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The possibility that a classical space-time and quantum matter cohabit at thedeepest level, i.e. the possibility of having a fundamental and notphenomenological semiclassical gravity, is often disregarded for lack of a goodcandidate theory. The standard semiclassical theory suffers from fundamentalinconsistencies (e.g.: Schr\"odinger cat sources, faster-than-lightcommunication and violation of the Born rule) which can only be ignored insimple typical situations. We harness the power of spontaneous localizationmodels, historically constructed to solve the measurement problem in quantummechanics, to build a consistent theory of (stochastic) semiclassical gravityin the Newtonian limit. Our model makes quantitative and potentially testablepredictions: we recover the Newtonian pair potential up to a short distancecut-off (hence we predict no 1 particle self-interaction) and uncover anadditional gravitational decoherence term which depends on the specifics of theunderlying spontaneous localization model considered. We hint at a possibleprogram to go past the Newtonian limit, towards a consistent generalrelativistic semiclassical gravity.

Sourcing semiclassical gravity from spontaneously localized quantum matter