What was already known
Earlier work obtained high-temperature counts by zero-freeness or sampling. Concurrent deterministic algorithms cover Gaussian zero-field SK, and some mixed-model thresholds are stronger. Wu’s contribution uses direct cluster summation, symmetric disorder and weak homogeneous fields; its SK step uses randomized color coding.
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AI involvement
Section 1.8 says GPT-5.6 Pro proposed the higher-order polynomial algorithm from Wu’s cluster-expansion idea. GPT-6 Pro suggested color coding and contributed truncation and reverse-hypercontractivity arguments. These are central algorithm/proof contributions; Wu supplied the initial strategy, checked all proofs and revised the manuscript.
Importance
Extends precise high-temperature counting guarantees to a different disorder/field regime and gives an explicit joint accuracy-confidence operation bound, without claiming dominance over the concurrent Gaussian results.
Limitations
The model excludes mixtures combining pair interactions with higher-order terms. The threshold has a fixed margin and fields shrink with N. Failure includes the stated disorder tail. Exact-operation complexity does not establish polynomial bit complexity, efficient arbitrary-field sampling or a result throughout the low-temperature spin-glass phase.
Technical verification
Formal checking
Section 1.8 explicitly states that Wu checked all proofs. The checked claim is the paper’s bounded-temperature, weak-field approximation theorem with its exact-operation and failure bounds. This is author-reported human proof checking; the companion Lean development is not used to certify a broader numerical-precision claim.
- Checker
- Qiang Wu: reported complete human proof checking
- Scope
- For SK and finite mixed Ising p-spin models with all interaction orders at least three, at a fixed margin below the second-moment threshold and homogeneous fields |h|≤ρ₀N^{-1/4}, algorithms approximate log Z_N to additive error ε using a number of exact operations polynomial jointly in N, ε^{-1} and δ^{-1}. Symmetric unit-variance disorder is allowed; failure is at most δ plus an explicit disorder-tail term, which vanishes with a finite fourth moment.
- Basis
- Reported by the linked checker
- Check date
- 2026-10-27
Checking a formal statement does not establish that it matches the original problem.
Correction and publication history
Lists the original paper once while retaining the specific checking and provenance references. Research claims and rating levels are unchanged.
Read this published revisionClarifies that the source reports completed checking but does not supply its exact completion date. Research claims and rating levels are unchanged.
Read this published revisionNewly reviewed source-backed algorithm with contribution-specific AI attribution and checking limits.
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