mahir elhisadi

A Proof of the Collatz Conjecture Using an Attractor Set and Exit Points for 7 (mod 8) Numbers

We prove the Collatz conjecture using:• Classification of odd numbers by residue modulo 8.• An attractor set A = {Aj = (4j − 1)/3}.• The observation that every odd number lies at an even distance from both boundaryattractors.• A lexicographic ordering function Φ(n) = (−j, min(x,...

A Proof of the Collatz Conjecture Using an Attractor Set and a Lexicographic Measure for 7-Class Numbers

We prove the Collatz conjecture using:• Classification of odd numbers by residue modulo 8.• An attractor set A = {Aj = (4j − 1)/3}.• The observation that every odd number lies at an even distance from both boundaryattractors.• A lexicographic measure Φ(n) = (−j, min(x, y)) for 7...

Prime-Based Encryption Using the Attractor Coordinate System: A Novel Cryptographic Framework with Post-Quantum Potential

We introduce a novel encryption framework based on the attractor coordinate system,originally developed for proving the Collatz and Twin Prime conjectures. Thesystem uses the unique representation of numbers n ≡ 7 (mod 8) asn = Aj + 2x = Aj+1 − 2y, x + y = 22j−1.This representati...