Fibonacci Causal Loop Theory: The Golden Ratio as the Stable Attractor of Necessity Recursion — Framework and Falsifiable Predictions

Fibonacci Causal Loop Theory (FCLT) proposes that physical, biological, and cognitive systems governed by depth-2 necessity recursion S(n) = S(n−1) + S(n−2) are driven toward the golden ratio φ = 1.618… as the unique stable attractor of that recursion; the uniqueness is proved analytically (Ostrogradsky stability, Gram–Schmidt orthogonality, Kolmogorov minimality; Paper 42). The recursion is bounded between a proposed floor at the Planck volume S(0), where the Binet remnant equals 1, and a cosmic depth near S(588), where the remnant φ⁻⁵⁸⁸ ≈ 10⁻¹²³ matches the observed cosmological constant to order of magnitude. The framework is stated under a strict honest-framing protocol (V3.1): δ 0.10 marks falsification.…