The Period Valley Bijection - Geometry Encodes Arithmetic
Year: 2025
Type: article
Abstract: We establish a bijection between periods in a symbolic sequence and valleys in its coor-dination surface. The correspondence preserves quantitative structure: valley depth equalsnormalized period depth (d∗/N ), and curvature is determined by depth via K = 3(d∗/N )2. Thebijection respects the divisor lattice: primitive periods correspond to primitive valleys, and theM¨obius function governs the extraction of primitives from harmonics. This unifies the geometric,arithmetic, and topological aspects of the theory.
Author: Taylor [email protected], John
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7108446965
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