A lower-bound conjecture for the regularity of long linear equations

For a positive integer $r$, let an equation be $r$-regular when every coloring of the positive integers with $r$ colors has a monochromatic positive-integer solution. Lower-bound conjecture. For each positive integer $r$, there is an integer $n(r)$ such that, whenever $n\geq n(r)$, every linear homogeneous equation in $n$ variables with nonzero integer coefficients not all of the same sign is $r$-regular. This asserts a nontrivial uniform lower bound on the degree of regularity for sufficiently long equations. The supplied text presents it as an apparent conjecture and gives no evidence of a resolution.