Exact two-scenario SSUF bound on the four-terminal planar gadget
For the released four-terminal planar acyclic single-source unsplittable-flow gadget, require one unsplittable routing to be no more expensive than a prescribed fractional routing under each of two positive cost scenarios. What is the worst-case normalized additive upper arc deviation? Theorem RB-003 proves as a non-attained supremum.
- Result
- Proved(see note)
- Status
- Variant only
- AI contribution
- AI co-developed
- Method
- Computation
- Field
- Combinatorial optimization; unsplittable flow
- Posed by
- Matthew Protti
- Year posed
- 2026
- Years open
- 0y
- Solved
- 2026-07-28
- Model
- GPT-5.6 Pro
- Vendor
- OpenAI
- Collaborators
- Matthew Protti
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Fixed graph; exactly two positive E-minus-C scenarios; cost non-increase; normalized additive upper arc deviation. Not an unrestricted planar, one-scenario, or many-scenario constant.
What the AI did
GPT-5.6 Pro developed substantial portions of the construction and parameter search, symbolic derivations, analytic proof, exact verifiers, adversarial analyses, and manuscript drafts. Matthew Protti selected and framed the target, required exact enumeration, mutation tests and hostile review, forced correction of material errors and overclaims, chose the final theorem scope, and authorized the release. Codex and other model sessions reconstructed checks and release controls. Role separation reduced some shared-context risk but was not independent human review.
Verification
The immutable v0.2.1 release contains a self-contained human-readable proof, exact rational construction, and deterministic verification artifacts. For the finite epsilon=1/1000 certificate, the graph-native checker enumerates all 16 routings and 13 arcs and obtains 1061/500; scaling demands by 4000 gives unavoidable upper deviation 8488. Exact algebraic checks, mutation tests, and two role-separated AI-assisted hostile-review rounds are included. The human-readable proof is authoritative. No external human mathematical or journal peer review is documented; v0.2.1 changes provenance and release hygiene only and leaves the v0.2.0 mathematics unchanged.
Sources
Submitted by LuckyHawk816