Are the quoted ordering-temperature error bars as wide as the model's own uncertainty?

EXPERIMENTS.md · lines 3690–3740

E68 — The ordering temperatures are quoted twice as tightly as they deserve

Every transition temperature in this record carries the scatter between Monte Carlo runs at different seeds. That is the sampling error of one fixed Hamiltonian and says nothing about whether the Hamiltonian is right. The expansion was fitted with a bootstrap and fifty parameter vectors sit unused in data/ce_8element.npz, each a defensible reading of the same 1,953 structures.

Predicted before running: 50 to 150 K between members, comparable to the sampling scatter, so the quoted bars would be about a factor of root two too tight.

The range was about right and the characterisation was wrong. The model does not merely contribute comparably - it dominates, and the bars are understated by 1.7 to 2.1 times, not root two.

The spread is not Gaussian. For the binary, six members cluster between 1263 and 1363 K and two sit at 950 and 1077. A standard deviation flatters that; what it means is that roughly a quarter of defensible parameter sets put the transition inside the service window rather than above it.

Five of six candidates now straddle the window edge at two sigma, MoNbTaW being the exception at 662 +/- 113. That includes both binaries, whose entire account of why they pass

• ordered above the window, never changing inside it - depends on the transition being above 1000 K.

The verdict survives; the mechanism does not. Re-running the binary's verdict at each member's own transition temperature:

It passes either way, because at 949 K its activation energy of 4.74 eV still leaves an atom 0.0016 nm in a thousand hours. So Mo.51 Ta.49 remains a candidate at P = 0.96 or better under every member, and E67's ranking stands.

What does not stand is the claim that it passes as a B2 intermetallic. On this evidence about a quarter of the time it would be a solid solution held by frozen kinetics instead. Whether the operator ends up with an intermetallic or a solid solution is not determined by this calculation, and the difference matters for ductility even though it does not matter for the requirement as written.

Every T_od quoted in E62 and E67 should be read with its bar multiplied by roughly two.