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Theorem

Sensitivity Theorem

Combinatorics and Graph Theory

The sensitivity theorem, in computational complexity, was proved by Hao Huang in 2019 and states that the sensitivity of a Boolean function on n bits is always at least the square root of its degree, resolving a conjecture Noam Nisan and Mario Szegedy had posed in 1992. The proof, notable for its brevity after decades of limited progress on the problem, establishes that sensitivity, degree and decision tree complexity, several of the standard measures of how complicated a Boolean function is, are all polynomially related to one another. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Classification
Statement Form
Inequality 1
Proof Year
2019 2
Connections

Has Statement Form

Inequality, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Sources
1. Sensitivity theorem (Wikipedia)
2. Sensitivity theorem (Wikipedia)
Wikipedia Sensitivity theorem lead paragraph (w-bbfill-psymath4-0926)
Quote, Wikipedia Sensitivity theorem lead paragraph (w-bbfill-psymath4-0926)
proved by Hao Huang in 2019
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