FCLT Minimal Application Protocol: How to Test Any System for Phi-Structured Scaling
Abstract
Fibonacci Causal Loop Theory (FCLT) predicts that stable hierarchical recursive constraint architectures (SHRCAs) exhibit phi-structured scaling: consecutive ratios between hierarchical levels converge toward φ ≈ 1.618. This paper provides the minimal operational protocol for testing any candidate system against this prediction. No prior knowledge of FCLT is required. The protocol specifies: (1) three qualification criteria for SHRCA membership; (2) a pre-specification rule for defining the measurable quantity S(n); (3) the phi-deviation formula δ(n) = |S(n)/S(n−1) − φ|; (4) a shuffle null model; and (5) a pass/fail threshold of z ≥ 2.0 and δ_mean < 0.10. A reporting template is provided. A pass result identifies a candidate SHRCA warranting further investigation; a fail result is an equally informative null finding. This protocol supersedes the measurement framework in Paper 18 (DOI: 10.5281/zenodo.19154098) as the canonical FCLT application standard. Keywords: phi-deviation | golden ratio | measurement protocol | FCLT | hierarchical systems | falsification | SHRCA | delta metric | recursion
Fields of Study & Subjects
Formal Methods in Verification
Logic
programming
and type systems
Constraint Satisfaction and Optimization
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 16 April 2026
- Document type
- Preprint