Tailings, coal-combustion residues, metallurgical residues and treatment precipitates are increasingly considered as secondary sources of critical elements. Early screening, however, is often based on concentration data without first establishing whether the sample represents the bulk material, which phases host the elements, or whether the selected analytical method is fit for the matrix and decision. This critical review synthesizes literature first published before 1 June 2026 on sampling theory, process mineralogy, analytical-method performance and laboratory quality assurance; bibliographic records were checked against Crossref or the issuing body. The evidence shows that sampling and mass-reduction errors can dominate total uncertainty; that X-ray fluorescence, X-ray diffraction and inductively coupled plasma methods provide complementary rather than interchangeable information; and that elemental occurrence, mineralogical host, liberation, technical recoverability and economic viability require different evidence. These findings are assembled into a nine-gate decision architecture linking decision-unit definition, heterogeneity assessment, traceable sample reduction, method qualification, elemental and mineralogical characterization, evidence reconciliation, uncertainty assessment and process-safety readiness. Four outcomes are distinguished: stop, resample, recharacterize, or advance to controlled bench-scale recovery testwork. The decision logic is intended to transfer across feedstock classes, while sampling density, preparation, digestion, calibration, detection capability, mineralogical methods and safety controls remain matrix-specific. The framework has not yet been validated; a validation pathway is proposed.Preprint version submitted to Minerals Engineering (Elsevier) for editorial consideration on 20 October 2026. This version has not been peer reviewed.
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