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 < 0.05 marks a prediction as surviving — not yet falsified, never confirmed — and δ > 0.10 marks falsification. Of 133 pre-registered, falsifiable predictions across 107 papers, 40 currently survive, three are genuine zero-free-parameter derivations (k(D)/P55, N = 3/P94, k(D) at D = 2/P100), and the remainder are falsified, gray-zone, or technology-gap. φ-deviation gradients consistent with the framework are reported in four domains — cancer histology, river-network architecture, galaxy morphology, and cosmic redshift; a previously claimed neural-complexity gradient, retested with a non-circular metric, is falsified and withdrawn. Independent parallel work by other groups is noted as corroborating context, not confirmation. The honest verdict is explicit: approximately zero clean empirical confirmations and three genuine derivations. The contribution is a single falsifiable recursion principle and a fully pre-registered prediction corpus, not a claim of established truth.