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W4: T_BKT target 0.003 is unresolvable at laptop L; L=24 validity is not a measurement #45

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@marcohost33-maker

W4 (T_BKT honeycomb against the literature) is not recorded in any issue. A feasibility study from 2026-09-11, checked against 03419c1, found three things.

1. Target (i) cannot be resolved with laptop-size L

  • 0.573 vs 0.576(3): the gap of 0.003 is one standard deviation of the reference value itself, and 0.573 (arXiv:2501.07388) has no error bar at all.
  • Separating the two at 3σ needs σ_T ≤ 0.001. The FSS model-choice systematic alone gives σ_T ≳ 0.003 at L ≤ 128 (plausibly 0.005–0.01). References: HKS arXiv:1302.2900v2 (polynomial vs ln² form differ by 7.5e-4 even at L ≤ 512); arXiv:2406.12076v4 (Υ 0.576(3) vs Υ4 0.568(1)).
  • Proposal: replace target (i) with a consistency band [0.560, 0.580] and pre-register it. A NEGATIVE_RESULT stop rule applies if fewer than 3 L-pairs fall inside the common validity domain, or if σ_T > 0.010.

2. L=24 validity in the PHY042 report is not a measurement

  • src/260706 PHY042 honeycomb wl fss v01.py:219 gives L < 32 a single walker.
  • :280-283: with fewer than 2 walkers, the spread is set to 0, the domain to "all valid", and domain_tmax to the grid end.
  • The report therefore records "domain_tmax_spread004": {"24": 0.67, ...} in the same form as the measured 0.6 (L32) and 0.585 (L48). The console says "Domaene formal voll" (:296); the JSON does not.
  • This does not bind in the pair gate today (min(T_max) takes L32), but any consumer of the JSON reads a non-measurement as a measurement.
  • Suggested fix: emit null plus a reason field for single-walker L, and require ≥ 3 walkers at every L used in a W4 run.

3. Report inconsistencies

  • results/260808 PHY043 ... report.txt: line 12 says n_seeds=8, line 165 (limits section) says n_seeds=4. The latter looks copied from the PHY030 budget (spec line 105).
  • REF_BAND["binder_beta"] (:111) could not be located in arXiv:2406.12076v4 by an automated extraction. Provenance has to be checked against the primary text.
  • The target value 0.576(3) itself is not in REF_BAND.

Before any large run

A calibration run is needed first: the real runtime and the wl_sweeps to convergence at L=64 with 2 walkers, so that the cost exponent is known. The rough extrapolation is L^3.0–3.4 for the budget actually spent, and ~L^5.4 for converged Wang–Landau (unverified). 3 walkers at L ∈ {64, 96, 128} on 4 cores is roughly 1 to 7.5 days of wall time.

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