MOSAIC Technical Papers I–IV and a Grothendieckian Side-Note

This Zenodo record collects five related MOSAIC technical manuscripts developing mathematical foundations for the Conservation of Differentiation framework. The collection contains four finite-first technical papers and one Grothendieckian side-note. The technical papers develop a finite mathematical spine for MOSAIC: safe deterministic partitions under permitted-merge and must-merge relations; finite stochastic realization for blur and separation constraints; fixed-cardinality total-variation realization geometry and two-sided max-divergence realization; and decision-risk realization bridges via simulation, reconstruction, sufficient statistics, and information bounds. The side-note transports the safe-quotient sandwich into finite étale descent, showing that global safe quotients correspond to monodromy-invariant safe partitions and that monodromy can obstruct desired local compressions. Files included: Safe Partitions: Approximate Quotients and Stochastic Blur for Conservation of Differentiation. MOSAIC Technical Paper I. Stochastic Realization Theory: Finite Total-Variation Channels for MOSAIC Blur and Separation. MOSAIC Technical Paper II. Realization Geometry for MOSAIC: Fixed-Cardinality TV and Two-Sided Max-Divergence. MOSAIC Technical Paper III. Decision-Risk Realization Bridges: Coupling, Reconstruction, and Information Bounds for MOSAIC Decision Preservation. MOSAIC Technical Paper IV. Safe Quotients and Descent: A Grothendieckian MOSAIC Note. These documents are intended as technical companions to the broader MOSAIC / Conservation of Differentiation framework. They are preliminary independent research manuscripts and should be read as a finite-first mathematical development rather than as a complete theory of all stochastic, institutional, infinite-dimensional, or governance aspects of MOSAIC.