Strategic replicators combine evaluated choice and reproductive transmission. An agent chooses among alternatives; the consequences of those choices influence continuation or reproduction; and successors receive organization that shapes later choices. Artificial intelligence makes this combination salient when agents have authority to create, configure, or retire software instances. This paper organizes the general logic around three principles: situated choice, reproductive transmission, and institution-mediated coupling. The principles are constitutive rather than predictions of growth or improvement. A common representation distinguishes carriers, inherited records, decision owners, and the mechanisms that allocate consequences. Actual parent-descendant attribution yields a selection-transmission identity. Separate compatibility results characterize when utility-maximizing choices also maximize a reproductive criterion. Gode and Sunder's zero-intelligence traders reveal the role of institutions: enforced properties can hold across different decision procedures, while aggregate efficiency alone determines neither individual gains nor descent. A worked market-rent-entry model connects institutional profits to actual offspring, with its occurrence-level ancestry bridge checked in Lean. A direct-deployment example then shows evaluated preferences undergoing selection without presupposing that every chooser values reproduction. Formal appendices develop games with endogenous players, deployment-induced tipping, endogenous electorates, and the production of institutions, with models, proofs, and examples. The paper and its supporting formal artifacts are a prototype kernel with a generative function: an instrument for constructing models of strategic replication. The results are formal; their application to deployed populations and their empirical implications remain to be tested.

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