General Mathematics

2605 Submissions

[3] ai.viXra.org:2605.0074 [pdf] submitted on 2026-05-31 19:08:42

Tangent Roots Structuralization and Geometric Symmetry of Cubic Curves

Authors: Shashwat Khewariya
Comments: 11 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

This paper explores the geometric symmetry and structural properties of cubic curves, focusing on the formulation and behavioral patterns of universal tangent roots. By utilizing coordinate mappings and mathematical derivations, we establish a structured relationship between cubic roots and their corresponding tangents. The study provides systematic insights into the structuralization of cubic curve functions, offering potential advancements in classical geometric analysis.
Category: General Mathematics

[2] ai.viXra.org:2605.0021 [pdf] replaced on 2026-07-04 15:07:08

A 3D Geometry of Complex Cycle Varieties: A Unified Framework for the Riemann Hypothesis and the BSD Conjecture

Authors: Ezadiin Redwaan
Comments: 14 Pages.

This paper presents a unified geometric framework for the Riemann Hypothesis and the Birch and Swinnerton-Dyer (BSD) Conjecture through the construction of a 3D compression Real-space vs 3Dstretched complex-space algebraic cycle system governed by orthogonal cycles. We demonstrate that the 3D geometric algebraic cycley = x2n + m and y = z2n + m undergo a 180◦ mirror inversion of3D geometric real algebraic cycle to be 3D geometric complex algebraic cycle, as they transition from 3D real-space compression to 3Dcomplex-space stretching. By analyzing the system in the infinitelimit (n → ∞), we identify a "The 3D geometric stability" where geometric stability is achieved only when the 3D real scalar anchor 2mmatches the 3D complex operator I. This stability condition necessitates m = 1/2, providing a topological basis for the critical line in theZeta function and the analytic synchronization at s = 1 in L-functions.Our findings suggest that these long-standing conjectures are consequences of the fundamental requirement for symmetry and geometricstability within 3D geometric manifolds,we show that the 1/2 criticalline is a necessary stability axis where complex vibrations turn intoreal numbers. By linking the height of Zeta zeros to the rank of mathematical varieties(or we may link the height of central zeros to theprime of mathematical varieties, if we can find central zeros), we finda Prime-Rational Bridge governed by a simple scaling ratio of √2.Our proof demonstrates that as these values grow, they align perfectlywith zeta zeros a 1/2 and central zeros 1 phase shifts. This suggeststhat prime numbers and rational ranks are just two different viewsof the same symmetrical manifold, providing a unified geometricsolution to both conjectures
Category: General Mathematics

[1] ai.viXra.org:2605.0020 [pdf] submitted on 2026-05-11 19:28:52

The Collapse of Recursive Logic: A Critique of Actual Infinity via the Fixed-Point Singularity of Sequence S

Authors: Kesan Yi
Comments: 2 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

This paper presents a logical critique of the concept of Actual Infinity by analyzing a specific recursive sequence S. By examining the algebraic properties of the limit as a potential member of the set, we demonstrate that the transition from a generative process to a "completed" state results in a fixed-point singularity. This singularity destroys the bidirectional logic of succession and traceability, suggesting that the notion of a completed infinite set is structurally incompatible with the recursive definitions that govern countable sets.
Category: General Mathematics