16 papers
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-Based Cryptography: Toward a General Framework
Stanislav Semenov
We develop a generalized framework for invariant-based cryptography by extending the use of structural identities as core cryptographic mechanisms. Starting from a previously intro…
Invariant-Based Cryptography
Stanislav Semenov
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integ…
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…
Fractal Analysis on the Real Interval: A Constructive Approach via Fractal Countability
Stanislav Semenov
This paper develops a technical and practical reinterpretation of the real interval [a,b] under the paradigm of fractal countability. Instead of assuming the continuum as a complet…
Smooth Integer Encoding via Integral Balance
Stanislav Semenov
We introduce a novel method for encoding integers using smooth real-valued functions whose integral properties implicitly reflect discrete quantities. In contrast to classical repr…
Smooth Approximations of the Rounding Function
Stanislav Semenov
We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based o…
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…
Fractal Origin of the Continuum: A Hypothesis on Process-Relative Definability
Stanislav Semenov
We propose a new constructive model of the real continuum based on the notion of fractal definability. Rather than assuming the continuum as a completed uncountable totality, we vi…
Axiomatic Foundations of Fractal Analysis and Fractal Number Theory
Stanislav Semenov
We develop an axiomatic framework for fractal analysis and fractal number theory grounded in hierarchies of definability. Central to this approach is a sequence of formal systems F…
Fractal Countability as a Constructive Alternative to the Power Set of N: A Meta-Formal Approach to Stratified Definability
Stanislav Semenov
Classical set theory constructs the continuum via the power set P(N), thereby postulating an uncountable totality. However, constructive and computability-based approaches reveal t…
Fractal Boundaries of Constructivity: A Meta-Theoretical Critique of Countability and Continuum
Stanislav Semenov
All constructive methods employed in modern mathematics produce only countable sets, even when designed to transcend countability. We show that any constructive argument for uncoun…
Constructive Limits of Cantor's Diagonal Method: Countability, Enumerability, and the Impossibility of Exhausting the Continuum
Stanislav Semenov
Cantor's diagonal method is traditionally used to prove the uncountability of the set of all infinite binary sequences. This paper analyzes the expressive limits of this method. It…