From quadratic and trigonometricfunctions to vectors and differentiation… Deepen Math with Python — Foundations“Curiosity about mathematics,the foundation of everything in the AI era.” Learn Math & Python Together on Colab!Free Downloadable Notebook file!FilesStart Instantly in Your Browser—No Setup! Download File : MP_Stage2_Colab.zip (English) Download File : MP_Stage2_Colab_Ja.zip (Japanese) Table of contentsChapter 1　Getting Started — Toward Mathematical Exploration1.1　How to… Read More »

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 & Python Stage 1. Chapter1~13 ) Download file: Japanese（日本語）ver. ( 数学 & Python Stage1. 1章～13章 ) CONTENTSChapter 1: Getting started with Python… 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 »