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[3] viXra:2606.0003 [pdf] submitted on 2026-06-01 20:52:50

From Ramanujan to Riemann Hypothesis

Authors: Payam Danesh, Raoul Bianchetti
Comments: 16 Pages.

In this work we offer a careful framework for approaching the critical-line problem associated with the Riemann zeta function. At its heart is a long-standing divide in the subject. On one side are analytic approaches, which study the completed zeta function through its reflection symmetry. On the other side are arithmetic approaches, where related criteria often appear through extreme behavior in divisor functions. The purpose of this paper is not to claim a proof of the Riemann Hypothesis, but to place these two perspectives into a clearer and more usable relationship. The argument begins with reflected analytic data for the completed zeta function. It shows that such data can be described through an odd analytic perturbation, giving a more organized way to understand the analytic side of the problem. This also resolves a common point of confusion: the full complex defect is not required to vanish on the critical line. What matters is more subtle. Under a natural real-symmetry condition, the real part of the defect vanishes on the critical line, and this is the feature that becomes useful for the bridge argument. The arithmetic side is built around Ramanujan’s logarithmic divisor profile. The paper establishes the existence and positivity of the relevant extreme scale in the range needed for the proposed connection. These analytic and arithmetic pieces are then brought together through a real bridge functional, made up of a main sign term and a correction term. The main outcome is a conditional criterion for the critical line. If the bridge functional is zero-adapted at the nontrivial zeros, if the real analytic defect satisfies the required one-sided sign condition, and if the correction term remains strictly smaller than the main term, then every nontrivial zero must lie on the critical line. The contribution of this work is therefore structural rather than conclusive. It does not present the Riemann Hypothesis as solved. Instead, it separates what is already established from what still needs to be proved. The key sign law, the domination estimate, and the zero-adaptation identity remain open requirements for any future application of the framework. Its practical value is that it gives researchers a precise checklist for testing whether a proposed analytic or arithmetic strategy can genuinely support a critical-line argument.
Category: Number Theory

[2] viXra:2606.0002 [pdf] submitted on 2026-06-01 20:50:54

Big Gravity Remains Elusive

Authors: Clark M. Thomas
Comments: 5 Pages.

Big Gravity’s (G) Newtonian constant for the local universe seems to be something that eludes astrophysicists seeking better numbersfor the claimed four forces. The latest G data have failed to confront the hermeneutical limits of what their experimental tools measure.We need better multiversal causative precision in 4D dimensions, not weak mathematical correlations. Big Gravity, and Earth’s variablesurface gravities (g), include electromagnetism, along with the properly conceived net push/shadow kinetics. Unifying harmony among all physics dimensions is needed for any elegant multiversal paradigm.
Category: Astrophysics

[1] viXra:2606.0001 [pdf] submitted on 2026-06-01 14:50:19

Motion, Mass, Space and Time: An Emergent Vector Field Framework

Authors: Mangleshwar Thakre
Comments: 41 Pages.

The primary objective of this paper is to investigate the fundamental cause underlying the motion of a massive object. In other words, it seeks to elucidate the nature of momentum and how it originates. To achieve this, a comprehensive literature review on space, time, mass, and motion is presented, offering a novel perspective on these foundational concepts. The mathematical framework is constructed using the core principles and equations of classical mechanics and the special theory of relativity, drawing some direct and substantial indirect influences from continuum mechanics. To analyze physical phenomena within a four-dimensional space-time continuum, the Hodge decomposition theorem and tensor decomposition methods are employed. This paper derives a new set of governing equations for the state of motion of a massive object, providing an entirely new interpretation of its dynamics. Ultimately, this work establishes that mass-energy and momentum are manifested forms of the periodic change of a vector field defined to characterize the system's physics. Within this research paper, the Translational Gravitomagnetic Field Tensor is derived using an entirely novel method. Furthermore, the physical mechanism responsible for giving rise to space-time is explicitly detailed, thereby reinforcing the contemporary paradigm in physics that space-time is an emergent property rather than a fundamental entity of nature. Ultimately, the research paper appears to advocate for an absolute background throughout its entire exposition.
Category: Classical Physics