Integer solutions to interval linear equations and unique measurement

Every system of n linearly independent homogeneous linear equations in n 1 unknowns with coefficients in {1, 0, -1} has a unique (up to multiplicati on by 1) non-zero solution vector d = (d(1), d(2),..., d(n+1)) in which the d(j)'s are integers with no common divisor greater than 1. It is known tha t, for large n, \Sigmad(j)\ can be arbitrarily greater than 2(n). We prove that if every equation, written as Sigma (A) x(i) - Sigma (B) x(i) = 0, is such that A and B are intervals of contiguous indices, then \Sigmad(j)\ les s than or equal to 2(n). This confirms conjectures of the author and Fred R oberts that arose in the theory of unique finite measurement.