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The Algebraic Genesis of Fibonacci Numbers: A Diagonal Projection Theory from Pascal's Combinatorial Space Open
This dissertation establishes a comprehensive algebraic framework demonstrating that the Fibonacci sequence emerges as the result of a diagonal projection operator TTT applied to Pascal’s triangle. We introduce the diagonal projection oper…
The Algebraic Genesis of Fibonacci Numbers: A Diagonal Projection Theory from Pascal's Combinatorial Space Open
This dissertation establishes a comprehensive algebraic framework demonstrating that the Fibonacci sequence emerges as the result of a diagonal projection operator TTT applied to Pascal’s triangle. We introduce the diagonal projection oper…
Asymptotic Behavior of Non-Linear Parabolic Systems Open
Research manuscript generated by Paper Architect 12+.
From Modular Exclusion to ppb Precision: Asymptotic Rational Scaling in Aligned Ten‑Number Windows Open
The project investigates the distribution of primes in aligned consecutive 10-number intervals, specifically \(I_k = [10k + 2,\,10k + 11]\). It proves a Restricted Modular Exclusion Law: in these aligned intervals it is impossible to have …
Non-Self-Adjoint Spectral Asymptotics Open
The spectral theory of non-self-adjoint differential operators constitutes one of the most challenging and rapidly evolving frontiers in modern mathematical analysis. Unlike their self-adjoint counterparts, which enjoy the stability guaran…
SCALE-INVARIANT PROPERTIES IN PRIME NUMBER DISTRIBUTION: A COMPREHENSIVE EMPIRICAL ANALYSIS WITH DETAILED NUMERICAL RESULTS Open
This paper presents a comprehensive empirical investigation into prime number distribution patterns using the Sieve of Eratosthenes algorithm. We analyze 805 consecutive intervals of 10 numbers each, ranging from 2 to 9,981, computing the …
SCALE-INVARIANT PROPERTIES IN PRIME NUMBER DISTRIBUTION: AA COMPREHENSIVE EMPIRICAL COMPREHENSIVE EMPIRICAL ANAL ANALYSIS YSIS WITH DET WITH DETAILED NUMERICAL AILED NUMERICAL RESUL RESULTSTS Open
This paper presents a comprehensive empirical investigation into prime number distribution patterns using the Sieve of Eratosthenes algorithm. We analyze 805 consecutive intervals of 10 numbers each, ranging from 2 to 9,981, computing the …
Non-Self-Adjoint Spectral Asymptotics Open
The spectral theory of non-self-adjoint differential operators constitutes one of the most challenging and rapidly evolving frontiers in modern mathematical analysis. Unlike their self-adjoint counterparts, which enjoy the stability guaran…
SCALE-INVARIANT PROPERTIES IN PRIME NUMBER DISTRIBUTION: A COMPREHENSIVE EMPIRICAL ANALYSIS WITH DETAILED NUMERICAL RESULTS Open
This paper presents a comprehensive empirical investigation into prime number distribution patterns using the Sieve of Eratosthenes algorithm. We analyze 805 consecutive intervals of 10 numbers each, ranging from 2 to 9,981, computing the …
View article: Hyper-Pascal Lattice: Infinite-Zoom Universal Coordinate System for Telescopes and Microscopes
Hyper-Pascal Lattice: Infinite-Zoom Universal Coordinate System for Telescopes and Microscopes Open
We present the Hyper-Pascal Lattice (HPL) — a revolutionary coordinate system with theoretically infinite zoom capability, enabling continuous magnification from galactic scales (~10²¹ m) to subatomic scales (~10⁻¹⁵ m) and beyond, without …
View article: The Infinite Cylinder of Number Systems: Geometric Unification of All Arithmetics
The Infinite Cylinder of Number Systems: Geometric Unification of All Arithmetics Open
We present a unified geometric framework that embeds all possible number sys-tems into a single three-dimensional structure: an infinite cylinder. Starting fromtwo parallel circular bases of diameter 1, each containing continuum-many point…
View article: Theory of the Infinite Numerical Sheaf: A Spherical Framework for Coexisting Number
Theory of the Infinite Numerical Sheaf: A Spherical Framework for Coexisting Number Open
We present the Theory of the Infinite Numerical Sheaf over the 2-sphere, a rig-orous mathematical framework that formalizes the geometric coexistence of struc-turally distinct number systems. We construct a fiber bundle π : E → S2 whereeac…
View article: The Infinite Conical Frustum of Number Systems: A Geometric Unification of All Arithmetics
The Infinite Conical Frustum of Number Systems: A Geometric Unification of All Arithmetics Open
We present a unified geometric framework that embeds all possible number sys-tems into a single three-dimensional structure: an infinite conical frustum (truncatedcone). Starting from two parallel circular bases—one with diameter 1 (bottom…
View article: Triangles at Infinity: Three Perspectives on Closure, Number Sets, and the Limit of Geometric Growth
Triangles at Infinity: Three Perspectives on Closure, Number Sets, and the Limit of Geometric Growth Open
We present three complementary mathematical investigations of a fundamental question in geometric analysis: does an equilateral triangle maintain closure as its side length grows to infinity, and what happens when each side becomes the com…
View article: The Hyper-Pascal Lattice: A Combinatorial Framework for Hierarchical Discrete Space
The Hyper-Pascal Lattice: A Combinatorial Framework for Hierarchical Discrete Space Open
We introduce the Hyper-Pascal Lattice (HPL), a novel mathematical structurethat reinterprets Pascal’s Triangle as an infinite hierarchical network with binaryaddressing. Unlike the classical arithmetic interpretation of binomial coefficien…
View article: The Infinite Conical Frustum of Number Systems: A Geometric Unification of All Arithmetics
The Infinite Conical Frustum of Number Systems: A Geometric Unification of All Arithmetics Open
We present a unified geometric framework that embeds all possible number sys-tems into a single three-dimensional structure: an infinite conical frustum (truncatedcone). Starting from two parallel circular bases—one with diameter 1 (bottom…
