Chronic pain affects approximately 1 in 5 adults globally and remains one of the most undertreated conditions in medicine, in part because no objective biomarker exists. Patients — disproportionately women, minorities, and those without visible injury — are routinely disbelieved, undertreated, or denied appropriate care. This paper applies Fibonacci Causal Loop Theory (FCLT) to propose the first phi-deviation-based objective biomarker for chronic pain. FCLT identifies the necessity recursion S(n) = S(n-1) + S(n-2) as the universal driver of organizational structure from the Planck vacuum floor S(0) upward. Paper 02 demonstrated that neural complexity tracks necessity depth with r = 0.9071 across 38 vertebrate species. This paper extends that framework to pain neuroscience, proposing that chronic pain represents a necessity depth disruption — a pathological lock in pain-processing neural networks at an elevated phi-deviation state that does not self-correct. Central sensitization is reframed as necessity recursion dysregulation. Prediction 14 is formally stated: phi-deviation in the anterior cingulate cortex, insula, thalamus, and default mode network will be systematically elevated in chronic pain patients compared to healthy controls, will correlate with pain severity independently of self-report, and will persist during pain-free periods. Testable immediately against the OpenPain Project and Human Connectome Project datasets. Confirmation would provide the first objective, non-self-report biomarker for chronic pain — with immediate implications for diagnosis, disability assessment, and the elimination of systemic bias against pain patients.