What was already known
The weak chromatic-splitting conjecture predicted a retraction for completions of finite spectra. Earlier failures of a stronger summand formula at height two did not refute this weak form.
AI involvement
OpenAI credits an internal model with the higher-height sphere-kernel and descent-exponent arguments.
OpenAI is the manuscript author and the release attributes its mathematical results to an internal model; individual autonomy is unproven.
- Supporting source (github.com) — Model-production and verification disclosure
Importance
The sphere gives counterexamples to the weak retraction prediction in two higher-height families.
Limitations
Neither the localized kernel argument nor an alternate descent-exponent route has a documented completed check. Strong-splitting and filtration claims in companion papers are distinct.
Technical verification
The manuscript gives proof arguments and an independent descent-exponent route, but no completed human or machine check of either route is documented. Reported is the evidence default and does not imply a failed check.
Human understanding
No named person explains the central localized sphere-kernel or descent-exponent mechanism; Few is the evidence default.
Correction and publication history
If correct, the sphere gives counterexamples to the weak retraction prediction in two higher-height families.
Read this published revision