Preliminary Notes on Prime Drum Conjectures

This document contains edited, preliminary and unpolished mathematical notes on number theoretic constructions (the "prime drum") and related proofs. The content is uploaded in raw form, including unrendered LaTeX and draft arguments, with the purpose of establishing an open, timestamped public record of these ideas. The mathematics here is experimental and incomplete in presentation. Readers should understand this version is not formatted for clarity and may be difficult to follow. A properly typeset and polished version will be released as a later update under the same Zenodo record. The author has chosen to remain anonymous for this draft release. Future versions may disclose authorship once the work is ready for full presentation. Keywords: number theory, prime numbers, conjectures, mathematical proofs, preliminary draft