CNBIT V4 – Bridge Edition: From Axiomatic Definition to Geometric–Quantum Necessity

This publication presents the fourth and academically formalized version of the CNBIT (Coherent Null-Bit Information Theory), reinterpreting its core energy-information relation as a mathematical and geometric necessity. The document bridges intuitive wave-based reasoning with rigorous mathematical structures. Key advances:– Derivation of the CNBIT constant (E_CNBIT = 1.988186 × 10⁻²³ J/bit) as a spectral closure threshold– Proof that a positive mass gap (Δ ≥ E_CNBIT) emerges naturally from quantized field entropy dynamics– Replacement of π with a time-dependent operator π(t), anchoring phase-locked closure behavior– Integration with gauge field geometry, entropy curvature, Hamiltonian spectral analysis This work is part of the *Pragmatica Universus* framework and responds formally to critiques that questioned prior heuristic formulations. The document is fully compliant with international authorship standards: the AI assistant referenced contributed only to documentation formatting; all scientific responsibility rests with the author.