What was already known
Arithmetic constructions gave exact Ramanujan bounds only at restricted degrees and order sequences; other lifting constructions did not give deterministic nonbipartite graphs at every prescribed large even size and the exact spectral threshold.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Gives an explicit exact-threshold construction at all sufficiently large admissible orders for each fixed degree.
Limitations
The degree d is fixed and the polynomial exponent may depend on d; the algorithm outputs the full adjacency list and is not a local adjacency-query construction. No completed proof check was documented in the available sources.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, and prior-work review for non-notifying local inclusion; technical check remains undocumented.
Read this published revision