A Note on the Intersection of the σ-Lattice and the Sixth Cyclotomic Tower

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.