How Do Sources of Indeterminacy Compose? Mixed Refined Neutrosophic Numbers, Selectors and the Multiplication Law of Sub-Indeterminacies, with Analyst Choices in AI Safety Ratings

Refined neutrosophic numbers a + Σ b_k I_k attach one sub-indeterminacy to each source of indeterminacy. We study how such sources compose within one estimate. Sources are combined by three operators: additive composition (Minkowski sum), alternative composition (union) and boundary inference. We prove an operator normal form for sums and unions, a masking theorem (additive sources can hide a separation between alternatives but never create one) and a representation theorem: interval-valued sub-indeterminacies represent additive branches, and adding idempotent selectors J, with J² = J as for Smarandache's literal indeterminacy, gives mixed refined numbers that represent every combination of sums and unions exactly. Their arithmetic keeps alternatives apart through sums and products, and Smarandache's multiplication law of sub-indeterminacies acquires two statistical instances: J_β J_γ = 0 for exclusive alternatives, and intersection of regions for the corrections of inclusion–exclusion. We distinguish a common target from different targets and show that alternatives estimated from the same data must be compared in pairs. In the DICES-990 safety ratings of conversational AI, eight analyst specifications give unsafe shares from 5% to 37%; their marginal intervals form one connected region, whereas paired comparisons separate the effect of each analyst decision.