Uniformly most split reliable graphs: a complete answer outside two edge counts

Unrefereed AI-assisted mathematical candidate. For connected simple two-terminal graphs, this work classifies existence of uniformly most split reliable graphs outside two edge counts for every n at least 7. Exact finite certificates and the written reduction complete the classification through n=51. An analytic extension proves sufficient cone comparisons for every cone order at least 7 on the probability interval [1/2,1], and on an explicit interval near zero. The intervening probability range and the two uniform boundary cases at unrestricted orders remain unresolved.

Written universal proofs, finite integer certificates and historical computational records have distinct scopes. No external peer review, unaffiliated reproduction, formal verification or exhaustive novelty clearance is established. Original prose and data are CC0-1.0; original executable code is MIT. External dependencies retain their own licences.