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Across the natural and life sciences, images have become a primary measurement modality, yet the dominant analytic paradigm remains semantics-first. Structure is recovered by predicting or enforcing domain-specific labels. This paradigm fails systematically under the conditions that make image-based science most valuable, including open-ended scientific discovery, cross-sensor and cross-site comparability, and long-term monitoring in which domain ontologies and associated label sets drift culturally, institutionally, and ecologically. A deductive inversion is proposed in the form of criteria-first and semantics-later. A unified framework for criteria-first structure discovery is introduced. It separates criterion-defined, semantics-free structure extraction from downstream semantic mapping into domain ontologies or vocabularies and provides a domain-general scaffold for reproducible analysis across image-based sciences. Reproducible science requires that the first analytic layer perform criterion-driven, semantics-free structure discovery, yielding stable partitions, structural fields, or hierarchies defined by explicit optimality criteria rather than local domain ontologies. Semantics is not discarded; it is relocated downstream as an explicit mapping from the discovered structural product to a domain ontology or vocabulary, enabling plural interpretations and explicit crosswalks without rewriting upstream extraction. Grounded in cybernetics, observation-as-distinction, and information theory's separation of information from meaning, the argument is supported by cross-domain evidence showing that criteria-first components recur whenever labels do not scale. Finally, consequences are outlined for validation beyond class accuracy and for treating structural products as FAIR, AI-ready digital objects for long-term monitoring and digital twins.