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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 »