Objectivity Without Observers: A Viability–Objectivity Separation Theorem (VOST)

Viability–Objectivity Separation Theorem (VOST): a measurement-independent impossibility result showing that when fragment-scale Holevo information lies below the Fano-critical threshold for bounded-error inference, no fragment-limited observer can exist at that access scale — even when macroscopic encodability of a pointer variable is present. The theorem formalizes a logically prior constraint missing from quantum Darwinism, spectrum broadcast structure, and encoding-transition frameworks: not whether many observers can agree, but whether any fragment-limited observer can exist at all. An exactly solvable controlled-imprinting collision model provides closed-form viability thresholds, objectivity capacity scaling, and explicit forbidden regions in parameter space. Robustness to mixed ancillas, correlations, and non-Markovianity is analyzed, with multi-outcome generalizations and breakdown regimes explicitly identified.