Is block sensitivity at most quadratic in sensitivity? (Nisan-Szegedy)

Lineage and corrections

Nisan, Szegedy, On the degree of Boolean functions as real polynomials (1994) evidence for this event

VibeMathed record: Is block sensitivity at most quadratic in sensitivity? (Nisan-Szegedy) evidence for this event

This event attributed to Unreleased internal OpenAI model

Is block sensitivity at most quadratic in sensitivity? (Nisan-Szegedy) evidence for this event

Theorem 1.1: for every integer $d\ge1$ an explicit recursive construction gives a nonconstant total Boolean function with $\mathrm{bs}(f)/s(f)^2\ge2^d/(4(d+2)^2)$, so no bound $\mathrm{bs}\le C s^2$ holds; the abstract also claims a fixed $\alpha>2$ with $\mathrm{bs}(f)\ge s(f)^\alpha$ along an unbounded family. This does not close the gap to Huang's upper bound $\mathrm{bs}\le s^4$; the true exponent remains open. Because $\lambda(f)\le s(f)$, it also implies a negative answer to the spectral-sensitivity question $\mathrm{bs}=O(\lambda^2)$, which Meiburg had already disproved (see block-sensitivity-spectral-sensitivity-squared). parent of this event

Lean proof (OAI.Paper320.quantitative_separation) evidence for this event

Meiburg, Block sensitivity can exceed spectral sensitivity squared (arXiv:2608.00851), the construction this adapts evidence for this event

Is block sensitivity at most quadratic in sensitivity? (Nisan-Szegedy) parent of this event