So on permissions: is there a primary owner that configures write-permitted collaborators per (fine-grained) graph chunk? And I'd guess a kinda separate read permissions for more people to see bigger chunks of your graph?
There's a 'grand vision' flavour of answer and an implementation-specific one. To start with the latter, let me first say that m-ld chunks the world into 'domains', which are generally expected to be file-size things, which are cloned in-full. Each domain is its own graph, and the convergence guarantee covers the contents of that domain.
Read permissions in practice (so far) have been nicely covered by just controlling who has access to the messaging channel for that domain. For example, using MQTT, the channel is a Topic, which can be access controlled.
The baseline position for write permissions is, everyone has them – the component is intended for multi-editor writing. But that's not going to be satisfactory for every use-case. I did a whole research project on decentralised fine-grained write permissions. The long answer is here. In short, the domain starts with the first "genesis" clone, which establishes the security model and its local user, identified by public key, as the authority over everything. After that, permissions can change by an 'agreement', which is a data update that disallows any concurrent update and so can be used to establish a kind of chain of custody which can be independently verified at each node. At the moment this model is tricky to set up and not well enough characterised, so for now, fine-grained write permissions are definitely in the realm of the experimental.
To return to the grand vision: we're pretty sure we can make domains less physically-bound, and be able to have big domains which are cloned only in part, as required. That would first require some refinements to the 'agreements' model. But also, these ideas go hand-in-hand with having untrusted nodes, which is the tricky bug-bear of any attempt to decentralise authority. (Sorry about the hand-waving. More thoughts on this are in the long answer linked above, in the 'trust' section at the end.)