The fundamental instability of the global world, associated with the technological limitation as a marker of globalization, precedes the crisis. Mankind is currently facing a succession of crises, in which the Covid-19 pandemic being only an outward representation, a media "face". The crisis of globalization can follow two paths: First, a transformation through chaos, a "savannah world", "grey zones" where no laws except the law of force apply. Second, transformation through the creation of macro-regions. Both options imply a high risk of military conflicts throughout the space of globalization and, above all, in Southeast Asia, which will lead to an arc of instability affecting Russian interests. The key area determining the behavior of the arc of instability is the Caspian Sea region. At present, of the four possible versions of the post-global world (as of 2015: infrastructure colonialism, cosmocolonialism, ecological capitalism, macro-regionalization) two remain. Ecological capitalism has been transformed into inclusive capitalism, and macro-regionalisation turned out to be the only alternative to the initiative of K. Schwab. Currently, the macro-region is understood in three senses - geopolitical, geographical and administrative. Geographically linked 'blocks', which are the basis of geoplanetary macro-regions, can be called meso-regions. The article considers six versions of the Caspian Sea mesoregionalization: "Transcaucasia", "Anatolia", SENTO, "Pre-Caspian", "Iranian-speaking Oikumene" and "Pyatimorye". It is stated that only the strategically grounded inertial "Anatolian mesoregion" scenario and the geographically grounded realistic "Pre-Caspian" scenario have a notable probability of implementation. Of these, only the second meets Russia's interests. The military, political and economic alliance between Russia and Iran could become the core of such a region. The Caspian Sea mesoregion is economically and logistically based on the meridional North- South transport corridor. It is shown that this corridor should be connected not only to the latitudinal routes, but also to the ring infrastructure, uniting the Transcaucasus in a single whole. hus, the transition from the necessary conditions for the formation of a mesoregion (geographical connectivity, broadly understood security, common interests) to sufficient conditions is carried out. These sufficient conditions include the transition from geographical connectivity to infrastructural and economic connectivity, the creation of a "ring economy" and a "ring identity". However, in addition to transport and economic connectivity and overall military and political security, the core of a mesoregion should also have a high level of social and socio-ethnic cohesion and a common goal setting, which would allow it to be stable against external cultural and semantic manipulation. In other words, one of the sufficient conditions for the existence of a mesoregion is the unity or, at least, the compatibility of the cultural codes of the ethnic groups comprising the region. The article gives a definition of the cultural code and a sketchy way of its calculation, briefly describes the cultural codes of the Caspian countries and draws a conclusion about their compatibility and the possibility of constructing a common cultural code of the region around the interaction of Russian and Persian/Iranian cultures. Such a cultural code can be transmitted through a geoplanetary educational canon.
Sufficient conditions for compactness of the
∂-Neumann operator on high level forms
