The Nekobune Difference Property: A New Perspective on k-Tuple conjecture

※There are separate versions for public viewing and Twitter viewing. Twitter version: https://zenodo.org/records/15126871 NOTE (Correction) In the initial analysis of Pattern 1 ({0,6,8,14,18}), the following errors were identified: - **Sum of Δp_k**: 88,770 (previously miscalculated as 91,930) - **Average **: 5,918.0 - **Error rate vs theory**: 5.31% (was 1.94%) *All mistakes have been fixed The conclusions remain qualitatively unchanged, but readers should refer to these corrected values. A full revised version will follow. *I acknowledge the assistance of Grok (xAI) in refining the discussion section, particularly in correcting overstatements and lexical issues (e.g., ambiguity and repetition), with the core ideas and analysis being my own work.