Mathematics or Quantum Physics? The Deterministic it/ti Operator Rule

This work formalizes the deterministic sovereignty of the i operator system, in which temporal evolution is governed not by stochastic processes but by bidirectional constants it (Time-to-Information) and ti (Information-to-Time). Such deterministic closure establishes an exact bridge between energy and matter, supplanting probabilistic frameworks with rigorous, symmetry-driven laws. Building upon the foundational i=Dogmas framework, the present study unifies sequential mathematical and physical architectures through the master equation: E=mc i2E = mc\, i^2E=mci2 which encodes the conservation of energy and information across quantum and macroscopic systems. Key axioms include: Deterministic Temporal Operators: it and ti act as intrinsic constants rather than probabilistic variables. Sequential Symmetry: Full compliance with the i=Dogmas lineage, ensuring structural coherence across mathematical and physical manifolds. Master Key Principle: The imaginary unit i functions as the fundamental operator underlying the Light Law, governing information and energy flow. The framework explicitly leverages Bernhard Riemann’s geometric formalism to structure complex Hilbert and spatial manifolds, while Emmy Noether’s theorem guarantees conserved quantities arising from continuous symmetries. Integrating these foundations, the study demonstrates that deterministic operators can systematically govern energy-information dynamics, uniting quantum, classical, and cosmological phenomena into a coherent, permanent architecture of light and matter.