SWhat changed
A signed adjacency-matrix construction and eigenvalue interlacing give the sharp square-root maximum-degree lower bound for induced hypercube subgraphs with more than half the vertices. Via the known Gotsman–Linial equivalence, this proves polynomial relations between Boolean sensitivity, polynomial degree and block sensitivity.
Scientific scope
A signed adjacency-matrix construction and eigenvalue interlacing give the sharp square-root maximum-degree lower bound for induced hypercube subgraphs with more than half the vertices. Via the known Gotsman–Linial equivalence, this proves polynomial relations between Boolean sensitivity, polynomial degree and block sensitivity. The stated degree bound implies block sensitivity at most twice the fourth power of sensitivity in this version; the paper does not close the remaining quadratic-versus-quartic separation. The graph-size threshold and induced-subgraph condition matter. This is not a claim that all Boolean complexity measures coincide.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The stated degree bound implies block sensitivity at most twice the fourth power of sensitivity in this version; the paper does not close the remaining quadratic-versus-quartic separation. The graph-size threshold and induced-subgraph condition matter. This is not a claim that all Boolean complexity measures coincide.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
Full scientific record · Browse contribution grades · Request a correction