Popular and semi-technical commentary increasingly describes generative articial intelli-gence as producing, or disclosing, a form of collective mind shared across its users. Thispaper argues that such framings conate three distinct phenomena functional collectiveintelligence, distributed cognition, and phenomenal collective consciousness and substi-tute rhetorical momentum for conceptual precision. We rst separate these notions. We thenconstruct a formal framework that isolates what is actually occurring when large popula-tions are mediated by a shared generative model, identifying three disjoint recursion regimes(training recursion, stylistic recursion, and cognitive recursion) whose evidence bases andintervention points dier sharply. Using epistemic logic in the HalpernMoses tradition,together with Aumann's agreement theorem, we show that AI-mediated populations exhibitan ersatz form of common knowledge that we term pseudo-common belief : the operatorC is approximated by Ek for bounded k via a shared channel, producing the coordina-tion consequences of common knowledge without its epistemic foundations. We derive adistribution-shift upper bound on the homogenization of public expression under mixedhumanmodel corpora, empirically calibrated via simulation with sub-1% identiability ofthe imitation-rate parameter. We then cast individual authorship as a signaling game andderive an explicit pooling threshold β∗(γ, κ) = (Δc−κ)/(Δc−κ+γ2ΔUR) above which allD1-stable perfect Bayesian equilibria pool, establishing a paradox of uency: better medi-ators force pooling at lower mediation intensities. We close with an impossibility theoremshowing that no intervention preserving the receiver's information set can restore separatingequilibria in the pooling regime; epistemic provenance infrastructure is therefore the struc-turally unique class of admissible solutions. We oer testable predictions and outline thecivic-design problem.