PHI AND THE PRIMON GAS: Convergence Between Fibonacci Causal Loop Theory and Prime Number Organization Near Black Hole Singularities

Recent work in theoretical physics has identified prime number organization near black hole singularities, connecting the Riemann zeta function, primon gas theory, and conformal symmetry at gravitational extremes (Hartnoll & Yang 2025; Hartnoll, Yang & De Clerck 2025; Perlmutter 2025). Independently, the Fibonacci Causal Loop Theory (FCLT) proposes that constrained systems converge toward phi-structured configurations via Binet necessity recursion, with the Davis Attractor at n_rho = 588.2629 reproducing the cosmological constant suppression as phi^{-588.263} = 10^{-123}. This paper identifies three structural convergences between these independently derived frameworks: (1) conformal scaling symmetry near singularities mirrors FCLT necessity recursion across organizational scales; (2) the primon gas partition function — the Riemann zeta function — encodes logarithms of primes in a manner structurally analogous to Binet recursion encoding phi; (3) Gaussian prime organization in 5D gravity connects to FCLT's complex-dimensional extension of the Davis Attractor. These convergences suggest that phi-structured necessity recursion and prime-structured zeta organization may be two mathematical expressions of the same underlying constraint principle operating at gravitational extremes. Keywords: FCLT, Fibonacci Causal Loop Theory, primon gas, Riemann zeta function, prime numbers, black holes, singularities, conformal symmetry, Davis Attractor, phi, golden ratio, quantum gravity, Binet recursion