Pythagorean Angle Lattice: The Governing Parameter \( n = 2a/c-b \) and the Universal Limit \( nθ → 4 \)

We prove that the product of the governing parameter \( n=2a/(c-b) \) and the smaller acute angle \(θ\) of any primitive Pythagorean triple tends to exactly 4 as \( n→∞ \). We study the Pythagorean Angle Lattice \(L\), a countable set of real numbers derived from primitive Pythagorean triples. We introduce the governing parameter \( n = 2a/c-b \) and prove the universal limit \( limn→∞ n·θ = 4 \), where \(θ\) is the smaller acute angle of the triple (in radians). The result holds for any sequence of primitive Pythagorean triples with \( n_k→∞ \). For 1-2-8 triples (where \( n \) is an integer) the lattice recovers the metallic means \( M_n=(θ/4) \). The limit unifies all primitive Pythagorean triples under a single asymptotic law.