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] submitted on 2026-05-12 19:24:03

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

Authors: Ezadiin Redwaan
Comments: 16 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 4D manifold system governed by orthogonal cycles. We demonstrate that the manifolds y = x2n + m and y = z2n + m undergo a 180◦ mirror inversion as they transition from real-space growth to complex-space equilibrium. By analyzing the system in the infinite limit (n → ∞), we identify a "The Unified Anchor Identity" where geometric stability is achieved only when the real scalar anchor 2m matches the complex operator I. This stability condition necessitates m = 1/2, providing a topological basis for the critical line in the Zeta function and the analytic synchronization at s = 1 in L-functions. Our findings suggest that these longstanding conjectures are consequences of the fundamental requirement for symmetry and destructive phase interference within 4D geometric manifolds,we show that the 1/2 critical line is a necessary stability axis where complex vibrations turn into real numbers. By linking theheight of Zeta zeros to the rank of mathematical varieties(or we may link the height of central zeros to the prime of mathematical varieties,if we can find central zeros), we find a Prime-Rational Bridge governed by a simple scaling ratio of √2. Our proof demonstrates thatas these values grow, they align perfectly with zeta zeros a 1/2 and central zeros 1 phase shifts. This suggests that prime numbers andrational ranks are just two different views of the same symmetrical manifold, providing a unified geometric solution 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