A Protected-Core Nonextendability Obstruction Under Uniqueness Constraints for a Restricted Difference Basis

This preprint establishes a finite nonextendability obstruction for a restricted difference basis under preserved uniqueness constraints. A fixed 46-element subset of ({0,…,9999}) is exhibited together with 17 protected differences that are each uniquely represented within the fixed set. Under any extension that preserves the uniqueness of those protected differences, the target difference 9983 cannot be represented. The obstruction is verified by exhaustively considering all 17 possible pairs at distance 9983. Each candidate pair requires at least one new endpoint whose addition would create a second representation of one of the protected differences, contradicting the preservation hypothesis. The accompanying reproducibility supplement contains the finite data and a standalone verifier. The verifier independently recomputes all 1,035 pairwise differences of the fixed set, confirms the uniqueness of the 17 protected differences, derives the forbidden-position set, and verifies that all 17 possible representations of 9983 are blocked. Version 1.1 incorporates strengthened reproducibility checks and corrected bibliographic metadata. DOI: 10.5281/zenodo.22151629