G-set G63 Max-Cut Certificate: A 7000-bit Assignment with Cut Value 27052
Year: 2026
Type: article
Abstract: This record publishes an explicit public Max-Cut certificate for the G-set G63 benchmark instance. The certificate is a 7000-bit vertex assignment, provided as a 1750-character hexadecimal string, that attains cut value 27052, or 27,052, on the standard G63 edge list. The comparison in this note is restricted to previously published explicit public certificates, defined here as vertex assignments whose cut values can be independently recomputed from the standard G63 edge list. Under this criterion, the highest-scoring previously published explicit public certificate identified in the note is Khan and Shukla's 27047 certificate. The present assignment improves that public verifiable value by 5. The note documents the encoding convention, the bit order, the mapping 0 -> -1 and 1 -> +1, and the direct cut recomputation procedure. It does not claim that 27052 is the global optimum, and it does not make any claim about search details or solver performance.
Authors: Ota, Rikito, Okada, Masato
Institution: The University of Tokyo
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140131995
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