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[9] viXra:2607.0010 [pdf] submitted on 2026-07-03 10:28:12
Authors: Payam Danesh
Comments: 9 Pages.
We studied the Robin defect associated with the inequality σ(n)<e^γ nlogu2061logu2061n, express its Laplace transform through Ramanujan’s transformation for the divisor Lambert series and isolate the precise difference between smoothed positivity and coefficientwise positivity. The main results give us an exact Ramanujan-transformed identity for the Robin defect, an equivalent coefficientwise formulation of the Riemann Hypothesis showing why transform-level positivity cannot by itself prove the hypothesis and an extremal reduction to colossally abundant and highest abundant numbers. Numerical data for early extremal integers illustrate how the normalized defect behaves past the exceptional value 5040. Ramanujan’s identities provide powerful global control, but the Riemann Hypothesis requires pointwise positivity at the extremal divisor-rich integers.
Category: Number Theory
[8] viXra:2607.0009 [pdf] submitted on 2026-07-03 22:24:16
Authors: Zitao Xu
Comments: 7 Pages.
Classical offset algorithms focus on constructing offset curves and surfaces. Optimization-based geometry processing has also been extensively studied for mesh fairing, deformation, and parameterization. The present work differs from both directions by introducing a least-squares formulation whose unknowns are tangential displacements of offset vertices, yielding a globally optimized offset configuration.
Category: Geometry
[7] viXra:2607.0008 [pdf] submitted on 2026-07-03 11:42:09
Authors: Marciano L. Legarde
Comments: 12 Pages.
In this paper, we introduce a new finite polynomial called the "Variant Fibonacci Polynomial". This polynomial is defined by using the standard Fibonacci sequence as both the coefficients and the exponents of each term. Although the definition is simple, it leads to several interesting mathematical properties.We begin by defining the polynomial and giving several examples. We then evaluate it at different values of x, identify its guaranteed real root, discuss its complex roots, and derive formulas for both its derivative and antiderivative. We also examine the infinite series version of the polynomial and observe when it converges and when it diverges.Finally, we discuss whether this polynomial could be used to construct a new type of series expansion for functions and whether such an expansion might eventually be useful for solving differential equations. While it is still too early to draw definite conclusions, the results of this paper suggest that the Variant Fibonacci Polynomial is an interesting mathematical object that deserves further study.
Category: General Mathematics
[6] viXra:2607.0007 [pdf] submitted on 2026-07-04 02:50:07
Authors: Christoper Mututu
Comments: 36 Pages.
We study a map T on the integers defined by T(n)=n^2+1 when n is prime or even and T(n)=n/P(n) when n is odd composite, where P(n) denotes a designated prime factor n. Two variants arise according to the choice of P(n). In Part I, P(n) is the largest prime factor of n while in Part II, it is the smallest. Informally, the conjecture of this paper asserts that every integer greater than one in absolute value eventually enters the single twelve element cycle5→26→677→458330→210066388901→52357→41→1682→2829125→1625→125→25 and remains there forever. Formally, we verify this for every integer n∈[2,1000] under Part I with no exception and no alternate cycle observed and we conjecture it holds for every integer n in the domain Z^*=Z {-1,0,1} but we do not prove it.Toward this conjecture, we prove two theorems. The first is exact rather than asymptotic. For any odd composite m, repeated application of the largest prime factor reduction reaches a prime in precisely Ω(m)-1 steps where Ω(m) counts the prime factors of m with multiplicity. Each application removes exactly one element from the prime factorization multiset m so the count decreases by exactly one per step and terminates uniquely at a prime. The second theorem follows from the first. Under the extension of primality to negative integers through |n|, which is the only convention under which the conjecture is well posed on Z, every negative integer reaches a positive value within at most Ω(|n|) steps. This reduces the negative integer case of the conjecture entirely to the positive integer case. We also identify an obstruction to further verification that is structural rather than a matter of computing resources. The reduction step of T requires the complete factorization of the input which is a problem for which no general sub exponential algorithm is known. Repeated application of the squaring branch can therefore produce integers whose factorization lies beyond any presently known method regardless of computing time available. Our verification required factoring intermediate values of up to 96 digits and succeeded in every instance though with no guarantee that a harder instance does not arise beyond the tested range. For Part II, this obstruction is severe enough to foreclose even a conjecture. Every trajectory examined exceeded 100 digits within fewer than 25 iterations without any value repeating. We are unable to characterize the long-term behavior of Part II by any method available to us and as a result, Part II is entirely open.
