Does reading the ordering rung by histogram reweighting of two seeds pass the exact known answers?

E245 — rung 1 read by histogram reweighting, from the literature (pre-registered 2026-09-24 08:30)

Why. E244's K3 showed rung 1 is overconfident on broad transitions. The operator asked for the literature and for Fable. Fable's review (full text in the session record) cites:

• Ferrenberg & Swendsen 1988 and 1989;
• Ferrenberg, Landau & Swendsen 1995;
• Janke 2003;
• Shirts & Chodera 2008 (MBAR);
• Kim & Widom 2023;
• Liu et al. 2021;
• Kostiuchenko et al. 2019;
• Sobieraj et al. 2020;
• Ångqvist et al. 2019;
• Barber et al. 1985;
• Fisher 1968.

What it found:

• Why the old reading failed. Under our swap dynamics τ_int(E) ≈ 17 sweeps at T_c, so 200 measurement sweeps hold only ~6–12 independent samples. The "local maxima" of a finite-difference dE/dT are noise, and σ from a 70 % half-width is not a sampling uncertainty.
• Finite size. On 432 sites the equilibrium C peak sits at 0.95 T_c.
• Wang–Landau is out of budget. It needs 10⁷–10⁸ sweeps (icet), 10²–10³ × ours.

The estimator (Fable's; scratch reference scratchpad/odt/bars.py, to be ported into the repo):

1. Sampling. Same swap Metropolis, 432 sites, 100 + 200 sweeps per T. A geometric grid, T_{i+1} = 0.92 T_i from 2600 K down to 60 K (46 points). Two independent cooling seeds. Every sweep's energy and acceptance are stored. The model's ground state E_gs is annealed on the same cell once per composition.
2. Reweighting. Pool the seeds and solve MBAR / multiple histograms for continuous C(T) on a 2 K grid.
3. Frozen region. T_freeze is the highest T with acceptance < 0.01.
   • If E(T_freeze) − E_gs ≤ 3 meV/atom, the region below is quiet.
   • Otherwise it reads "not established below T_freeze". If T_freeze > 90 K, p = 0.
4. Significant peaks. Local maxima above T_freeze with prominence > max(0.25 k_B, 3 s_C), where s_C comes from a moving-block bootstrap (block 20 sweeps, B = 150).
   • No peak, with the maximum at the floor, reads "censored, T_c ≤ T_floor/r".
   • No peak otherwise triggers the 3 meV/atom movement guard.
5. Uncertainty. σ_stat = max(bootstrap sd of the peak, half the seed difference). T_c = T̂/r with r = 0.95 ± 0.03, calibrated on the exact Ising (18 cases, mean 0.945 ± 0.030). σ_tot adds the statistical and systematic parts in quadrature.
6. p. P(every significant peak outside [90, 1000]) from the joint draws. For one peak this equals passes_window(T_c, σ_tot, window, scale=(1, 1)).
7. Broad flag. FWHM/T̂ > 0.5 means a crossover or unresolved multi-stage ordering. If its FWHM interval meets the window: not established, never a pass.

Known answers, through the repo's own sampler and analysed by the ported estimator. The bars are Fable's, derived from its measured readings (scratchpad/odt/runs/bars.log):

Any Ising leg with a second significant peak voids the rule. Any failed bar stops the walk.

Accepted assumptions (Fable's list):

• a broad feature inside the window reads "not established";
• r is applied to every composition;
• the budget is ≈ 3 core-hours per composition (two seeds × ~88 min).

Stated limitation. CE model uncertainty (±65–100 K in the literature) is not in σ. The e6 ensemble spread enters only when p is compared with DFT. The multi-stage known answer (bcc J1–J2 Ising, Dünweg & Binder 1987) is not run; the frozen-region rule is the guard.

Then E244's walk runs on E245's rung 1: the 16 HEA leaders, two seeds each, about 12 h on 4 cores. The port is reviewed adversarially before any find is read.

E245 port (2026-09-24 08:43). forager/ladder/reweight.py wires the estimator through ECEVerifier (FORAGER_RUNG1_METHOD=reweighted) and Verifier, which now take the rung's own p_rung1. passes_requirement accepts a supplied p_lattice. The port reproduces Fable's table exactly on Fable's saved Ising runs:

Two notes. The grid has 47 points, not the 46 written above: 46 ratio steps, then the 60 K floor (61.0 → 60); Fable's runs used the same function. And K1's frozen state sits 2.999 meV/atom above the exact ground state against the 3 meV bar. That is legitimate thermal energy at T_freeze = 744 K, passing by a hair, and it errs toward "not established" rather than toward a false pass. Tests: tests/test_reweight_rung1.py.

E245 known answers on FRESH seeds (2, 3) (2026-09-24 09:13): two of six FAIL; the walk stays blocked. Read through the ported estimator after the port review's fixes:

Fable's bars were read on seeds 0 and 1, where K1 cleared the 3 meV frozen-gap bar by 0.001. On fresh seeds it does not. The gap compares E(T_freeze), which includes ordinary thermal energy of the ordered phase, with E_gs, so a 3 meV bar is fragile. K5's second peak says the significance rule is not robust at 2 × 200 sweeps. The reweighting itself is sound: every production mismatch is ≤ 1.2 meV/atom. Mo–Ta (K3) is still sampling. Port-review fixes applied first:

• MBAR convergence and finiteness are checked, and the moments are plain sums;
• the reweighted curve must reproduce the sampled means within 2 meV/atom;
• the floor p is continuous in the censored edge;
• the seed scatter is half the seed range;
• the ground state is annealed on the same 432-site cell with 200 measurement sweeps;
• the resampling seed is threaded from the verifier;
• kinetics never takes a NaN temperature.

The two frozen-region unit tests fail at their 30 + 60-sweep scale on the new consistency check; their cooling legs lag equilibrium. They are to be re-scaled, not the check loosened.