Cross-agent memory
Cross-agent memory is durable context more than one AI assistant can read and write, held in a store none of them own, so switching tools scatters nothing.
Every major assistant now ships memory of its own, and it is genuinely useful. It is also memory inside a product, so it ends at that product's boundary. Cross-agent memory moves the same idea outside: one store, several clients, reached over a standard interface such as MCP. In practice it means something recorded in one conversation is available in a different assistant that evening, and that a person running Claude for one kind of work and ChatGPT for another is not maintaining two half-records.
Two properties carry the concept. Portability, so the store outlives any client. Concurrency, so several agents can be connected at the same time. The second is what forces the governance questions, because once two agents can write to the same record something has to decide which claim stands, what evidence each carries, and who resolves a disagreement. Cross-agent memory without write arbitration is a shared record that degrades as more writers are added to it.
It is worth being precise about who is likely to supply this layer. Assistant vendors have strong reasons to support rich third-party ecosystems, which is why MCP was donated to a foundation, and no reason at all to make their own memory portable. Memory is the mechanism of switching cost: what a product remembers about you is what makes leaving expensive. Portable memory is therefore, by definition, the feature that makes a model replaceable. That is a permanent structural position rather than a gap somebody is about to close, and it is why the layer is built by parties with no model to protect.
Why it matters
Most people will change their default assistant more than once this decade, and many already run several. Context stored inside whichever one is current carries an expiry date set by a vendor decision. Anything you expect to still want in ten years belongs in a store the assistants read rather than one they own, and the clearest example is people: a model can be swapped in an afternoon, and a decade of relationships cannot be rebuilt at all.