Does the generator return only tantalum–tungsten alloys because the other elements are genuinely worse?

EXPERIMENTS.md · lines 5870–5918

E100 — Why only tantalum and tungsten: the search, not the physics

Asked why every campaign returns Ta-W. Two candidate explanations: the fixed lattice structurally favours elements near 3.2935 A, or those elements genuinely win. Both were tested.

The lattice bias is real but partial. Correlation between an element's shared-lattice anchor and how often the generator uses it is -0.516, and four elements appear in none of the 74 compositions found:

But the physics does not reject them. Scanning 400 random compositions containing at least ten per cent of each element:

Cr-Ni scores -82 against the generator's own best of -88, and Cr0.64Ni0.36 is essentially nichrome. V-Mo is -83. Neither was ever reported, though the generator did propose chromium in six of 74 compositions and nickel in five - it reached the neighbourhood and converged elsewhere before finding the floor of it.

So the answer is convergence, not chemistry. Only hafnium and zirconium are genuinely rejected, and for the reason E56 established: they form C15 Laves phases that beat any bcc solid solution. The other nine elements all support a composition within 90 meV/atom of the best found.

The fault is mine twice over. The generator is an elitist hill-climber with a learned readout and no mechanism that requires it to report more than one basin, and every report I have written quoted its single best. Nothing in the pipeline ever asked "what is the best composition containing element X", which is one line of screening and answers the question the operator asked in under a minute. A search that returns one answer, reported by someone who never asks for a second, produces exactly this.

EXPERIMENTS.md · lines 6044–6061

E100's claim that the generator "never reported" Cr-Ni is withdrawn. It found it, at an L1 distance of 0.04 from the brute-force optimum, and I never looked past the top eight rows. Every report in this file has quoted the single best row of a 74-row file.

And I quoted the wrong quantity. "The generator's best was -88" was the best reward. The best drive in the same campaign is Mo0.62 Nb0.38 at -108 - better physics than anything W-Ta - demoted to rank 20-something by a 44 meV/atom ordering penalty from the gate E99 showed under-predicts by two to three times.

So the mechanism is not the barrier. E101's 403 meV/atom ridge between W-Ta and Cr-Ni is a real property of the landscape and is not why the generator converged: the walkers relocate by Dirichlet draw on stall, so they do not have to cross it. The convergence is in the reward. sigma = hypot(24.5*sqrt(h/0.17), 18.9) roughly doubles between the refractory corner and the late transition metals, because those four are sparse in the expansion's training set, and reward = drive + sigma therefore ranks by training-set density. The squash makes it worse: 2/(1+exp(d/25))-1 gives 0.90 at -73 and 0.97 at -108, so below about -75 meV/atom the fly cannot separate basins by drive at all while a 20 meV sigma difference moves the reward by 0.4.