Additive function
View article: GTUD Rotation as Josephson Phase: Calibrating G = E² (Δθ)² in Macroscopic Quantum‑Tunneling Circuits
GTUD Rotation as Josephson Phase: Calibrating G = E² (Δθ)² in Macroscopic Quantum‑Tunneling Circuits Open
We operationalize the GTUD relation G = E² (Δθ)² by identifying Δθ with the Josephson phase excursion Δφ in macroscopic quantum‑tunneling (MQT) circuits. Using the washboard potential U(φ) = −E_J cos φ − (ħ/2e) I φ with effective mass M_φ …
View article: GTUD Rotation as Josephson Phase: Calibrating G = E² (Δθ)² in Macroscopic Quantum‑Tunneling Circuits
GTUD Rotation as Josephson Phase: Calibrating G = E² (Δθ)² in Macroscopic Quantum‑Tunneling Circuits Open
We operationalize the GTUD relation G = E² (Δθ)² by identifying Δθ with the Josephson phase excursion Δφ in macroscopic quantum‑tunneling (MQT) circuits. Using the washboard potential U(φ) = −E_J cos φ − (ħ/2e) I φ with effective mass M_φ …
View article: Windowed Energy as Measure Theory\\(WEM: Windowed Energy as Measure)
Windowed Energy as Measure Theory\\(WEM: Windowed Energy as Measure) Open
Establish self-consistent framework characterizing energy via first moment of windowed relative spectral density. Core scale chain holds almost everywhere on absolutely continuous spectrum: $ \ \frac{\varphi'(E){\pi}\;=\;\rho_{rel}(E)\;=\;…
View article: Majority additive coloring and the maximum degree
Majority additive coloring and the maximum degree Open
Kamyczura introduced the notion of a majority additive $k$-coloring of a graph $G$ as a function $c: V(G) \to \{1,2,\ldots,k\}$ such that $$\left|\left\{u \in N_G(v):\sum_{w \in N_G(u)} c(w) = s \right\}\right|\leq \max\left\{1,\frac{d_G(v…
View article: Windowed Energy as Measure Theory\\(WEM: Windowed Energy as Measure)
Windowed Energy as Measure Theory\\(WEM: Windowed Energy as Measure) Open
Establish self-consistent framework characterizing energy via first moment of windowed relative spectral density. Core scale chain holds almost everywhere on absolutely continuous spectrum: $ \ \frac{\varphi'(E){\pi}\;=\;\rho_{rel}(E)\;=\;…
View article: <sup>17</sup> O Chemical Shifts in Water
<sup>17</sup> O Chemical Shifts in Water Open
How hydrogen bonding affects the 17O chemical shift in water is analyzed in depth in this work. It is found that the 17O chemical shift in water is sensitive to both hydrogen bond distance and the OH covalent bond len…
View article: Majority additive coloring and the maximum degree
Majority additive coloring and the maximum degree Open
Kamyczura introduced the notion of a majority additive $k$-coloring of a graph $G$ as a function $c: V(G) \to \{1,2,\ldots,k\}$ such that $$\left|\left\{u \in N_G(v):\sum_{w \in N_G(u)} c(w) = s \right\}\right|\leq \max\left\{1,\frac{d_G(v…
View article: Dual--Flux Part IX: Arithmetic - The Balance of Addition and Multiplication
Dual--Flux Part IX: Arithmetic - The Balance of Addition and Multiplication Open
This document is Part IX of the Dual Flux series. It extends the Dual Flux framework from physics to arithmetic by showing that the additive and multiplicative structures of the integers form an exact analogue of the coherent and fragmenta…
View article: Dual--Flux Part IX: Arithmetic - The Balance of Addition and Multiplication
Dual--Flux Part IX: Arithmetic - The Balance of Addition and Multiplication Open
This document is Part IX of the Dual Flux series. It extends the Dual Flux framework from physics to arithmetic by showing that the additive and multiplicative structures of the integers form an exact analogue of the coherent and fragmenta…
View article: Squared-Multiplicity Additive Functions and a CLT in the Kubilius Model
Squared-Multiplicity Additive Functions and a CLT in the Kubilius Model Open
We study nonlinear additive arithmetic functions built from the multiplicities of primes in the factorization of an integer, with particular emphasis on a squared--multiplicity family depending on a real parameter alpha. For each integer, …
View article: Squared-Multiplicity Additive Functions and a CLT in the Kubilius Model
Squared-Multiplicity Additive Functions and a CLT in the Kubilius Model Open
We study nonlinear additive arithmetic functions built from the multiplicities of primes in the factorization of an integer, with particular emphasis on a squared--multiplicity family depending on a real parameter alpha. For each integer, …
