Title:Tetrahedral Hyperdimensional Algebra — Formal Mathematical Manuscript (JMP Submission Version) Description:This record contains the formal mathematical version of Tetrahedral Hyperdimensional Algebra (THA) submitted to Journal of Mathematical Physics (AIP Publishing) under Manuscript ID JMP25-AR-00697.This manuscript presents the algebraic foundations of THA, including: tetrahedral operator definitions Clifford-phase embeddings morphism rules recursion operators preliminary structural theorems This version restricts itself strictly to mathematical formalism and does not include speculative cosmology, consciousness models, or extended philosophical material.It represents the academically aligned, publication-ready form of the work. A separate Zenodo record contains the extended Experimental Research Monograph, which preserves exploratory, speculative, and developmental content for R&D purposes. Intended Use: peer-review academic citation mathematical analysis formal comparison with existing algebraic structures Note:This version supersedes all earlier draft forms for the purposes of scholarly review but does not replace the extended research monograph, which is archived independently for traceability.