Sign-Symmetric (3,1) Algebra: A Framework for Universal Integer Factorization

We present a new 4D algebra that introduces sign symmetry into classical identities and extends Gaussian integers to allow universal integer factorization, even for primes of the form 4n+3. This framework covers all integers, whether prime or composite, through trivial factorizations, algebraic rotations, and non-trivial factorizations. We then focus on sign-irreducible 4n+1 primes, which open a side door into Landau’s 4th Problem via a conjectured prime-counting function. To conclude, we build a minimal Clifford algebra that captures the geometric structure underlying these factorizations. 00:04 The Motivation for a New 4D Non-Associative Algebra 04:46 Universal Integer Factorization 16:31 Table of Integer Factorizations (1-100) 17:03 A Side Door into Landau's 4th Problem 28:38 An Original Clifford Algebra Cl(1,5) Hosting SS(3,1) 35:06 TL;DR my blog: https://pablonumbertheory.blogspot.com/ # Pablo Pintabona