Irreducible Uncertainty Classes in Coherence-Constrained Paleoclimate Reconstruction

This paper defines a taxonomy of irreducible residual uncertainty in coherence-constrained paleoclimate reconstruction. While coherence-based frameworks substantially reduce the space of admissible historical trajectories by enforcing cross-proxy consistency, they do not guarantee unique historical inference. This work shows that, after coherence filtering, remaining ambiguity collapses into a finite set of structurally irreducible identifiability classes. Six uncertainty classes are formalized and grounded in canonical paleoclimate examples, including forcing attribution ambiguity, coupling strength indeterminacy, intra-interval temporal sequencing uncertainty, threshold localization uncertainty, external shock degeneracy, and trajectory degeneracy. These limits arise from intrinsic properties of proxy observability, coupling inference, and temporal resolution rather than from data scarcity or methodological shortcomings. The taxonomy provides a framework for interpreting coherent reconstruction ensembles without over-claiming causality, distinguishing reducible from irreducible uncertainty, and guiding future proxy development toward observables that target specific identifiability gaps. Although motivated by paleoclimate reconstruction, the framework applies broadly to coherence-constrained and data-assimilation-adjacent inverse problems.