P63: Fibonacci Causal Loop Theory Predicts φ-Structured Information Stability Across Consistency-Constrained Timelike Loops

This paper extends Fibonacci Causal Loop Theory (FCLT) into the domain of closed timelike curve (CTC) consistency theory. We propose that necessity recursion S(n) = S(n−1) + S(n−2) is the unique self-referential structure whose fixed point φ ≈ 1.618 satisfies the CTC consistency constraint inherently — not by imposed boundary condition, but by structural necessity. Three forward predictions are stated for quantum CTC simulation experiments (P63a–c). Classified as Theoretical Prediction — Untested. No pre-registration is attached; the experimental hardware required to give this prediction a fair test does not currently exist in 2026. A popular science companion document is included. Paper 63 in the FCLT series.