OpenAI · 132-01 · 2026-09-25 · Theoretical computer science
A superquadratic separation between sensitivity and block sensitivity
preprints/A-superquadratic-separation-between-sensitivity-and-block-sensitivity-September-25-2026
Family 132. A counterexample to the quadratic sensitivity conjecture.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Constructs total Boolean functions with block sensitivity for a fixed , disproving the quadratic strengthening of the Sensitivity Conjecture. Here counts influential individual-bit flips, while block sensitivity allows disjoint groups of bits to change together.
We disprove the quadratic strengthening of the Sensitivity Conjecture by constructing nonconstant total Boolean functions whose block sensitivity grows faster than any constant multiple of sensitivity squared. In fact, for some fixed α > 2, our examples have unbounded block sensitivity and satisfy .
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 132: A superquadratic separation of sensitivity and block sensitivity. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.