OpenAI reports filtered chromatic splitting at generic primes

For each n≥1 and prime p>n+1, the spectrum Lₙ₋₁L_{K(n)} of the p-completed sphere has an ordered 2ⁿ-stage filtration with the classical chromatic-splitting cofibers, whose first-stage map to the target is the canonical localization unit.

Sources for this record

What was already known

Hopkins’s chromatic splitting conjecture was known at height one and in height-two cases, while the original strong formula fails at height two and prime two. The manuscript proves a filtered classical cofiber pattern in the generic-prime range.

AI involvement AI-led

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 Notable

Realizes the expected chromatic-splitting layers and canonical unit across all heights at primes p>n+1.

Limitations

The selected claim is an ordered filtration with specified cofibers, not a direct-sum splitting at every prime.

Technical verification Reported

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

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

2026-10-18 · publication

Primary manuscript, attribution, and prior-work review for non-notifying local inclusion; technical verification remains Reported.

Read this published revision