FUNDAMENTAL NT-THEOREM

In this introduces a novel topological and algebraic framework designated as the Eugenio Numbers, establishing a rigorous mathematical mechanism to map coordinate trajectories from the complex plane into structured free monoids without geometric or informational degeneration. Traditional scalar representations of numeric systems intrinsically suffer from an irreversible loss of syntactic data, characteristically collapsing leading zeros and volatile word lengths. To resolve this fundamental limitation, we formalize the Factorized Floor Operator acting strictly upon the syntactic decomposition of structural expressions, anchoring the discrete projections of the complex domain via the newly defined Krishna Function. By equipping this sequential space with the non-Archimedean ultrametric of the Cantor topology, we prove the Fundamental Embedding Theorem, demonstrating that the analytical truncation error drives asymptotically to zero while completely preserving the spatial length and structural memory of digit blocks. Computational verification of the framework, including deterministic sequence indexing, is successfully implemented within the SageMath environment, opening new paradigms for lossless data compression, exact string indexing, and non-conventional numeration tracking. Synergy: Souza and Numerical Theorgyas (NT). There are gaps in Math(Art), made for those who cultivate curiosity.