Entropy Loss and Invertibility in a Fixed-Position Binary Deletion Map

We study a deterministic transformation on the natural numbers obtained by deleting a fixed-position bit from their binary representation. Although the map is non-injective, it exhibits a structured pattern of collisions. Using elementary information-theoretic tools, we quantify the resulting entropy loss and characterize the minimal auxiliary information required to recover original values uniquely. This exposition provides a concrete number-theoretic model of invertibility under constraints, illustrating connections to deletion channels, redundancy-based recovery, and error-correcting codes.