reading, worst where the search goes. The sign is the consoling part — the finds are more favourable than they were paid for, not less. The uncomfortable part is the ordering temperature: rung 1's T_order for this composition (709 K, inside the window, so a fail) is proportional to the ordering energy the same models supply; under-read by 4×, the true ordering temperature is well above the window, which is a pass by the ladder's own rule ("ordered throughout, a different material"). The cheap rungs are not just miscalibrating the reward; they are placing the transition on the wrong side of 1000 K for the search's best basin.
Branch. (a) The flywheel refit must be local, not a scale — the eCE's species embedding can carry per-composition corrections, but only if the QE cells sit in its training set with the per-source term, and three points are still too few. (b) Before that, the most load-bearing claim tonight rests on one decoration: E179 replicates E177 with the seed-1 decoration of Mo₂₇Ta₁₈Ti₅Hf₂V₂ at the same Vegard a (19 of 54 sites coincide with seed 0; eCE scores it −11.9 vs seed 0's −17.9 — a 6 meV decoration spread on the model's side, recorded before DFT). Prediction: E_form within the decoration noise floor, |ΔE| ≤ 12.4 meV/atom of −71.1; if the two decorations differ by more than 25, ordering within the cell (a lucky Mo–Ta arrangement) is doing the work and the composition-level number needs several decorations. (c) The icet CE's 60 meV miss at its own find is the number that should replace "8.1 meV vs DFT" in every summary of the bottom rung: that figure was a fit residual on RHEA's distribution; this is the error where the search lives.
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