Constrained Recursive Hypothesis Inference (CRHI) is a generalized framework for structured exploratory reasoning under uncertainty. The framework formalizes anomaly investigation and inverse scientific exploration through recursive mechanism generation, conservation-law filtering, probabilistic ranking, recursive decomposition, and convergence analysis. CRHI emphasizes falsifiability, elimination pathways, and disciplined constraint testing while minimizing confirmation bias and unconstrained speculation. The framework is intentionally domain-agnostic and may be applied to exploratory physics, complex systems analysis, machine-assisted discovery, nonlinear systems, signal interpretation, probabilistic inference, and interdisciplinary scientific reasoning. Rather than functioning as a theory of anomalous phenomena, CRHI is proposed as a methodological architecture for navigating uncertainty while preserving scientific rigor in exploratory scientific domains.