Approximate Counting for Spin Systems on Planar Graphs
resolvedconfidence 70%
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Precise statement
Does planarity help approximate counting? The paper gives an FPRAS for the planar hard-core partition function at small activity, proves that approximately counting $q$-colourings on planar graphs is NP-hard for every constant $q \geq 4$, and completely characterizes when an FPRAS exists for 2-spin systems on planar graphs at small external field.
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fidelity, correctness, priority, or novelty.
What AI did
GPT-5.6 Sol Ultra
"The main ideas of all proofs in this paper were found by GPT-5.6 Sol Ultra. For consistency with standard mathematical exposition, the words we and our are used throughout the paper, including when presenting ideas that originate in the output of the model. The authors simplified, streamlined, and wrote all of the proofs." The paper singles out finding the right problem to reduce from as where the model was particularly helpful.
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.