Abstract The Nullivance Logic System and Nullivance Mathematics are non-binary theoretical frameworks designed to model dynamic states, contradictions, and quasivance (quasi-isolated) entities through the logic unit δ_S(A) = α · Φ(Θ(t)). This report presents the background, development motivation, initiating philosophical inquiries, objectives, vision, and a system overview, including a comparative analysis between Nullivance Logic and traditional logic . Detailed examples—ranging from food selection and weather forecasting to DNA analysis and image classification—illustrate core concepts, accompanied by distinct logic network diagrams that visualize how Nullivance processes data and contradictions. Key Innovations & Vision Nullivance is not merely an alternative to binary or fuzzy logic—it is a framework for perceiving the "pulse" of reality. Instead of viewing reality as a collection of static snapshots, Nullivance models it as a breathing network of oscillating entities and entangled interactions . Dynamic Existence: Entities oscillate between manifestation and potentiality based on their Phase Tensor (Θ) and Existence Level (α). Paraconsistency without Explosion: The system handles contradictions naturally through "Conflict Harmonization" and phase fusion, preventing logical collapse . The Science of the Unmanifested: Introduces the concept of Quasivance to mathematically model entities that "do not exist" (α ≈ 0) but still exert structural influence (ρ > 0) on the system . Part 1: Foundations covers: Philosophical Inquiries: The origin of thought via sensory input and the ontology of the "Void" as a reservoir of potential. Formal Syntax & Semantics: The axiomatic structure of NPL-2D and the mathematical formulation of Phase Stability (Φ). Applications: Demonstrations in AI (Neural Networks), Bioinformatics (DNA), and Complex Systems.