What was already known
Goemans’ factor-one conjecture had been refuted at 16/15; the earlier planar lower bound was about 1.139747. Alfredo De la Fuente later improved this 17-terminal line to 1.28260069012508836.
AI involvement
Nikolenko framed and wrote the theory and credits GPT-5.6 Sol, Claude Fable 5 and Claude Opus 5 with the construction search, certificates and much theory. De la Fuente’s later refinement is separate human work.
The author expressly credits models with the construction search and much theory development, and says the work was predominantly theirs; it does not document an autonomous session.
Importance
The construction substantially raised the general lower bound and clarified some restricted upper bounds.
Limitations
The 1.282494 value is no longer the numerical record; the restricted ceilings do not bound all instances. Complete checking of those analytic ceilings is not documented.
Technical verification
Exact machine checks cover the 17-terminal lower-bound certificate, all 131,072 routings, and sample/exhaustive tests of parts of the restricted-class theory. The source does not document a complete proof check of every analytic ceiling in this combined assessment.
Formal checking
Raw-arc path rediscovery, exhaustive routing enumeration, exact rational hull certificate and finite theorem tests
- Checker
- Nikolenko project’s independently written verifier scripts
- Scope
- The 17-terminal lower bound and finite certificate; selected restricted-class checks
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Nikolenko explains the common-point two-order reduction, record witness and deletion-star residual, including why its ceilings do not bound the universal constant.
Correction and publication history
The construction substantially raised the general lower bound and clarified some restricted upper bounds.
Read this published revision