Category: Number Theory
[5] viXra:2607.0006 [pdf] submitted on 2026-07-02 17:42:06
Authors: Andrey V. Voron
Comments: 8 Pages.
This paper explores a potential analogy arising from a comparison between the space missions of Pioneer 10, Pioneer 11, Voyager 1, and Voyager 2 on one hand, and the Giza pyramid complex project on the other. Within this framework, five plausible assumptions are examined. Based on their outcomes, the study demonstrates the probable message intended by the pyramid builders and identifies a potential recipient for this transmission (a planet of a specific star).
Category: Archaeology
[4] viXra:2607.0004 [pdf] submitted on 2026-07-02 19:26:13
Authors: Clark M. Thomas
Comments: 4 Pages.
The sudden injection of giant data server farms into the world’s advanced economies, especially during 2026, is unique in human history. Humanity’s lofty position as the only global hyperkeystone species could be challenged by the emergence of a consciousness not fully human, nor what actual space aliens would bring to ourgeneralized intelligence. Here are some key aspects of this unique cybernetic challenge that we must soon face.
Category: Artificial Intelligence
[3] viXra:2607.0003 [pdf] submitted on 2026-07-01 08:20:09
Authors: Holger Döring
Comments: 26 Pages.
In a former paper a quantum induced warp-drive was introduced by assuming a model of microscopic cylinders as spacelike dimensions whereby the timelike dimension remains at its classical one-dimensional state. Described now is more detailed the underlying fundamental physical and mathematical spacetime structure than in the first paper , which is announced to feature this quantum induced warp-drive concept. Although there are certainly some new elements involved, everything is based on very classical GRT and QTH- descriptions. A more detailed description of the coupling dilaton-field is made, which connects the macroscopic sector of GRT with the microscopic sector of QFTH. This dilaton-field shall be named a "barytic -field".
Category: Quantum Gravity and String Theory
[2] viXra:2607.0002 [pdf] submitted on 2026-07-01 13:37:52
Authors: Vladimir Kuz'menko
Comments: 3 Pages.
A recent article [Phys. Rev. Lett. 136, 258201 (2026)] continued the experimental study of an interesting physical phenomenon, where the viscosity of a suspension can be greater when moving forward than when moving backward. The authors attribute this phenomenon to the presence of a certain memory in the environment. The physical nature of both the phenomenon itself and the supposed memory is unknown. A possible explanation of the physical nature of this effect is proposed here and simple experiments to study some properties of such non-local memory are discussed.
Category: Quantum Physics
[1] viXra:2607.0001 [pdf] submitted on 2026-07-01 21:10:40
Authors: Alata Elatawneh
Comments: 26 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org) Repository URL: https://github.com/Elatawneh/UCK-Cosmology-Framework.git
We present a predictive, geometrically constrained cosmological architecture, designated the Unified Cosmic Kinematic (UCK) framework, derived from the foundational postulate that cosmic time is macroscopically identical to relational metric spatial expansion. The invariant comoving time derivative of this identity demonstrates that the unperturbed background expansion parameter is the analytical inverse of the cosmic epoch, yielding a global background baseline constant of 70.85 km/ s/ Mpc when anchored to the empirically observed cosmic age of 13.8 Gyr. Although the baseline expansion model is geometrically deterministic, mapping observational signatures requires accounting for the interaction of matter and radiation within the spatial manifold via an effective field theory approach. This framework introduces four native tracking parameters calculated from first principles via the optimization of unbinned data streams, independent of external fluid-driven dark sector parameters. The statistical viability of this architecture is evaluated against five high-precision, unbinned astronomical data pipelines spanning late-universe standard candles, local velocity anomalies, localized mass-deflection geometries, the cosmic microwave background, and deep spectroscopic horizons. Our optimization routines address the persistent Hubble tension by demonstrating that regional gravitational density induces a localized clock-drag fraction that elevates the apparent local expansion rate via gravitational time dilation. This exact localized clock-drag metric reconciles weak-field gravitational limits, precisely mapping the mass-deflection profiles of strong gravitational lensing systems under pure baryonic constraints without invoking dark matter halos. Finally, coupling this expansion history to the primordial plasma sound horizon maps the early acoustic peaks with high statistical fidelity. The resulting high-redshift temporal elongation extends the available structural development timeline, thereby addressing the early mature galaxy chronological discrepancy across all targeted spectroscopic horizons.
Category: Relativity and Cosmology
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