Dependence-Sensitive Overflow Analysis for Interval-Valued (T, I, N, F) Neutrosophic Evidence

A (T, I, N, F) neutrosophic quadruple records support, pure indeterminacy, neutrality and refutation as four free intensities. When a panel of sources reports point quadruples and each channel is summarised by an interval, the resulting box contains combinations that no source reported, and an index that adds channels of different sources may overflow the unit although every source is consistent. For the range box, the direct overflow of the box bounds the largest per-source overflow from above, and, as the main result, the marginal ranges of any subset of channels identify the largest per-source sum only up to a sharp interval: sum of lower bounds plus the largest width at one end, sum of upper bounds at the other, every value between them being realisable. The classification of a box by its upper corner into six overflow types is proved to be a partition. A closed-form overflow probability, 1/72 per source under a stated generative model, anchors a simulation in which, for twenty independent sources under the scaled model, range boxes flag a direct overflow in 99% of panels while 25% contain an overflowing source. Panel diagnostics and a reference implementation accompany the results.