Does a search confined to true high-entropy alloys find candidates worth walking up the ladder?

E244 — the HEA regime, walked all the way up (pre-registered 2026-09-24 03:42)

The operator's decision. Search only true high-entropy alloys and take the leaders through every rung. "HEA" here is Yeh's definition: ≥ 5 principal elements, each ≥ 5 at.%; no element above 35 at.%; trace elements (< 5 at.%) allowed. The search runs over the model's nine elements. Every find so far failed this definition (0 of 32; memory note 2026-09-24): the rung-0 reward pays nothing for entropy, and E134 measured the drift to binaries.

Rung 1 as used here ("E243c", the minimal fix; it replaces E243/E243b). Everything is E240's rung 1 except the grid and the reading of it.

• Sampler. E240's rung 1: one cooling leg, e6 ensemble mean, 432 sites, 100 + 200 sweeps.
• Grid. 2600, 2000 and 1400 K, then 60 K steps down to 80 K, plus 60 K.
• In-sweep peak. The existing reader, with its fluctuation-channel rule, gives T and σ; then p = passes_window(T, σ, window, scale=(1.0, 1.0)).
• The 1.0–1.35 scale is dropped. Rung 1 has run on the physical axis since E215c, and the scale's justification was withdrawn in E109/E111. It still credited an 800 K transition with p = 0.33.
• No in-sweep peak. A bounded pass at the floor only if |E(1000) − E(90)| < 3 meV/atom on the curve. Otherwise not established, p = 0. This closes E242's blind spot.

Known answers, single leg at production settings. Each bar was computed from the formula before it was written; the E243b cooling legs for K1, K2a, K4 and K5 had already been seen (peaks 1323, 458, 929 K, and the floor).

K4's bar is low on purpose. On 432 sites the peak sits 6–12 % below T_c, so a transition near the hot edge reads low; that is the conservative direction, and it is stated here. Any failure stops the experiment before a find is scored.

Search. E223's design: 200 rounds × 4 proposals × 2 seeds, pure rung-0 reward on e6, E223's brain flags. The HEA space comes from FORAGER_ELEMENTS (the nine), FORAGER_MIN_ELEMENTS=5, FORAGER_ELEMENT_FLOOR=0.05 and a new FORAGER_ELEMENT_CEIL=0.35, all inside HEASpace's exact projection. There are three arms: fly, elitist, and uniform (random within the HEA space). Uniform is the baseline every generator must beat on enrichment.

Walk.

• The pooled niche leaders, de-duplicated, capped at 16 by rung-0 p.
• Each goes up rung 1 (E243c) and rung 2 (the MACE hull). Rung 3 is reported but does not gate.
• Finds with p ≥ 0.5 after rung 2 go to DFT, chosen by E241's agreement rule. The ordered and random cells are built with identical counts (random_cell.py --counts), and the model's ground state is annealed first (E242's design).

Predictions.

• (1) Enrichment. Fly and elitist each beat uniform on the mean rung-0 drive of their top 10.
• (2) Of the 16 walked, ≥ 10 show an in-window peak or come out not established on rung 1. Most RHEAs order in the window: 7 of the 12 published ODTs sit inside it.
• (3) At most 3 pass rungs 0–2 (p ≥ 0.5).
• (4) Any that reach DFT are scored on E242's bars: ΔE_order ≤ 5 meV/atom confirms, 5–15 is not established, > 15 fails.

Cost. Search about 3 h; walk 16 × ~50 min on one core; about 2.6 h of A100 per DFT pair. Code changes: FORAGER_ELEMENT_CEIL; a rung-1 grid override, the no-peak guard and scale (1, 1) on the ECEVerifier path. Each is tested, then adversarially reviewed before any find is scored.

E244 known answers, first reading (2026-09-24 03:52): two of five Ising bars FAIL; the experiment stops and is amended before any find. runs/e244_known.log, through Verifier.expansion:

The cause is mine. The bars assumed a floor reading carries σ = 60 K (one in-window grid step). The code takes σ from the gap above the floor, which on this grid is 80 → 60 K = 20 K: an artefact of the extra 60 K point. So a transition at the window's cold edge (K5) reads as a confident pass.

Amendment (rule only; bars unchanged). On every branch (peak, fluctuation peak, floor bound), σ is never below the grid's median spacing inside the window. That is 60 K here, and 227 K on E240's coarse grid, where floor passes rightly become less confident. The stored rung-1 curves are re-read under the amendment and nothing is re-sampled; K3 (Mo–Ta) is read once it finishes. If any bar still fails, rung 1 stays as E240 had it, with the blind spot stated, and E244 walks nothing.

E244 known answers under the amendment (2026-09-24 03:55). Re-read from the stored curves; nothing was re-sampled.

