Note_Fibonacci_Triples_Classification

We present a Diophantine investigation concerning the classification of integer triples subject to simultaneous divisibility conditions, a Pythagorean constraint, and a quadratic growth bound. Our analysis reduces an infinite classification problem to a finite set of exceptional cases and identifies infinite families governed by the Fibonacci sequence. The results are supported by two independent arithmetic verification procedures implemented in Python and C++. The complete manuscript, including the equations, mathematical proofs, and detailed results, is preserved in this dated, restricted-access version pending independent scientific evaluation.