Can the ordering rung decide from two cooling legs, with no pass without evidence?

E243b — rung 1 on two legs, with no pass without evidence (pre-registered 2026-09-24 02:35)

Blindness. The survivor's E242 diagnostic (a single cooling leg) has been seen down to 620 K: the energy falls faster and Cv rises (0.37 at 620 K). The survivor is therefore not a blind test. The other ten E241-eligible finds have no curve on this grid.

Instrument. E210b's scorecard protocol, which gave six of seven comparable systems within 22 %.

• Legs. A cooling leg, then a heating leg continuing the same chain from the cold configuration (metropolis.run(..., start=cold), as v5_metropolis.py does).
• Grid, both ways. 2600, 2000 and 1400 K, then 60 K steps down to 60 K.
• Model and cell. e6 ensemble mean, 432 sites, 100 + 200 sweeps.

Reading.

• (a) Reversibility, E210b (1). The legs' 60 K energies agree within 3 meV/atom, and their highest-T dE/dT peaks sit within one grid step. Otherwise the reading is not established (p = 0). This is the equilibrium check the single leg lacked: a frozen wrong state shows up as hysteresis.
• (b) Transition. peak(T, dE/dT, which="highest") on each leg. T_c is the mean of the two legs; σ is the largest of 60 K, half the legs' difference and the peak's half-width. p = passes_requirement(T_c, σ, window), rung 1's existing probability.
• (c) No in-sweep peak on either leg. A pass only if the cooling leg's |E(1000) − E(90)| is under 3 meV/atom, i.e. nothing moves in the window. Otherwise not established (p = 0). This closes E242's blind spot without an energy-fraction threshold. A peak always takes precedence over (c).

Known answers at production settings, before any find is scored. If any fails, E243b is withdrawn.

A synthetic gradual-ordering curve with no peak and a large in-window release must read "not established" (unit test).

Predictions.

• (1) The survivor fails, p < 0.1. Not blind; stated as such.
• (2) Of the other ten, which are blind, at most five keep p ≥ 0.5.
• (3) At least three of the ten show a reversible peak inside 90–1000 K.

Cost. About 100 min per composition on one core (two legs): the known answers and then the ten finds overnight and into the day, each written as it lands to runs/e243b/. A second adversarial review of the code runs before any find is scored.

E243b withdrawn before any find was scored (2026-09-24 03:00). A second adversarial review (Sonnet) ran the exact production job for K4 (Ising, T_c 1050 K, seed 0): the legs peak at 929 and 1022 K, 93 K apart against a 60 K tolerance, so the reading is "not established" (p = 0). The bar itself (0.5 ≤ p < 0.95) was unreachable in any case. passes_window integrates the model-to-real temperature scale 1.0–1.35, and gives p = 0.98 at 1050 ± 60 K. I set the bar without computing it first. By the entry's own clause, E243b is withdrawn.

The known-answer runs that completed (runs/e243b/K*.json):

On 432 sites the peak falls 6–12 % below the exact T_c. The review's other findings stand for any successor:

• "Not established" and a confident fail are both p = 0.
• Branch (c)'s equilibrium check is vacuous when both legs are frozen at the floor. They continue the same configuration.
• No known answer decouples the ordering-energy scale from T_c.
• passes_window's 1.0–1.35 scale still credits an 800 K transition with p = 0.33, a scale that is meaningless now that rung 1 runs on the physical axis.