The current regulatory process allows for the use of models employing realistic assumptions as opposed to conservative bounding approaches, requiring a concerted use of best-estimate modeling and comprehensive estimation of uncertainties, collectively referred to as best-estimate-plus-uncertainty methods. This necessitates access to an integrated and automated procedure for the propagation and understanding of key sources of uncertainties. Focusing on neutronic reactor core simulation, this paper lays the theoretical foundations for an uncertainty characterization framework that is comprehensive, informative, and efficient, implying its ability to propagate all sources of uncertainties and identify key contributors in a computationally efficient manner. This paper represents the overarching objective of our work to propagate multigroup (MG) cross section uncertainties through lattice physics calculations and core-wide simulation. This requires the evaluation of few-group parameters uncertainties in terms of a wide range of local conditions, e.g., burnup, fuel temperature, etc., which results in a very high dimensional uncertainty space. The first strategy employed to compress the few-group uncertainties is the physics-guided coverage mapping (PCM) methodology developed to assess the similarity between the branch and base uncertainties in lattice calculation. To further compress the uncertainty propagated, this paper employs an accuracy-preserving reduced order modeling (ROM) technique relying on the use of range finding algorithms to construct all few-group parameters variations to a very small preset tolerance. In a separate cosubmitted paper, this framework is demonstrated to thermal reactors including both light and heavy water systems using a number of computer codes, including NESTLE-C, SERPENT, SCALE's NEWT, and SAMPLER codes.