Constraint-Mediated Dynamics in S&P~500 Markets: CPA+C Universality Signatures and Exponent Deviation

This study examines structural signatures associated with Continuous Present Actualization under Constraint (CPA+C) in S&P 500 market data (1993–2023). Four diagnostics were evaluated: critical slowing near pivots, scale structure in constraint statistics, response–constraint scaling behavior, and dispersion ordering under elevated constraint. Three structural signatures: critical slowing, swarm-like ordering (ρ = −0.952), and partial scale structure, are observed consistently across the sample. In contrast to non-reflexive physical domains previously examined under CPA+C, the response–constraint mapping in markets does not reduce to a single β ≈ 3/4 exponent. Instead, instantaneous constraint level is negatively associated with near-term return magnitude, while cumulative constraint traversal (constraint journey) across full price waves positively predicts wave amplitude (r = 0.283, p < 10⁻⁵), surviving comparison against a GARCH(1,1) null model (z = 3.6σ; 1,000 simulations). These findings suggest that structural constraint signatures may persist in reflexive adaptive systems even when feedback modifies observable scaling exponents. Financial markets are therefore examined here as a boundary case for constraint-mediated dynamics under internal feedback. This work is presented as an exploratory cross-domain analysis extending CPA+C diagnostics into financial systems.