What was already known
Wang and Wu had proved the diagonal estimate for p>22/7 on such surfaces; earlier bounds also had narrower exponent or input ranges.
AI involvement
OpenAI credits an internal model with the manuscripts. No individual interaction record establishes autonomous discovery.
OpenAI institutional authorship plus the released release’s internal-model production account supports model leadership, without an individual autonomy record.
Importance
Reaches the conjectured p>3 diagonal range for general positively curved surfaces in three dimensions.
Limitations
The separate bounded-data sphere theorem has an L∞ input and is only one input here. No completed human or machine check of the general-surface proof is documented.
Technical verification
The manuscripts provide proofs and dependencies, but no completed human or machine check of the assessed general-surface theorem is documented.
Human understanding
No named person is documented as explaining the packet, density, and sparse-ball mechanism of the assessed result; this is a missing-evidence default.
Correction and publication history
Reaches the conjectured p>3 diagonal range for general positively curved surfaces in three dimensions.
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