K3 (Mo–Ta on e6) is running. The E244 chain (runs/e244_chain.sh) has two gates: the search starts only when every known answer holds (e244_known.py exit 0), and the walk only after the adversarial review clears (runs/e244_review.ok). The walk runs in 4 shards, as E240 did, because DFT now runs on the A100 and not on local ranks.

E244 code review (2026-09-24 04:16): NOT SAFE as first written; three fixes before any find is scored. An adversarial review (Sonnet, probes in scratch; the related suites green) found:

1. stage_b.confirm() bypassed the axis fix. It called passes_requirement directly, so it kept the 1.0–1.35 scale (an 800 K transition read p 0.33) and would take NaN from a censored reading. It now goes through Verifier._requirement. E244 runs without --confirm, so no E244 number is touched.
2. A slope reading censored at the grid's floor or ceiling kept a finite T. A "still rising at the floor" verdict pre-empted both the fluctuation peak and the no-peak guard: a survivor-shaped curve read p 0.56. On the physical axis only a peak inside the sweep is now a temperature.
   • A floor-censored slope defers to the fluctuation peak, then to the guard and the floor bound.
   • A ceiling-censored slope passes only if the window is quiet.
   • Four tests pin these branches (tests/test_e244_rung1.py).
3. The uniform baseline was not uniform. Projection pinned an element at 0.05 or 0.35 in 32 % of draws. FORAGER_UNIFORM_EXACT=1 (set for E244) samples by rejection from the uniform simplex: 0 % on a bound, 69 % acceptance. Old runs are unchanged without the flag.

Also: HEASpace now refuses a floor above the ceiling. The review's σ point is covered by the E244 amendment (σ ≥ the in-window step). Items 1–3 were fixed after the known answers were read, and K5's reading is NOT unchanged (corrected on re-reading): fix 2 routes K5's floor-censored slope to its fluctuation peak at 79 K, p 0.572 (was 0.691), still inside 0.5–0.8. That is the more honest reading of a transition at the window's cold edge. K1 1.000, K4 0.118, K2a 0.000 and K2b 0.691 are unchanged; all five hold. A narrow re-review of the three fixes clears runs/e244_review.ok before the walk.

E244 re-review CLEARED (2026-09-24 04:30). A narrow adversarial re-review (Sonnet) checked the three fixes and cleared each: confirm() now goes through _requirement, the censored-slope branches, and the exact-uniform baseline with its floor/ceiling guard. It found no new problem. It replayed confirm() against all seven expansion() branches (every p finite) and re-read the cached known answers through the current code, reproducing the table above exactly. The regression run was 251 tests over the 31 related files, all passing. Two repo tests were added for what the re-review had covered only by probes (the exact-uniform baseline and the floor/ceiling guard). The walk's gate runs/e244_review.ok is set. The search itself still waits for K3.

E244 K3 FAILS (2026-09-24 04:39): the walk is blocked; the rung-0 search proceeds. Mo–Ta on e6 (runs/e244_known/K3_MoTa_e6.json), read on the fine grid:

• the slope channel peaks at 969 ± 30 K;
• the fluctuation channel peaks at 1109 ± 20 K;
• p = 0.304 against the bar ≥ 0.7.

The curve shows why. The energy falls over about 920–1280 K (−153 → −186 meV/atom), and dE/dT has local maxima at 980 (1.23), 1100 (1.02) and 1160 K (1.14). On a 60 K grid, single-temperature noise at 432 sites × 200 sweeps decides which is highest. The contiguous-half-width σ (30 K, floored to 60) is far too confident for a transition this broad. E242 (4)'s 1149 ± 114 K on the 227 K grid is consistent with a centre near 1100 K. The rule as written is therefore overconfident on broad transitions near an edge. That is a defect of the estimator, found by a known answer, and it is not re-tuned here after the fact.

Status:

• The walk's gate (runs/e244_review.ok) is removed until rung 1's peak location carries an honest uncertainty. A proposal (independent seeds, σ from their spread) is to be pre-registered.
• Deviation: the rung-0 search starts now although the chain's gate required all known answers. The search never calls rung 1 (no --confirm), so no search number depends on the failed reading.

E244 search RESULT (2026-09-24 09:54). runs/odt_map/stage_b_e244.json, HEA space: every stored find has ≥ 5 principal elements and a largest share ≤ 0.350.

The fly's score–reward correlation is +0.84. (1) Confirmed. Both generators out-enrich the exact uniform baseline by more than two orders of magnitude in finds. In the HEA regime the fly leads elitist on AUC_Q and on finds, on two seeds with a wide spread; this is not a claim. The walk ((2)–(4)) waits for rung 1 (E245b).