Beyond Scalar Uncertainty: Independent Neutrosophic Evidence Coordinates for Conflict-Aware Retrieval-Augmented Generation

Abstract

Retrieval-augmented generation (RAG) pipelines reduce the quality of retrieved evidence to one number, and common scalar uncertainty summaries conflate evidential distinctions that a three-coordinate representation keeps apart: insufficient, contradictory and explicitly indeterminate evidence. We use the non-normalized neutrosophic triple (T, I, F) as a testable multidimensional evidence representation, with independent channels for support, explicit indeterminacy and opposition, and subject its defining design principle, independent evidence coordinates, to a controlled empirical test. A companion paper proved what the free triple represents and what it does not; here its results become hypotheses that can fail. On a pre-specified battery built on Climate-FEVER with real hedged sentences mined from the claims' Wikipedia articles, hard negatives and collision pairs built by duplicating documents, we compare five representations of the same per-document judgements (independent triple, polar pair, normalized triple, per-document renormalization, scalar) under a common rule family and under a common learned classifier, with two independent evaluators (an LLM in log-probability mode under two framings and an NLI cross-encoder), cluster-level statistics and an equivalence test, and we validate externally on ConfRAG, a benchmark of real conflicting web references. The third coordinate is not well predicted from the polar pair; with the LLM evaluator the independent triple gives the best five-way behaviour (macro-F1 0.48 against 0.38 for the polar pair, 0.36 for the normalized triple and 0.17 for the scalar; Holm-adjusted permutation ) and the gain survives the same-classifier test; normalization deletes the magnitude that signals insufficiency, and a learned reader separates duplicated from thin records only from non-normalized coordinates. The benefit is task-dependent rather than universal: on ConfRAG, which requires only conflict detection, the triple and the polar pair are equivalent within 0.02 and normalized representations detect conflict better; the pre-specified quantitative criteria for indeterminacy and for the collision test are not met, and over-answering under conflict depends on the framing of the evaluator. The scalar over-answers under conflict in 82% to 99% of cases and prompt-only generators in 47% to 70% (both ranges from the conditions where each representation was evaluated); the coordinate-based controller over-answers at 9% and 10% under the two conditions that meet the pre-specified 25% criterion, but at 39% under a framing that does not — the benefit is real but framing-dependent, not a uniformly tight 9–22% band.

https://doi.org/10.5281/zenodo.22304233