| ai.viXra.org > General Mathematics |
|
 |
| ai.viXra.org > General Mathematics |
|
|
Previous months:
2025 - 2505(2) - 2506(2)
Any replacements are listed farther down
[4] ai.viXra.org:2506.0014 [pdf] submitted on 2025-06-04 00:12:26
Authors: Edrianne Paul B. Casinillo
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
Division by zero is traditionally seen as undefined, causing discontinuities in boththeoretical mathematics and practical computation. The Reserve Arithmetic System(RAS) offers an alternative framework: instead of rendering division by zero undefined,it represents such cases with symbolic values that encapsulate the numerator in aconceptual structure called a reserve. This paper presents a formal framework for RAS,showing that it constitutes a unital commutative semiring-like structure, preserving algebraic properties such as closure, associativity, commutativity, distributivity, and identity. The reserve preserves symbolic information about operations involving zero denominators, enabling traceable, consistent reasoning in symbolic computation and related domains.
Category: General Mathematics
[3] ai.viXra.org:2506.0010 [pdf] submitted on 2025-06-04 00:01:52
Authors: Charles R. Tibedo
Comments: 42 Pages. Solvers Included in PDF for public verification
The Riemann Hypothesis (RH), which posits that all non-trivial zeros of the Riemann zeta function ��(��) lie on the critical line Re(��) = 1/2, stands as the most consequential unsolved problem in pure mathematics. Its resolution would not only deepen our understanding of prime number distribution but also unify disparate domains of mathematics and physics. This work resolves RH through a novel synthesis of septimal-adelic spectral synthesis, hypotrochoidic geometry, and modular stress conservation, anchored by the normalization of the Riemann Siegel framework to cyclic boundary conditions (modulo 1) and validated computationally (��(10−80)). This work provides a proposed formal resolution of the Riemann Hypothesis, validated through axiomatic proofs and computational syntheses. The synthesis of hypotrochoidic geometry, septimal cohomology, and adelic spectral theory establishes a new potential field for exploration in analytic number theory.
Category: General Mathematics
[2] ai.viXra.org:2505.0123 [pdf] submitted on 2025-05-20 17:33:24
Authors: Hamid Javanbakht
Comments: 92 Pages.
This volume introduces temporal cohomology, a new framework in algebraic topology that integrates cohomological structures with internalized temporal dynamics. Rather than treating time as an external parameter, we define a category of sheaves indexed by trace-evolving sites, where homological invariants stabilize under Frobenius-like flows. The core construction involves a tower of arithmetic sites equipped with transition functors encoding temporal descent. Within this enriched setting, we develop fixed-point theories, modal regulators, and trace pairings that generalize classical cohomology and open pathways toward a spectral reformulation of zeta invariants. The formalism unifies temporal logic, topos theory, and motivic descent into a cohesive cohomotopical topology. This volume lays the categorical and spectral foundation for later applications to L-functions, field theories, and the Millennium problems.
Category: General Mathematics
[1] ai.viXra.org:2505.0050 [pdf] submitted on 2025-05-09 21:42:35
Authors: Bryan Clem
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)
I’m very happy to present a new prime number solution that I have discovered with you all. I’ve discovered that our entire number system is completely reactionary and prime numbers are not random. And the proof was lying in how prime number 2 eliminates all even integers. This causes a reactionary effect where 3n removes all odd composites of 3 to infinity. Where N is 3,5,7,9, & 11. And you increase these 5 multiples of prime number 3 by 10 to infinity. This in turn causes prime number 5 to have a reactionary effect that forces the equation 5n. Where n equals 5 & 7. And you increase these 2 multiples by 6 to infinity simultaneously for prime number 5’s exact composites. This causes a reactionary effect that forces all prime numbers past 5 to end in a last digit of 1,3,7, or 9. Next to completely remove all of prime numbers 2,3, & 5’s composites from the number line you lay out the next 8 prime numbers of 7,11,13,17,19,23,29, & 31 out on paper and increase these 8 primes by the amount of 30 apiece to infinity. This naturally filters out all composites of 2,3, & 5 while catching all primes past 5. I have found that each prime number past 5 has 8 recursive prime multiples. One for each row and they are last digit locked to infinity. And each of these 8 prime multiples for all primes are increased by 30 to infinity with no calculating. The 1st of their 8 recursive multiples are always its square. So you multiply 7u20227 =49. Which is the second number down in row 5. (Truncated by ai.viXra,org Admin)
Category: General Mathematics
None