View article: Additivity of Crossing Number via Restricted Reidemeister Moves
Additivity of Crossing Number via Restricted Reidemeister Moves Open
We define a set of restricted Reidemeister moves and show that if $K$ is obtained from $K_0\,\#\,K_1$ using those moves, then the crossing number of $K$ is at least $c(K_0)+c(K_1)$. We also explore topological interpretations of this resul…
View article: Densitometria I. Discrete groups
Densitometria I. Discrete groups Open
An upper mean here is a subadditive functional $\overline M$ defined on bounded functions on a commutative group which has, beside some natural requirements, the property we call restricted additivity: if $g(x)= f(x)+f(x+t)$, then $\overli…
View article: Densitometria I. Discrete groups
Densitometria I. Discrete groups Open
An upper mean here is a subadditive functional $\overline M$ defined on bounded functions on a commutative group which has, beside some natural requirements, the property we call restricted additivity: if $g(x)= f(x)+f(x+t)$, then $\overli…
View article: Additivity of Crossing Number via Restricted Reidemeister Moves
Additivity of Crossing Number via Restricted Reidemeister Moves Open
We define a set of restricted Reidemeister moves and show that if $K$ is obtained from $K_0\,\#\,K_1$ using those moves, then the crossing number of $K$ is at least $c(K_0)+c(K_1)$. We also explore topological interpretations of this resul…
View article: A sharp threshold for arithmetic effects on the tail probabilities of lacunary sums
A sharp threshold for arithmetic effects on the tail probabilities of lacunary sums Open
A classical observation in analysis asserts that lacunary systems of dilated functions show many properties which are also typical for systems of independent random variables. For example, if $(n_k)_{k \ge 1}$ is a sequence of integers sat…
View article: A sharp threshold for arithmetic effects on the tail probabilities of lacunary sums
A sharp threshold for arithmetic effects on the tail probabilities of lacunary sums Open
A classical observation in analysis asserts that lacunary systems of dilated functions show many properties which are also typical for systems of independent random variables. For example, if $(n_k)_{k \ge 1}$ is a sequence of integers sat…
View article: Arithmetic Spectra in the PAC–u8 Framework: A Six-Part Program from Primes to Motives
Arithmetic Spectra in the PAC–u8 Framework: A Six-Part Program from Primes to Motives Open
This six-part arithmetic subseries develops a coherent interface between modern arithmetic theory and the operator–spectral, compression-based architecture of the PAC–$\mu^8$ framework. Starting from the most elementary additive and …
View article: Constructive Additive Theory of Natural Numbers
Constructive Additive Theory of Natural Numbers Open
This work proposes a paradigm shift in number theory: moving from theclassical multiplicative language (based on divisors and sieves) to a constructiveadditive theory. We introduce a positive definition of prime numbers asadditive atoms, b…
View article: Constructive Additive Theory of Natural Numbers
Constructive Additive Theory of Natural Numbers Open
This work proposes a paradigm shift in number theory: moving from theclassical multiplicative language (based on divisors and sieves) to a constructiveadditive theory. We introduce a positive definition of prime numbers asadditive atoms, b…
View article: Holonomy–Integerization: Quantitative Stability, Cocycle Algebra, and a Readout–Transport Bridge
Holonomy–Integerization: Quantitative Stability, Cocycle Algebra, and a Readout–Transport Bridge Open
We solve the following quantitative margin-preserving alignment problem for phase signals on S¹. Given BV phase data γ, a uniform sup-error budget ε, and a required readout integrity (no false carries), we choose a smoothing degree N and a…
View article: Holonomy–Integerization: Quantitative Stability, Cocycle Algebra, and a Readout–Transport Bridge
Holonomy–Integerization: Quantitative Stability, Cocycle Algebra, and a Readout–Transport Bridge Open
We solve the following quantitative margin-preserving alignment problem for phase signals on S¹. Given BV phase data γ, a uniform sup-error budget ε, and a required readout integrity (no false carries), we choose a smoothing degree N and a…
View article: Additivity of the genetic load revealed to be a product of both synergistic and antagonistic epistasis in Drosophila.
