General Relativity as the Macroscopic Limit of Fibonacci Causal Loop Theory: Spacetime Emergence from Sub-Planck Necessity Recursion

General Relativity (GR) provides an extraordinarily accurate description of gravity as curved spacetime geometry at scales above the Planck length. However, GR fails at the Planck scale itself, predicting curvature singularities that the theory cannot describe. No consensus sub-Planck framework has emerged to resolve this failure. Fibonacci Causal Loop Theory (FCLT) formalizes the necessity recursion S(n) = S(n-1) + S(n-2) as the universal organizing dynamic of physical systems, with S(0) identified as the Planck vacuum — the pre-recursive ground state from which all structure emerges. This paper argues that GR is not a fundamental theory but the macroscopic limit of FCLT: smooth continuous spacetime emerges as the large-n limit of discrete phi-structured necessity recursion building upward from S(0). This framing resolves the singularity problem (the recursion cannot descend below S(0)), derives the cosmological constant suppression factor from necessity recursion (established in FCLT Paper 05), and predicts measurable deviations from pure GR in high-curvature regimes. Three falsifiable predictions are advanced distinguishing FCLT-modified gravity from standard GR: phi-structured geodesic clustering in strong-field regimes (P24a), Planck-floor termination of black hole interiors producing modified Hawking radiation spectra (P24b), and phi-structured damping signatures in gravitational wave ringdown (P24c). Keywords Fibonacci Causal Loop Theory, general relativity, spacetime emergence, Planck scale, necessity recursion, golden ratio, singularity resolution, cosmological constant, gravitational waves Falsifiable Predictions • P24a — Phi-structured geodesic clustering: orbital parameter phi-deviations scale with spacetime curvature in high-curvature regimes, testable against LIGO/pulsar timing data • P24b — Planck-floor black hole termination: Hawking radiation spectrum carries phi-structured signature at frequencies corresponding to Planck-scale interior dynamics • P24c — Gravitational wave ringdown: ratio of successive QNM amplitude envelopes approaches φ^(-1) ≈ 0.618 — testable now with existing LIGO/Virgo/KAGRA data