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Anonymous at Wed, 6 Mar 2024 12:12:13 UTC No. 16059774

post science and math related PDF files (articles, books, etc.)

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El Arcón at Wed, 6 Mar 2024 13:15:42 UTC No. 16059825

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El Arcón at Wed, 6 Mar 2024 13:16:18 UTC No. 16059827

Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
>https://vixra.org/abs/2111.0072
>http://gg762.net/d0cs/papers/Fractional_Distance_v8-20230808.pdf
Recent analysis has uncovered a broad swath of rarely considered real numbers called real numbers in the neighborhood of infinity. Here we extend the catalog of the rudimentary analytical properties of all real numbers by defining a set of fractional distance functions on the real number line and studying their behavior. The main results of are (1) to prove with modest axioms that some real numbers are greater than any natural number, (2) to develop a technique for taking a limit at infinity via the ordinary Cauchy definition reliant on the classical epsilon-delta formalism, and (3) to demonstrate an infinite number of non-trivial zeros of the Riemann zeta function in the neighborhood of infinity. We define numbers in the neighborhood of infinity as Cartesian products of Cauchy equivalence classes of rationals. We axiomatize the arithmetic of such numbers, prove all the operations are well-defined, and then make comparisons to the similar axioms of a complete ordered field. After developing the many underlying foundations, we present a basis for a topology.

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El Arcón at Wed, 6 Mar 2024 13:17:25 UTC No. 16059831

Sixty-Six Theses: Next Steps and the Way Forward in the Modified Cosmological Model
>https://vixra.org/abs/2206.0152
>http://gg762.net/d0cs/papers/Sixty-Six_Theses__v4-20230726.pdf
The purpose is to review and lay out a plan for future inquiry pertaining to the modified cosmological model (MCM) and its overarching research program. The material is modularized as a catalog of open questions that seem likely to support productive research work. The main focus is quantum theory, but the material spans a breadth of physics and mathematics. Cosmology is heavily weighted, and some Millennium Prize problems are included. A comprehensive introduction contains a survey of falsifiable MCM predictions and associated experimental results. Listed problems include original ideas deserving further study as well as investigations of others' work when it may be germane. A longstanding and important conceptual hurdle in the approach to MCM quantum gravity is resolved with a framework for quantum cosmology time arrow eigenstates. A new elliptic curve application is presented. With several exceptions, the presentation is high-level and qualitative. Formal analyses are mostly relegated to the future work which is the topic of this book. Sufficient technical context is given that third parties might independently undertake the suggested work units.