A New Identity for Euler's Constant via Binary Segmentation of the Odd Harmonic Series - A Handwritten Manuscript

This is a scanned copy of the handwritten manuscript. This manuscript presents several brand-new mathematical formulas and identities regarding Euler's constant and the Odd Harmonic Series with Binary Segmentation, which were independently derived by the author. The uploaded file contains detailed handwritten logical derivations and step-by-step proofs. This work is made publicly available under the CC-BY 4.0 license, primarily intended for academic exchange and intellectual property archiving (timestamping). Peers and researchers are highly welcome to perform computational numerical verifications or theoretical extensions based on these results. For any future citations or derivative works, please properly cite the DOI of this Zenodo record.