The Concept of Vernier Calculus and Absolute Discretization of Computational Fields via Dynamic Autoresonant Flow
Abstract
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.
Related
- “The Information as Absolute” Concept and Basic Physics
- Computational Fluid Dynamics Analysis of Contrast Agent Distribution in Acute Large Artery Occlusive Stroke: A Preliminary Proof-of-Concept Study
- A General Computational Framework for Sequence-Level Thermodynamic Analysis of Modeled RNA-DNA and DNA-DNA Duplex States: A Proof-of-Concept Study in HIV-1
- The Degree of Neural Awareness: A Generalized Mathematical Framework and Synthetic Computational Proof of Concept for Cross-Species Comparison of Consciousness-Related Neurobiological Parameters
- Tunnelling Through the Discretization Gap: A Quantum-Inspired Formalism for Accent-Robust Intent Parsing in Speech-to-RAG Pipelines
BibTeX
@misc{saltykov2026concept,
title = {{The Concept of Vernier Calculus and Absolute Discretization of Computational Fields via Dynamic Autoresonant Flow}},
author = {Saltykov},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23574023},
url = {https://zenodo.org/records/23574023},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Concept of Vernier Calculus and Absolute Discretization of Computational Fields via Dynamic Autoresonant Flow
AU - Saltykov
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23574023
UR - https://zenodo.org/records/23574023
AB - 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.
ER -