Hidden-sector elimination in a composite system can leave an induced correction on aretained channel; the central question of this note is when that correction should be readas a genuine mass/gap term rather than as a generic effective correction. We consider acomposite system observed through a channel that does not separately resolve all internaldegrees of freedom entering the full dynamics. Requiring a closed observable law on thatchannel forces explicit hidden variables to be eliminated and returns their influence througha reduced operator.For a retained/hidden block decomposition with solvable hidden sector, exact closureyields a Schur-type reduced operator. The paper isolates a restricted regime in which thatoperator admits a mass/gap reading: its principal symbol is preserved, while the inducedorder-zero residue is a positive scalar. This separates three operator-level outcomes ofreduction—propagation-class change, generic lower-order effective correction, and genuinemass/gap readout—and gives a checkable sufficient condition for the third.The claim is intentionally modest. The paper does not replace microscopic theories ofmass generation, and it does not assert that every physical mass arises in this way. Itscontribution is not a new elimination formula, but a structural reading criterion for theoutcome of familiar elimination procedures.
Yi (Sat,) studied this question.