Division Algebra Tower — Paper + Author's Note

The complete package for The Division Algebra Tower (Paper 4 of 30), by Daniel Toupin.

Includes:

• The research paper: holographic_chain_dtoupin_v2.pdf
• Author's note PDF: a personal account of what drove the paper, what it finds, and how it fits within the project

The paper argues that the four normed division algebras over the reals are special precisely because they are the only stages of the Cayley-Dickson tower at which the shadow transform remains unitary. The sedenions fail as division algebras for the same algebraic reason that a Riemann zero off the critical line would fail: both represent the breakdown of the shadow pairing that the Haar measure forces on well-defined spectral theories.

Instant download, delivered automatically.