Centered Rank-Two Sign Matrices

This report proves the spread of the best rank-two block matrix as an upper bound for every endpoint matrix whose centered sign matrix has rank at most two, in every dimension and throughout the normalized interval $-1\le a<1$. An analytic monotonicity lemma retains integer block sizes, avoiding a fractional-mass relaxation. The negative-parameter comparison is analytic; the nonnegative comparison is established by exact rational polynomial identities, checked by a standard-library program. A consequence is the unrestricted strip $-1\le a\le-1+(1+\sqrt2)/n^2$, improving the coefficient $1/3$ in an earlier boundary-strip argument. The unrestricted conjecture is not proved here. Higher-rank indefinite deficits remain outside the argument.