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math.NT2026
The Octonionic Rational Wave Numbers: Non-Associative Sequence Algebras, Moufang Loops, and Exceptional Symmetries
Terence R. Smith
We generalize discrete rational wave numbers (arXiv:2609.23233) to the octonionic rational wave numbers over Cayley's octonions . Rather than as…
math.NT2026
Wave Numbers: Discrete Sequence Algebras, Sieve Projectors, and Dynamical Geometry
Terence R. Smith
We establish a comprehensive algebraic, geometric, and physical classification of the wave closure space generated from primitive plane wave sequences on the discrete spatial latti…
math.GM2026
Algebraic Structure and Orthogonality Properties of Rational Polynomial Phase Rings on Discrete Lattices
Terence R. Smith
We formalize the algebraic structure of rational polynomial phase sequences (discrete chirps) over the integer lattice . By constructing a convolution algebra generated…