View article: The Infinite Cylinder of Number Systems: Geometric Unification of All Arithmetics
The Infinite Cylinder of Number Systems: Geometric Unification of All Arithmetics Open
We present a unified geometric framework that embeds all possible number sys-tems into a single three-dimensional structure: an infinite cylinder. Starting fromtwo parallel circular bases of diameter 1, each containing continuum-many point…
View article: Hyper-Pascal Lattice: Infinite-Zoom Universal Coordinate System for Telescopes and Microscopes
Hyper-Pascal Lattice: Infinite-Zoom Universal Coordinate System for Telescopes and Microscopes Open
We present the Hyper-Pascal Lattice (HPL) — a revolutionary coordinate system with theoretically infinite zoom capability, enabling continuous magnification from galactic scales (~10²¹ m) to subatomic scales (~10⁻¹⁵ m) and beyond, without …
View article: Triangles at Infinity: Three Perspectives on Closure, Number Sets, and the Limit of Geometric Growth
Triangles at Infinity: Three Perspectives on Closure, Number Sets, and the Limit of Geometric Growth Open
We present three complementary mathematical investigations of a fundamental question in geometric analysis: does an equilateral triangle maintain closure as its side length grows to infinity, and what happens when each side becomes the com…
View article: The Infinite Expanding Sphere of Number Systems: Radial Embedding of All Arithmetics from Origin to Infinity
The Infinite Expanding Sphere of Number Systems: Radial Embedding of All Arithmetics from Origin to Infinity Open
We present a unified geometric framework that embeds all possible number systems into a single structure: an infinitely expanding sphere.Starting from a sphere of diameter 1, we let the diameter grow through all positive reals:( d ∈ {1, 10…
View article: Theory of the Infinite Numerical Sheaf: A Spherical Framework for Coexisting Number
Theory of the Infinite Numerical Sheaf: A Spherical Framework for Coexisting Number Open
We present the Theory of the Infinite Numerical Sheaf over the 2-sphere, a rig-orous mathematical framework that formalizes the geometric coexistence of struc-turally distinct number systems. We construct a fiber bundle π : E → S2 whereeac…
View article: The Hyper-Pascal Lattice: A Combinatorial Framework for Hierarchical Discrete Space
The Hyper-Pascal Lattice: A Combinatorial Framework for Hierarchical Discrete Space Open
We introduce the Hyper-Pascal Lattice (HPL), a novel mathematical structurethat reinterprets Pascal’s Triangle as an infinite hierarchical network with binaryaddressing. Unlike the classical arithmetic interpretation of binomial coefficien…
View article: The Infinite Expanding Sphere of Number Systems: Radial Embedding of All Arithmetics from Origin to Infinity
The Infinite Expanding Sphere of Number Systems: Radial Embedding of All Arithmetics from Origin to Infinity Open
We present a unified geometric framework that embeds all possible number systems into a single structure: an infinitely expanding sphere.Starting from a sphere of diameter 1, we let the diameter grow through all positive reals:( d ∈ {1, 10…
View article: The Infinite Conical Frustum: A Geometric Embedding of the Real Number Line
The Infinite Conical Frustum: A Geometric Embedding of the Real Number Line Open
We explore the geometric properties of a conical frustum whose height extendsalong the entire positive real number line. Starting with a frustum of finite di-mensions (minor base diameter 1, major base diameter 10, height 1), we investigat…
View article: The Infinite Conical Frustum: A Geometric Embedding of the Real Number Line
The Infinite Conical Frustum: A Geometric Embedding of the Real Number Line Open
We explore the geometric properties of a conical frustum whose height extendsalong the entire positive real number line. Starting with a frustum of finite di-mensions (minor base diameter 1, major base diameter 10, height 1), we investigat…
View article: Theory of the Infinite Numerical Sheaf: A Spherical Framework for Coexisting Number
Theory of the Infinite Numerical Sheaf: A Spherical Framework for Coexisting Number Open
We present the Theory of the Infinite Numerical Sheaf over the 2-sphere, a rig-orous mathematical framework that formalizes the geometric coexistence of struc-turally distinct number systems. We construct a fiber bundle π : E → S2 whereeac…
View article: Theory of the Infinite Numerical Sheaf: A Framework for Coexisting Number Systems
Theory of the Infinite Numerical Sheaf: A Framework for Coexisting Number Systems Open
We present the Theory of the Infinite Numerical Sheaf, a rigorous mathematicalframework that formalizes the geometric coexistence of structurally distinct numbersystems. We construct a fiber bundle π : E → S ^1 where each fiber representsa…
View article: Paper Architect 12+
Paper Architect 12+ Open
The program runs inside Google’s app creator, AI Studio. Paper Architect 12+ is a multidisciplinary research engine designed to assist in the creation and structuring of complex scientific papers.It integrates methods from fields such as m…
View article: Self-Generative Mathematics
Self-Generative Mathematics Open
The program runs inside Google’s app creator, AI Studio. This research delineates a formal framework for Self-Generative Mathematics (SGM), char-acterized by the autonomous derivation of axiomatic sets and procedural theorem discoverywithi…
View article: Theory of the Infinite Numerical Sheaf: A Framework for Coexisting Number Systems
Theory of the Infinite Numerical Sheaf: A Framework for Coexisting Number Systems Open
We present the Theory of the Infinite Numerical Sheaf, a rigorous mathematicalframework that formalizes the geometric coexistence of structurally distinct numbersystems. We construct a fiber bundle π : E → S ^1 where each fiber representsa…