A Note on the Intersection of the σ-Lattice and the Sixth Cyclotomic Tower
Year: 2026
Type: preprint
Abstract: This note establishes a specific arithmetic structure built from the first four primes {2,3,5,7} and the lattice constant σ=6. We define the σ-lattice (integers of the form P=6q−1) and the Φ₆-tower (values of the sixth cyclotomic polynomial at the epoch primes). We prove that these two independently defined structures intersect at a unique prime r=43 (Theorem 1), that this forces ord₄₃(7)=6=σ (Corollary 1), and that from this single fact a cooperative prime chain {13,17,31,43,79} is derived without additional parameters (Theorem 2). Two cooperative closure results follow: the matter quartet product is 1 mod 43 (Theorem 3), and a secondary prime satisfies q≡−1 mod 43 (Theorem 4). All results are elementary and self-contained. This note is arithmetic groundwork for the Entropy Driven Expansion Model (EDEM); no physical claims are made here.
Author: Watson, Jeff
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162681780
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