What was already known
Earlier hard-core schemes required an activity bound that shrank with maximum degree. Planar graphs can have unbounded degree.
AI involvement
Guo and Zhang credit GPT-5.6 Sol Ultra with the main proof ideas. They simplified, streamlined and wrote the proofs and explain the star-colouring and block-dynamics mechanism.
Guo and Zhang explicitly credit GPT-5.6 Sol Ultra with the main ideas of all proofs, while they simplified, streamlined and wrote the proofs.
Importance
Gives an approximation scheme at constant activity across all planar graphs, improving the earlier degree-dependent scope.
Limitations
The paper also proves separate colouring hardness and two-spin results. Its written proof and author responsibility statement do not identify a completed check of this theorem.
Technical verification
The source provides complete written proofs and an author responsibility statement, but no explicit completed proof check, formal check or reproducible test of the assessed theorem is documented. Reported is the evidence default.
Human understanding
The human authors supply a technical overview of the star-colouring/block-dynamics argument and say they simplified and wrote the proofs, explaining the central mechanism.
Correction and publication history
Gives an approximation scheme at constant activity across all planar graphs, improving the earlier degree-dependent scope.
Read this published revision