11 papers · 1 filter
One-way multilinear functions of the second order with linear shifts
Stanislav Semenov
We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts.…
Stratified Algebra
Stanislav Semenov
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms gove…
Invariant Bridges Between Four Successive Points: A New Tool for Data Coding
Stanislav Semenov
We introduce a simple yet powerful invariant relation connecting four successive terms of a class of exponentially decaying alternating functions. Specifically, for the sequence de…
Wave Arithmetic: A Smooth Integral Representation of Number Theory
Stanislav Semenov
We introduce Wave Arithmetic, a smooth analytical framework in which natural, integer, and rational numbers are represented not as discrete entities, but as integrals of smooth, co…
A Smooth Analytical Approximation of the Prime Characteristic Function
Stanislav Semenov
We construct a smooth real-valued function P(n) in [0,1], defined via a triple integral with a periodic kernel, that approximates the characteristic function of prime numbers. The…
On the Nature of Fractal Numbers and the Classical Continuum Hypothesis (CH)
Stanislav Semenov
We propose a reinterpretation of the continuum grounded in the stratified structure of definability rather than classical cardinality. In this framework, a real number is not an ab…