Fibonacci Recursion as the Unique Stable Constraint Architecture: A Derivation of φ from Ostrogradsky Stability and Hierarchical Lossy Compression

The Fibonacci Constraint Limit Theory (FCLT) series has documented φ-structured scaling across nuclear physics, cosmology, neuroscience, and biology. Until now, these results have been empirical: the pattern was observed but not derived. This paper supplies the missing mechanism. We show that the golden ratio φ ≈ 1.618 is not a free parameter of nature, but the unique and necessary fixed-point attractor of the only stable non-trivial recursive constraint architecture permitted by the action principle. The argument proceeds in five steps: (1) The Ostrogradsky instability theorem establishes that Lagrangians with depth ≥ 3 produce ghost degrees of freedom with unbounded negative energy; (2) depth-1 (Markovian)…