What was already known
The cost-preserving unsplittable-flow question remained open in this planar setting, though Rybin had announced a different counterexample shortly before this work.
AI involvement
GPT-5.6 Pro carried out most construction search, symbolic derivation and verifier work. Matthew Protti chose the target, directed the work and corrected a cost-normalization error.
GPT-5.6 Pro reportedly performed most active construction and proof work within a human-directed research loop.
Importance
The example gives a small planar witness and a stronger lower bound for this rounding problem.
Limitations
The value is sharp only in Protti’s fixed-topology, equal-full-cost, two-cheap-choice model. The release does not prove global planar optimality or priority over unindexed work.
Technical verification
Independent checking
exhaustive exact computation and symbolic identity checks
- Checker
- v0.1.0 exact-arithmetic verifier and separate Codex reimplementation
- Scope
- The 335/294 instance, all 16 routings and 13 arcs; symbolic checks of the family and restricted identities
- Basis
- Reported by the linked checker
Human understanding
Protti describes the construction, caught a normalization error and explains the claim boundaries and mechanism.
Correction and publication history
The example gives a small planar witness and a stronger lower bound for this rounding problem.
Read this published revision