Additivity of the genetic load revealed to be a product of both synergistic and antagonistic epistasis in Drosophila. Open
Epistasis has been theoretically implicated in several major evolutionary processes, including the evolution of sex and speciation, but empirical evidence for its impact is still lacking. We tested for epistatic interactions using a full-s…
View article: Interaction of Red Cabbage Extract with Exogenous Antioxidants
Interaction of Red Cabbage Extract with Exogenous Antioxidants Open
Interactions between antioxidants are of interest, mainly for understanding their action in complex biological and food systems. This study aimed to evaluate interactions between the anthocyanin-rich aqueous red cabbage extract and several…
View article: Padé approximations for products of functions
Padé approximations for products of functions Open
In this article, we construct new Padé approximations for the \emph{product} of binomial functions and powers of logarithmic functions. While several explicit Padé approximants are known for powers of exponential functions, binomial functi…
View article: Padé approximations for products of functions
Padé approximations for products of functions Open
In this article, we construct new Padé approximations for the \emph{product} of binomial functions and powers of logarithmic functions. While several explicit Padé approximants are known for powers of exponential functions, binomial functi…
View article: On the mean square of the error term for the asymmetric two-dimensional divisor problem with congruence conditions
On the mean square of the error term for the asymmetric two-dimensional divisor problem with congruence conditions Open
Suppose that $a$ and $b$ are positive integers subject to $(a,b)=1$. For $n\in\mathbb{Z}^+$, denote by $τ_{a,b}(n;\ell_1,M_1,l_2,M_2)$ the asymmetric two--dimensional divisor function with congruence conditions, i.e., \begin{equation*} τ_{…
View article: On the mean square of the error term for the asymmetric two-dimensional divisor problem with congruence conditions
On the mean square of the error term for the asymmetric two-dimensional divisor problem with congruence conditions Open
Suppose that $a$ and $b$ are positive integers subject to $(a,b)=1$. For $n\in\mathbb{Z}^+$, denote by $τ_{a,b}(n;\ell_1,M_1,l_2,M_2)$ the asymmetric two--dimensional divisor function with congruence conditions, i.e., \begin{equation*} τ_{…
View article: Privacy-Preserving Cramér-Rao Lower Bound
Privacy-Preserving Cramér-Rao Lower Bound Open
This paper establishes the privacy-preserving Cramér-Rao (CR) lower bound theory, characterizing the fundamental limit of identification accuracy under privacy constraint. An identifiability criterion under privacy constraint is derived by…
View article: The Emergent ζ: Primeonic Self-Organization and the Ground State of Arithmetic Space
The Emergent ζ: Primeonic Self-Organization and the Ground State of Arithmetic Space Open
We reverse the causal direction of earlier Primeon models: rather than positing the Riemann ζ-function as a stabilizing scaffold, we derive it as the inevitable equilibrium configuration of self-coupled primeons in p-space. Primeons, index…