The Concept of Vernier Calculus and Absolute Discretization of Computational  Fields via Dynamic Autoresonant Flow

This paper proposes a radical shift in the foundations of classical calculus 
and computational mathematics — a transition from approximate linear computations 
under the IEEE 754 standard to Vernier Calculus. Within this paradigm, the 
continuous field is replaced by the interference effect of two dynamically shifting 
numerical scales, transforming mathematics from a process of counting infinite 
fractions into a search for absolute nodes of harmony. The paper derives a monolithic 
iterative formula for the dynamic vernier, which completely eliminates the accumulation 
of digital rounding noise in computer systems. Using a comprehensive end-to-end 
calculation of a base quantum (the number four), we demonstrate how root, logarithm, 
and integral functions simultaneously unfold from a single numerical log. A fundamental 
feature of autofixation is revealed: as the flow approaches the precision of unity, 
it naturally hits a prime number, scanning the structural matrix of space. This work 
justifies the urgency of the new mathematics for applications in supercomputers, 
quantum computing, and resonant neural networks.