set_site_transient_update_core

See hook in action

See this hook used in plugins:

Select Pluginjetpack.6.2.1jetpack.6.4.2jetpack.6.5jetpack.6.6.1jetpack.6.7jetpack.6.8jetpack.6.8.1jetpack.6.9jetpack.7.0jetpack.7.0.1jetpack.7.1.1jetpack.7.2jetpack.7.2.1jetpack.7.3.0jetpack.7.3.1jetpack.7.4jetpack.7.4.1jetpack.7.5.1jetpack.7.5.3jetpack.7.6jetpack.7.7jetpack.7.7.1jetpack.7.7.2jetpack.7.8jetpack.7.9jetpack.7.9.1jetpack.8.0jetpack.8.1jetpack.8.1.1jetpack.8.2jetpack.8.2.1jetpack.8.2.2jetpack.8.2.3jetpack.8.3jetpack.8.4.1jetpack.8.4.2jetpack.8.5jetpack.8.6jetpack.8.6.1jetpack.8.8jetpack.8.8.1jetpack.8.8.2jetpack.8.9jetpack.8.9.1jetpack.9.0.1jetpack.9.0.2jetpack.9.1jetpack.9.2jetpack.9.2.1jetpack.9.3jetpack.9.3.1jetpack.9.4jetpack.9.5jetpack.9.6jetpack.9.6.1jetpack.9.7jetpack.9.8jetpack.9.8.1jetpack.9.9jetpack.9.9.1jetpack.10.0jetpack.10.1jetpack.10.2jetpack.10.2.1jetpack.10.7jetpack.10.9jetpack.11.0jetpack.11.1jetpack.11.1.2jetpack.11.2jetpack.11.3.1jetpack.11.3.2jetpack.11.4jetpack.11.5.1jetpack.11.6jetpack.11.8jetpack.11.8.4jetpack.11.9jetpack.11.9.1jetpack.12.0jetpack.12.1jetpack.12.1.1jetpack.12.2.1jetpack.12.3jetpack.12.5jetpack.12.6jetpack.12.6.1jetpack.12.7.1jetpack.12.8jetpack.12.8.1jetpack.12.9jetpack.12.9.3jetpack.13.0jetpack.13.1.1jetpack.13.1.3jetpack.13.2jetpack.13.2.1