What does "part of a space" mean in terms of the space hierarchy?

Link to problem area:

Rooms can additionally claim to be part of a space by populating their own state with a parent event.

-- https://spec.matrix.org/v1.4/client-server-api/#mspaceparent-relationships

Relevant MSC1772

Issue: What is wrong? How can we improve?

Confusion as experienced #synapse-dev (most of this is cribbed from @reivilibre's comments),

It's not clear what "part of a space" means here.

• Are rooms, with m.space.parent → some space, meant to show up in the space hierarchy for that space?
• Or is that only for rooms which are a m.space.child of the space?

Element (the client) will display the room in the active space if it has a parent of that active space, but not in the hierarchy.

rstrst room with m.space.parent shows up when viewing the space	rstrst room with m.space.parent does not show when viewing it in the space hierarchy

Start with the m.space.parent section of the Client-Server API and compare it with MSC1772, especially the definitions of m.space.parent and m.space.child. Resolve whether a parent relationship should affect the space hierarchy, then update the specification so the intended behavior is explicit and consistent with the examples.