Can the ordering rung see an alloy splitting into two phases, not only ordering?

E248–E255 — the review's experiments: one per open question, parameters fixed (registered 2026-09-27 22:50)

The external review (Jan, 2026-09-26) asked questions that could show the ladder is wrong. The ones not already answered become these eight experiments, run one at a time in this order. Each gets its own entry, with bars, before it runs; the parameters and predictions below are fixed now. Already settled: R0 is a ranking (J1–J2); the Mo–Ta reference is corrected (J5); the requirement is one disordered phase (J14, E247).

E248 — Can rung 1 see decomposition, not only ordering? (J2: "two bcc solutions with different compositions"; rung 1 has only ever been tested on ordering.)

• Model: exact bcc Ising, 50/50, with J < 0, so like neighbours attract and the lattice phase-separates. |J| is set for T_c = 500 K (kT_c = 6.354 |J|).
• Protocol: E245c's exactly: 432 sites, geometric grid 2600 → 60 K, 300 + 1000 sweeps, seeds 6 and 7, read_legs under E247.
• Bars: p_rung1 ≤ 0.01; the cold state clusters (nearest-neighbour Warren–Cowley α₁ > 0). T is reported, not gated: the size factor r was calibrated on ordering, and a conserved order parameter may shift it.
• Prediction: both bars hold, with T within 15 % of 500 K. ~1 core-hour.

E248 RESULT (2026-09-27 23:00). runs/e248/: the clustering Ising (exact T_c 500 K), seeds 6 and 7, read under E247.

• Bar 1 holds: p_rung1 = 0.000. Rung 1 does not pass a decomposing alloy.
• Bar 2 holds: the cold state clusters, with nearest-neighbour α₁ = +0.667 on both seeds (like neighbours; ordering would read negative).
• The prediction is falsified. The heat-capacity peak sits at 332 K, which reads as 349 ± 16 K after the ordering-calibrated factor 0.95. That is 30 % below the exact 500 K, and the feature is broad (FWHM/T 0.66), so the verdict is "not established" rather than a sharp transition. At fixed 50/50 composition on a periodic 432-site cell, separation means building interfaces, and the peak comes broad and low. The size factor calibrated on ordering does not carry over.

Consequence. The pass rule is "below 90 K". A decomposing alloy read 30 % low could pass: a true separation at about 120 K would read as about 84 K. That is a possible false pass, and exactly the failure the review asked about.