The (extended) Binary Value Principle (eBVP, the equation $\sum x_i 2^{i-1} = -k$ for $k > 0$
and in the presence of $x_i^2=x_i$) has received a lot of attention recently, several lower
bounds have been proved for it [Alekseev et al 20, Alekseev 21, Part and Tzameret 21].
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We introduce the `binary value principle' which is a simple subset-sum instance expressing that a natural number written in binary cannot be negative, relating it to central problems in proof and algebraic complexity. We prove conditional superpolynomial lower bounds on the Ideal Proof System (IPS) refutation size of this instance, ... more >>>