White Noise as Pre-Recursive Signal: Testing the Davis Attractor in Unconstrained Systems

The Fibonacci Causal Loop Theory (FCLT) predicts that constrained systems converge toward phi-structured configurations via Binet necessity recursion. This paper asks the inverse question: what is the state of a system before constraint is applied? We hypothesize that white noise — traditionally characterized as maximally random, uncorrelated signal — is not the absence of structure but rather pre-recursive signal: the state of a system at S(0), before the necessity ladder begins. Under progressive constraint (coarse-graining), we predict that power ratios in white noise will show directional drift toward phi. We test this hypothesis using synthetic white noise, a phi-structured control signal, and publicly available Planck 2018 CMB acoustic peak multipole data. Results show: (1) white noise power ratios drift directionally toward phi under progressive constraint (x1: 1.0076 to x64: 1.0514), consistent with FCLT pre-recursive signal hypothesis; (2) CMB acoustic peaks at multipoles 540→0810 and 810→1120 show phi-proximity within 7.3% and 14.5% respectively, suggesting phi-adjacent structure in the universe’s oldest background signal. These preliminary results are consistent with the hypothesis that white noise is not structureless noise but unresolved pre-recursive signal awaiting constraint initiation. Keywords: FCLT, Fibonacci Causal Loop Theory, white noise, phi-convergence, Davis Attractor, golden ratio, CMB, coarse-graining, pre-recursive signal, necessity recursion