With a phase-identity check on frozen samples and a rule for which peaks count, does the reweighted rung pass the known answers?

E245b — rung 1 with a phase-identity frozen test and reproducible peaks (pre-registered 2026-09-24 09:54)

From Fable's second review (after E245 failed K1 and K5 on fresh seeds). E245 is unchanged except for two rules, R1 and R2 below.

• Why K1 failed. The 3 meV frozen-gap bar measured the ordered phase's own thermal energy. Perfect B2 heated to 744 K sits 2.40 ± 0.26 meV/atom above E_gs in equilibrium, so the gap crosses 3 meV wherever acceptance happens to cross 0.01.
• Why K5 failed. Its second peak at 74 K is real in the pooled curve: a split of the cold-edge peak from sluggish sampling below it.
• Rejected. Replica exchange (≥ 30× the budget: a round trip across 46 slots needs ~10⁴ rounds). DFT ΔE_order as a pass path: it is a 0 K quantity, so an alloy ordered above 1000 K has a large ΔE_order and yet meets the requirement. DFT stays a FAIL gate and the disposition of the residue.

R1: the frozen region is judged by phase identity, not an energy gap.

• When T_freeze ≥ 90 K, anneal the model's ground state on the same 432-site cell and heat it to T_freeze (100 + 200 sweeps).
• Quiet if the cooling legs' frozen state has the same Warren–Cowley pattern: |Δα_ij| ≤ 0.15 on shells 1 and 2, for every readable pair.
• E_cool(T_freeze) − E_heated(T_freeze) is reported and flagged above 5 meV/atom, not gated. The legs scatter ±2–3 meV/atom there, and no positive control for a wrongly frozen state exists at 432 sites.
• Caveat: R1 is only as good as the annealed ground state. QUIET_MEV is dropped.

R2: a peak must reproduce.

• Significant if its prominence is ≥ 0.25 k_B AND a local maximum within ±max(15 %, 2 grid steps) appears in ≥ 90 % of bootstrap curves AND in each seed's own curve.
• A significant maximum within one FWHM of a larger one is the same feature and is merged.

Otherwise unchanged:

• PROM_MIN 0.25, ACC_FROZEN 0.01, BROAD 0.5, r = 0.95 ± 0.03;
• σ_stat = max(bootstrap sd, half the seed range), no grid-step floor;
• the fixes from the port review.

Known answers on FRESH seeds 4 and 5. Bars are Fable's, computed with R2 on seed pairs 0+1 and 2+3:

Voiding: any Ising pair with ≥ 2 significant peaks, or K1/K4/K2a read not quiet by R1.

Predictions for the 16 HEA leaders. ≥ 10 read FAIL or not established; ≤ 3 pass rung 1; every pass has R1 quiet. The cost is about 3 core-hours per candidate plus the ground state when needed.

E245b known answers on FRESH seeds 4 and 5 (2026-09-24 10:31): verdicts right, the voiding clause fires on K1.

Every pass/fail verdict is right. K1's n_sig = 2 fires the pre-registered voiding clause ("any Ising pair with ≥ 2 significant peaks").

Diagnosis. Three rounds of rules have now each met a new artefact. The reading is not the root cause. At 100 + 200 sweeps per temperature the cooling leg lags equilibrium, and that leaves reproducible artefacts: split cold-edge peaks (K5, seeds 2+3) and a shoulder below a real transition (K1, seeds 4+5). Fable measured the hysteresis collapsing at 300 + 1000 sweeps. The observed artefacts sit below the true peak, so they can produce false fails near the hot edge. No false pass has appeared in any known answer on any seed pair (0+1, 2+3, 4+5). The walk is not started; the choice is the operator's:

1. E245b as a knowingly conservative filter, with the deviation recorded;
2. more sampling (~1000 sweeps per T near and below the peak; ~4× the cost), on the top 8;
3. Fable again.

K3 (Mo–Ta) and the code review are still running.

E245b port review and fidelity check (2026-09-24 10:52). An adversarial review (Sonnet) found the port had drifted from Fable's reference (scratchpad/odt/bars2.py) in three places:

• the reproducibility test counted any unfiltered local maximum, frozen region included;
• the merge window was one FWHM narrower;
• p was not widened to σ_stat when the seed scatter exceeded the bootstrap spread (K4 read 0.975 against a 0.98 cap).

It also found:

• R1 passed vacuously with no readable pair;
• R1 ran on, and could overwrite, an already-clear in-window fail;
• a control flow keyed on verdict text.

All fixed:

• the port now follows the reference;
• no readable pair means not quiet;
• R1 runs only when p ≥ 0.1;
• frozen_check_pending is an explicit flag.

Run side by side on seeds 4+5, the port and the reference agree:

• K1, n_sig 2, peaks 1376 and 1166 → T_c 1448, p 1.000;
• K4 1052.6 (p 0.927 port / 0.940 reference);
• K2a 490.5, p 0;
• K5 88.4 (0.720 / 0.750);
• K2b censored;
• the ring is never a pass (the port flags it broad, the reference reads no significant peak, which the movement guard then holds).

The reference itself gives K1 two peaks on these seeds, so the voiding is the method's, not the port's. At 100 + 200 sweeps a cooling leg leaves a reproducible shoulder below a real transition. The operator's choice stands (options above).