Boolean logic gates form the foundation of computation and cryptography. Classical gates (AND, OR, XOR, NOT) and their combinations are well understood; linear threshold gates (TLGs) extend these by allowing weighted inputs. All classical and threshold gates share a fundamental property: their behavior is determined solely by the multiset of input values, independent of the positions of those values. The CIG breaks this symmetry. Inspired by the inverse-square law of electrostatics, the gate assigns signed, distance-dependent weights to the neighbors of a passing bit. The sign of the weight depends on which side of the passing bit the neighbor occupies. As a result, permuting the gate bits changes the output even when the Hamming weight is preserved --- a property absent in all classical gate families. Beyond theoretical interest, this positional sensitivity makes the gate attractive as a primitive for lightweight cryptography: it achieves full bijection and strong avalanche behavior with a compact, parameter-free formula.
Güven Acar (Wed,) studied this question.