Spherical Number Algebras: An Invariant-First Framework with Quotient Semantics and Symbolic-Numeric Translation
Year: 2026
Type: preprint
Abstract: This work introduces Spherical Number Algebras (SNA) as a foundational invariant-first framework in pure mathematics. Rather than taking numbers, objects, or metric continua as primitive, the theory begins with admissible assembly-events endowed with invariant packages from which observable, symbolic, and numerical descriptions are derived. The paper is divided into three parts: a conceptual architecture of admissibility and invariant primacy; a point-free pre-numeric formal core based on normalization, quotient semantics, and rewriting-theoretic convergence; and a translation layer in which symbolic codings and numeric valuations appear as tertiary projections. The framework thereby establishes a structurally coherent basis for future realizations involving stabilization theory, derived observables, and richer algebraic forms.
Author: Alaei jordehi, Mohammad Reza
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169667343
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