Is block sensitivity at most quadratic in spectral sensitivity? (Aaronson, Ben-David, Kothari, Rao and Tal)

Lineage and corrections

Is block sensitivity at most quadratic in spectral sensitivity? (Aaronson, Ben-David, Kothari, Rao and Tal) parent of this event

This event attributed to Claude Opus 5 with Harmonic's Aristotle (Lean)

VibeMathed record: Is block sensitivity at most quadratic in spectral sensitivity? (Aaronson, Ben-David, Kothari, Rao and Tal) evidence for this event

This event attributed to GPT-5.6-Sol (ideas)

Lean formalization: Timeroot/BS_Lam evidence for this event

This event attributed to Alexander Meiburg

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

Theorem 6.1: a total Boolean function on 2,017,584 variables with $\mathrm{bs}(f)\ge14011$ and $\lambda(f)\le89.0162$, so $\mathrm{bs}(f)\ge\lambda(f)^{2.127}$; composition gives a family with $\lambda\to\infty$ and $\mathrm{bs}=\Omega(\lambda^{2.127})$, so no quadratic bound holds. The function is a union of subcubes indexed by a doubly regular tournament with gates fixed by the Lovász local lemma. An exponent near 2.20 on 1,255 variables is numerical evidence only. The true exponent, between 2.127 and 4, stays open. Since $\lambda(f)\le s(f)$, OpenAI's later disproof of $\mathrm{bs}=O(s^2)$ (25 September 2026), which adapts this gated-tournament construction, implies this result. parent of this event

Headline Lean statements (BSLambda/Main.lean) evidence for this event

Aaronson-Ben-David-Kothari-Rao-Tal, Degree vs. approximate degree (arXiv) evidence for this event

Stronger later result: block sensitivity is not quadratic in sensitivity (OpenAI release) evidence for this event