GPT-5.6 Sol Pro disproves Benjamini-Hochberg conjecture

This is a watershed moment where LLMs transition from summarizing existing human knowledge to generating entirely new scientific discoveries by solving mathematical problems that previously eluded human researchers.

* The "Pro" mode differentiator: Using the `reasoning.mode` parameter set to "pro" enables deep, multi-step reasoning capabilities that successfully tackle long-running mathematical proofs where standard configurations or previous-generation models fall short.

* Superhuman speedup: Disproving a 30-year-old conjecture in 90 minutes versus a predecessor model failing after 20 hours indicates a significant leap in reasoning efficiency and agentic capability.

* Actionable verification: Crucially, the model did not just output natural language math; it generated both the mathematical proof and runnable python code for a numerical certificate, enabling immediate human validation.

* FDR implications: The discovery that the Benjamini-Hochberg procedure can fail to control FDR under correlated two-sided Gaussian tests has broad implications for existing and future statistical analyses that rely on this method.