You can learn mathematics and Python (programming) simultaneously on Colab.Curiosity about mathmatics, the foundation of everything the AI era. You can download the book-linked learning files for use with Colab from here. Download file: ( Math and Python Stage 1. Chapter1~13 ) CONTENTSChapter 1: Getting started with Python 8Introduction 9Before we start ~ Using Google Colab ~ 101.1… Read More »
English Summary | Number-Theoretic Holography Toy Model Executive Summary This report evaluates a hybrid link combining Dirichlet characters with a discrete Fourier transform (DFT) applied to a prime-ledger signal. The originally observed -28σ to -42σ “arithmetic signal” does not survive as evidence of a non-trivial number-theoretic signature. After improved null models were introduced, the signal was decomposed into… Read More »
Four Main Findings Exact Equivalence of Quadratic Twists: Quadratic-twist pairs of CM elliptic curveswith the same CM type are majorization-equivalent, meaning their descending sortedspectra are identical to numerical precision. Furthermore, the majorization frameworkcleanly separates these from cubic twists. Incomparability of Distinct CM Types: All 24 pairs of CM curves with distinct CMtypes (such as Z[i], Z[ω], and D=-7)… Read More »
Four Main Findings Exact Equivalence of Quadratic Twists: Quadratic-twist pairs of CM elliptic curveswith the same CM type are majorization-equivalent, meaning their descending sortedspectra are identical to numerical precision. Furthermore, the majorization frameworkcleanly separates these from cubic twists. Incomparability of Distinct CM Types: All 24 pairs of CM curves with distinct CMtypes (such as Z[i], Z[ω], and D=-7)… Read More »
This report details Step 4 of the Number-Theoretic Holography Toy-Model Series. It builds upon the statistical findings of Step 3 by investigating whether probability spectra derived from elliptic curves and Dirichlet L-values are related structurally via finite channels, specifically through doubly stochastic transformations (majorization). Four Main Findings Exact Equivalence of Quadratic Twists: Quadratic-twist pairs of CM elliptic curveswith… Read More »
Three Main Findings Interpretation and Limitations Future Outlook by CHIC INSTITUTE
Inter-universal Teichmüller Theory (IUT) is a mathematical theory developed by Professor Shinichi Mochizuki of Kyoto University, made public around 2012. The Goal The main objective is to prove the ABC conjecture, a long-standing open problem in number theory. Roughly speaking, the ABC conjecture says that there’s a deep constraint between two seemingly unrelated operations: addition (a + b = c) and multiplication (prime factorization). What… Read More »
In short, the ABC Conjecture states that “in a simple addition equation ($a + b = c$), it is extremely rare for the numbers involved to be made by multiplying the same small prime numbers over and over again.” Proposed in 1985, it has long been considered one of the ultimate master-puzzles in modern mathematics, exploring the profound relationship between addition… Read More »
The clash over “Corollary 3.12” is not a simple disagreement over a calculation error. Instead, it is a profound conflict between two fundamentally different mathematical visions regarding what the true identity of a “number” actually is. Here is a deeper look into the core of this dispute. 1. The Critics’ Stance (Prof. Scholze et al.): “A Logical Collapse”… Read More »
simple algorithm The Euclidean algorithm is a classical method for computing the greatest common divisor (GCD) of two non‑negative integers.The key idea is based on the following property: For any integers a and b (with a ≥ b), the GCD of a and b is the same as the GCD of b and a mod b. Because the remainder becomes strictly smaller each step, the process terminates after only a few iterations, even… Read More »