Irreducible Uncertainty Classes in Coherence-Constrained Paleoclimate Reconstruction

Coherence-constrained backward reconstruction frameworks substantially reduce the space of admissible historical trajectories by enforcing global consistency across heterogeneous proxy observations. Recent implementations, including the Synthesis & Estimation Architecture (SEA), demonstrate that large classes of historically inconsistent reconstructions can be eliminated without reliance on forward dynamical modeling. However, coherence constraints alone do not guarantee unique historical inference. This paper characterizes the residual uncertainty that persists after coherence-based reconstruction, demonstrating that remaining ambiguity collapses into a finite set of structurally irreducible identifiability classes. These residuals arise from limitations inherent to proxy structure, coupling observability, and temporal resolution, rather than from data scarcity or methodological insufficiency. We formalize six residual uncertainty classes, ground each in well-established paleoclimate case studies, explain why additional data within existing proxy subspaces cannot resolve them, and identify the types of new observables or constraints required for further reduction. This work defines the epistemic boundary between coherent reconstruction and uniquely identifiable history, and outlines how the proposed taxonomy can be operationally applied to ensemble interpretation in coherence-constrained and data-assimilation-adjacent reconstruction frameworks. This paper forms part of a broader series developing the Synthesis & Estimation Architecture (SEA) as a domain-general framework for coherence-constrained reconstruction and observabilitylimited inference.